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Evolutionary algorithms (EAs) that integrate niching techniques are among the most effective methods for multimodal optimization problems. However, most algorithmic contributions are based on empirical performance observations rather than rigorous mathematical convergence support; this makes most existing methods parameter sensitive. Inspired by a recently proposed deterministic global optimization method, granular sieving (GrS), an extended global optimization method named collaborative GrS (Co-GrS) and a novel deterministic multi-EA design framework are proposed in this paper. The innovations are threefold. (1) Existing EAs are stochastic methods, and this paper introduces the principle of deterministic global optimization into EA for the first time in the literature. (2) A deterministic multi-EA framework is designed and implemented in the paper; from the perspective of population evolution, an easy-to-operate survival-of-the-fittest strategy based on mathematical principles is established in Co-GrS. (3) Unlike existing stochastic EAs, where the reproducibility of optimal solutions is achieved in a statistical sense, Co-GrS does not involve random parameters, and it automatically runs the algorithm only once with pre-set fixed parameters to find all optimal solutions. The experimental results demonstrate the effectiveness and competitiveness of our method compared to 16 state-of-the-art multimodal algorithms on the CEC'2013 benchmark suite. [ABSTRACT FROM AUTHOR]

[Display omitted] • Comparing to the other research papers, this paper compares the performance of the oldest, newest, more minor and well-known algorithms on deterministic chaos generators in one massive and unique study. • Paper show that by precision tuning, the original chaotic series convert into short N periodic time series (PTS). Thus no randomness as usually understand is there. These series are then used instead of classics pseudorandom numbers with positive impact. • Paper reveal the clearly visible positive impact of PTS on evolutionary algorithms (EAs) dynamics, which is visible almost on all algorithms used in this paper. Compared with the same EAs with classic random generators. • Paper open the question of whether standard random (nonchaotic) processes are really necessary for algorithm dynamics and suggest relations between randomness in EAs and noise in dynamical system control and theory. • Paper open, sketch and suggest new ideas and strategies on how to understand algorithm dynamics as the discrete feedback dynamical systems. Random mechanisms including mutations are an internal part of evolutionary algorithms, which are based on the fundamental ideas of Darwin's theory of evolution as well as Mendel's theory of genetic heritage. In this paper, we debate whether pseudo-random processes are needed for evolutionary algorithms or whether deterministic chaos, which is not a random process, can be suitably used instead. Specifically, we compare the performance of 10 evolutionary algorithms driven by chaotic dynamics and pseudo-random number generators using chaotic processes as a comparative study. In this study, the logistic equation is employed for generating periodical sequences of different lengths, which are used in evolutionary algorithms instead of randomness. We suggest that, instead of pseudo-random number generators, a specific class of deterministic processes (based on deterministic chaos) can be used to improve the performance of evolutionary algorithms. Finally, based on our findings, we propose new research questions. [ABSTRACT FROM AUTHOR]

In this paper, a new many-objective optimization evolutionary algorithm (MaOEA), namely Many-Objective Evolutionary Algorithm Based on Spatial Distance and Decision Vector Self-Learning (DVSLEA), is proposed for many-objective optimization. The core idea of the algorithm is to use spatial distance to influence the value of disturbance ratio and then affect the generation of offspring. In order to make the algorithm have a good distribution, distribution vector is introduced for the procedure of disturbance. Moreover, a self-learning process is corporated to ascertain the value of disturbance ratio. To evaluate the performance of DVSLEA, the DTLZ and WFG test suites with 3, 5, 8, 10, and 15 objectives are adopted. The experimental results indicate that DVSLEA shows superior performance over nine competitive evolutionary algorithms(MOEA/DD, NSGA-III, VaEA, SPEA2, SPEA2-SDE, MOEADAWA, onebyoneEA, PREA, RVEA), when solving most of the test problems used. [ABSTRACT FROM AUTHOR]

Standard evolutionary optimization algorithms assume that the evaluation of the objective and constraint functions is straightforward and computationally cheap. However, in many real-world optimization problems, these evaluations involve computationally expensive numerical simulations or physical experiments. Surrogate-assisted evolutionary algorithms (SAEAs) have recently gained increased attention for their performance in solving these types of problems. The main idea of SAEAs is the integration of an evolutionary algorithm with a selected surrogate model that approximates the computationally expensive function. In this paper, we propose a surrogate model based on a Lipschitz underestimation and use it to develop a differential evolution-based algorithm. The algorithm, called Lipschitz Surrogate-assisted Differential Evolution (LSADE), utilizes the Lipschitz-based surrogate model, along with a standard radial basis function surrogate model and a local search procedure. The experimental results on seven benchmark functions of dimensions 30, 50, 100, and 200 show that the proposed LSADE algorithm is competitive compared with the state-of-the-art algorithms under a limited computational budget, being especially effective for the very complicated benchmark functions in high dimensions. [ABSTRACT FROM AUTHOR]

Many variants with various strategies have been proposed to improve the efficiency of Particle Swarm Optimization (PSO) algorithm. These strategies are a precious resource waiting to be exploited. We conjecture that some new combinations of strategies selected from different PSO variants may better improve the performance of PSO. Inspired by this idea, this paper proposes a strategy learning framework to learn an optimal combination of strategies and thus derive a new PSO variant based on this combination. In this framework, a strategy pool with strategies selected from existing PSO variants is first constructed. Then, a training engine, implemented by an adaptive differential evolutionary algorithm, is employed to evaluate the performance of strategy combinations on training benchmark functions. Furthermore, a new PSO variant, named SLFPSO, is created based on the strategies learned from training results. This framework provides a novel method to design PSO variants by learning from existing algorithms through a learning mechanism. The performance and scalability of SLFPSO are compared with ten state-of-the-art PSO variants on 10/30/50/100-dimensional CEC2013/2014/2017 benchmark functions. The results verify that SLFPSO performs significantly better than the compared algorithms in most test scenarios. [ABSTRACT FROM AUTHOR]

In evolutionary multiobjective optimization, effectiveness refers to how an evolutionary algorithm performs in terms of converging its solutions into the Pareto front and also diversifying them over the front. This is not an easy job, particularly for optimization problems with more than three objectives, dubbed many-objective optimization problems. In such problems, classic Pareto-based algorithms fail to provide sufficient selection pressure towards the Pareto front, whilst recently developed algorithms, such as decomposition-based ones, may struggle to maintain a set of well-distributed solutions on certain problems (e.g., those with irregular Pareto fronts). Another issue in some many-objective optimizers is rapidly increasing computational requirement with the number of objectives, such as hypervolume-based algorithms and shift-based density estimation (SDE) methods. In this paper, we aim to address this problem and develop an effective and efficient evolutionary algorithm (E3A) that can handle various many-objective problems. In E3A, inspired by SDE, a novel population maintenance method is proposed to select high-quality solutions in the environmental selection procedure. We conduct extensive experiments and show that E3A performs better than 11 state-of-the-art many-objective evolutionary algorithms in quickly finding a set of well-converged and well-diversified solutions. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms are widely used to solve multimodal optimization problems. The two main challenges faced while solving MMOPs are locating multiple optimal solutions and improving the accuracy of these solutions. In this paper, we have proposed an adaptive algorithm based on differential evolution using the distributed framework in mutation strategy and an elite archive mechanism termed Adaptive Differential Evolution with Archive to deal with these challenges. The following techniques have been proposed and integrated to locate multiple diverse optimal solutions with refined accuracy. Firstly, each individual in the population is treated as a possible exemplar and is expected to reach an optimal value by exploring the nearby search space. The search space is controlled by using an adjustable range mechanism. An adaptive mutation strategy is then used to ensure that all the good solutions or individuals of the population move to better positions. Next, an elite archive is constructed for stagnated individuals to avoid getting stuck in local optimas. The experimental results on the 20 multimodal functions from IEEE Congress on Evolutionary Computation 2013 illustrate that the performance of the proposed algorithm is better than the existing multimodal optimization algorithms in terms of finding more number of accurate solutions. [ABSTRACT FROM AUTHOR]

Multiobjective optimization problems (MOPs) are the optimization problem with multiple conflicting objectives. Generally, an optimization algorithm can find a large number of optimal solutions for MOPs, which easily overwhelm decision makers (DMs) and make it difficult for decision-making. Preference-based evolutionary multiobjective optimization (EMO) aims to find the partial optima in the regions preferred by the DM. Although it narrows the scope of the optimal solutions, it usually still returns a population of optimal solutions (typically 100 or larger in EMO) with a small distance between adjacent optima. Top-K, which is a well-established research subject in many fields to find the best K solutions, may be a direction to reduce the number of optimal solutions. In this paper, first, we introduce the top-K notion into preference-based EMO and propose the top-K model to obtain the best K individuals of multiobjective optimization problems (MOPs). Then, with the top-K model, we propose NSGA-II-TopK and SPEA2-TopK to search for the top-K preferred solutions for preference-based continuous and combinatorial MOPs, respectively. Finally, the proposed algorithms with several representative preference-based EMO algorithms are compared in different preference situations for MOPs. Experimental results show the proposed algorithms have strong performances against the compared algorithms. [ABSTRACT FROM AUTHOR]

• A novel mean-median velocity updating formula is proposed to guide individuals motion. • A new random differential mutation strategy is devised. • A back-diffusion strategy is proposed to restore the diversity of population. To accelerate the convergence speed and enhance robustness, a back-diffusion median integrated evolutionary algorithm (BMIEA) is proposed combining the advantages of particle swarm optimization (PSO) and differential evolution algorithm (DE) in this paper. The BMIEA includes three mainly optimization strategies. (1) Firstly, a new mean-median velocity updating formula is proposed to control optimal path of individuals. It can accelerate the convergence speed via reducing adverse effects of outliers on the population. (2) Secondly, a random differential mutation (RDM) inspired by the DE is devised to avoid the individuals trapping into local optimum via getting one more chance to explore optimal position while exploiting local region in each evolution. (3) Thirdly, a targeted exploration method i.e., back-diffusion operation, is proposed inspired by the duality principle to further accelerate the convergence rate and enhance robustness of algorithm. A series of simulation experiments have verified that BMIEA algorithm has revealed competitiveness compared with 13 state-of-art GOBL-based optimization algorithms. [ABSTRACT FROM AUTHOR]

• A novel mean-median velocity updating formula is proposed to guide individuals motion. • A new random differential mutation strategy is devised. • A back-diffusion strategy is proposed to restore the diversity of population. To accelerate the convergence speed and enhance robustness, a back-diffusion median integrated evolutionary algorithm (BMIEA) is proposed combining the advantages of particle swarm optimization (PSO) and differential evolution algorithm (DE) in this paper. The BMIEA includes three mainly optimization strategies. (1) Firstly, a new mean-median velocity updating formula is proposed to control optimal path of individuals. It can accelerate the convergence speed via reducing adverse effects of outliers on the population. (2) Secondly, a random differential mutation (RDM) inspired by the DE is devised to avoid the individuals trapping into local optimum via getting one more chance to explore optimal position while exploiting local region in each evolution. (3) Thirdly, a targeted exploration method i.e., back-diffusion operation, is proposed inspired by the duality principle to further accelerate the convergence rate and enhance robustness of algorithm. A series of simulation experiments have verified that BMIEA algorithm has revealed competitiveness compared with 13 state-of-art GOBL-based optimization algorithms. [ABSTRACT FROM AUTHOR]

With the popularity of "flipped classrooms," teachers pay more attention to cultivating students' autonomous learning ability while imparting knowledge. Inspired by this, this paper proposes a Self-exploratory Competitive Swarm Optimization algorithm for Large-scale Multiobjective Optimization (SECSO). Its idea is very simple and there are no parameters that need to be adjusted. Particles evolve by exploring their neighboring space and learning from other particles in the swarm, thereby simultaneously enhancing the diversity and convergence performance of the algorithm. Compared with eight state-of-the-art large-scale multiobjective evolutionary algorithms, the proposed method exhibited outstanding performance on LSMOP problems with up to 10,000 decision variables. Unlike most existing large-scale evolutionary algorithms that usually require a large number of objective evaluations, SECSO shows the ability to find a set of well converged and diverse non-dominated solutions. [ABSTRACT FROM AUTHOR]

• A level-based population structure is adopted to exploration ability. • A reinforcement learning strategy is introduced to improve the search efficiency. • A level competition mechanism is proposed to optimize the convergence performance. • RLLPSO can achieve good performance for large-scale optimization. Large-scale optimization problems (LSOPs) have drawn researchers' increasing attention since their resemblance to real-world problems. However, due to the complex search space and massive local optima, it is challenging to simultaneously guarantee the diversity and convergence of the algorithms. As a widely used evolutionary algorithm with fast convergence, particle swarm optimization (PSO) shows competitive performances on some LSOPs. Nevertheless, it can easily get trapped into local optima. Overcoming the complexity of LSOPs and improving search efficiency have become vital issues. The reinforcement learning method has proven to be an effective technique in self-adaptive adjustment, which can help search for better results in large-scale solution space more effectively. In this paper, we propose a large-scale optimization algorithm called reinforcement learning level-based particle swarm optimization algorithm (RLLPSO). In RLLPSO, a level-based population structure is constructed to improve population diversity. A reinforcement learning strategy for level number control is employed to help improve the search efficiency of RLLPSO. To further enhance the convergence ability of RLLPSO, a level competition mechanism is introduced. The experimental results from two large-scale benchmark test suites demonstrate that, compared with five state-of-the-art large-scale optimization algorithms, RLLPSO shows superiority in most cases. [ABSTRACT FROM AUTHOR]

• Proposes a distributed adaptive optimization spiking neural P system with a distributed population structure and a new adaptive learning rate considering population diversity. • Extensive experiments on knapsack problems show that DAOSNPS gains much better and more stable solutions than OSNPS, AOSNPS and other two optimization algorithms. An optimization spiking neural P system (OSNPS) aims to obtain the approximate solutions of combinatorial optimization problems without the aid of evolutionary operators of evolutionary algorithms or swarm intelligence algorithms. To develop the promising and significant research direction, this paper proposes a distributed adaptive optimization spiking neural P system (DAOSNPS) with a distributed population structure and a new adaptive learning rate considering population diversity. Extensive experiments on knapsack problems show that DAOSNPS gains much better solutions than OSNPS, adaptive optimization spiking neural P system, genetic quantum algorithm and novel quantum evolutionary algorithm. Population diversity and convergence analysis indicate that DAOSNPS achieves a better balance between exploration and exploitation than OSNPS and AOSNPS. [ABSTRACT FROM AUTHOR]

In the constrained multi-objective optimization problems, the pursuit of feasibility could improve convergence but will lead to the loss of diversity. For optimization algorithm, balancing the weight between convergence and diversity dynamically is a challenge, especially in problems with low proportion of feasible regions. In this paper, a constrained multi-objective optimization algorithm is proposed based on a hybrid driven strategy to enhance both the feasibility and diversity performance of the approximate Pareto solutions. The proposed algorithm contains two archives, that one is driven by feasibility information and the other is driven by diversity information. A self-adaptive archive selection mechanism and a conditional tournament selection strategy are proposed to provide mating parent solutions according to the evolutionary stage. Moreover, in the update of the feasibility archive, an evolutionary direction prediction mechanism is proposed and adopted to improve the evolutionary efficiency. Compared to four other multi-objective algorithms on three benchmark suits of different types, the performance of the proposed algorithm is better than the peer algorithms, especially in large-infeasible-regions multi-objective optimization problems. [ABSTRACT FROM AUTHOR]

For many-objective problems, how to maintain the diversity and convergence of the distribution of the solution set over Pareto front (PF) has always been the research emphasis. In the iteration process, the state of population is critical to improve the level of evolution. Therefore, this paper will use two convergence and diversity indicators to further strengthen the usage of evolutionary state information and propose a dynamic learning strategy. In addition, a dynamic learning strategy based many-objective evolutionary algorithm (MaOEA) is proposed, called dynamic learning evolution algorithm (DLEA), which continuously changes the direction of learning: convergence and diversity in the iteration process. The purpose is to make the algorithm prefer to convergence in the early iteration and prefer to diversity when it is close to PF in the late iteration, so that the convergence and diversity of the final solution set can be well maintained. And then, the performance of DLEA is measured by two indicators. Meanwhile, DLEA will be compared with four state-of-the-art algorithms on the DTLZ and MaF, and its performance will be verified on a many-objective combinatorial problem. And the experimental results and Friedman test show that DLEA has great advantages. [ABSTRACT FROM AUTHOR]

Penalty function is well-known for constrained evolutionary optimization. An open question in the penalty function is how to tune the penalty coefficient. This paper proposes an adaptive fuzzy penalty method to address this issue, where the coefficient is adjusted at both the individual level and the population level. At the individual level, each individual chooses a penalty coefficient from a predefined domain according to some fuzzy rules. At the population level, the domain of the crisp output is adjusted adaptively by using population information. To enhance the population diversity, an effective mutation scheme is developed. Due to its numerous merits, differential evolution is used to design a search algorithm. By the above processes, a constrained optimization evolutionary algorithm called AFPDE is proposed. Since the objective function value and the degree of constraint violation are normalized, AFPDE is less problem-dependent than the seminal work of the fuzzy penalty method. AFPDE introduces a lower penalty value in the early stage of AFPDE while a higher one in the later stage. Thus, it can escape local optima in the infeasible region. Experiments on three well-known benchmark test sets and two mechanical design problems validate that AFPDE is competitive. [ABSTRACT FROM AUTHOR]

To solve constrained optimization problems (COPs), it is crucial to guide the infeasible solution to a feasible region. Gradient-based repair (GR) is a successful repair strategy, where the forward difference is often used to estimate the gradient. However, GR has major deficiencies. First, it is difficult to deal with individuals falling into the local optima. Second, large amounts of fitness evaluations are required to estimate the gradient. In this paper, we proposed a new repair strategy, random direction repair (RDR). RDR generates a set of random directions, and calculates the repair direction and the repair step size of infeasible individual to reduce its constraint violation. Since the introduction of randomness, RDR could deal with individuals falling into the local optima. Furthermore, RDR only requires a few number of fitness evaluation. To demonstrate the performance of RDR, RDR was embedded into two state-of-the-art evolutionary continuous constrained optimization algorithms, tested on the Congress on Evolutionary Computation 2017 constrained real-parameter optimization benchmark. Experimental results demonstrated that RDR combined with evolutionary algorithms are highly competitive. [ABSTRACT FROM AUTHOR]

• Average convergence rate measures the convergence speed of evolutionary algorithms by the geometric average of the reduction rate of the approximation error over consecutive generations. • Evolutionary programming with landscape-invariant or zero landscape-adaptive mutation converges slowly, while that with positive landscape-adaptive mutation converges fast. • Average convergence rate are classified into two types: polynomial or exponential as a function of the decision space dimension. The average convergence rate (ACR) measures how fast the approximation error of an evolutionary algorithm converges to zero per generation. It is defined as the geometric average of the reduction rate of the approximation error over consecutive generations. This paper makes a theoretical analysis of the ACR in continuous optimization. The obtained results are summarized as follows. According to the limit property, the ACR is classified into two categories: (1) linear ACR whose limit inferior value is larger than a positive and (2) sublinear ACR whose value converges to zero. Then, it is proven that the ACR is linear for evolutionary programming using positive landscape-adaptive mutation, but sublinear for that using landscape-invariant or zero landscape-adaptive mutation. The relationship between the ACR and the decision space dimension is also classified into two categories: (1) polynomial ACR whose value is larger than the reciprocal of a polynomial function of the dimension for any generation, and (2) exponential ACR whose value is less than the reciprocal of an exponential function of the dimension for an exponential long period. It is proven that for easy problems such as linear functions, the ACR of the (1 + 1) adaptive random univariate search is polynomial. But for hard functions such as the deceptive function, the ACR of both the (1 + 1) adaptive random univariate search and evolutionary programming is exponential. [ABSTRACT FROM AUTHOR]

Constrained multi-objective optimization problems (CMOPs) are difficult to handle because objectives and constraints need to be considered simultaneously, especially when the constraints are extremely complex. Some recent algorithms work well when dealing with CMOPs with a simple feasible region; however, the effectiveness of most algorithms degrades considerably for CMOPs with complex feasible regions. To address this issue, this paper proposes a multi-stage evolutionary algorithm, where constraints are added one after the other and handled in different stages of evolution. Specifically, in the early stages, the algorithm only considers a small number of constraints, which can make the population efficiently converge to the potential feasible region with good diversity. As the algorithm moves to the later stages, more constraints are considered to search the optimal solutions based on the solutions obtained in the previous stages. Furthermore, a strategy for sorting the constraint-handling priority according to the impact on the unconstrained Pareto front is proposed, which can accelerate the convergence of the algorithm. Experimental results on five benchmark suites and three real-world applications showed that the proposed algorithm outperforms several state-of-the-art constraint multi-objective evolutionary algorithms when dealing with CMOPs, especially for problems with complex constraints. [ABSTRACT FROM AUTHOR]

In the last decade, the decomposition-based multiobjective optimization evolutionary algorithm (MOEA/D) has displayed promising performance when dealing with multiobjective optimization problems (MOPs). However, for some complex MOPs, the conventional MOEA/D often leads to the loss of population diversity in the iterative process, and the convergence performance of the population is weakened in the mean time. In this paper, a novel MOEA/D, based on improved multiple adaptive dynamic selection strategies and elite archive strategy (MOEA/D-IMA), is proposed to improve the population diversity and convergence. First, a novel differential evolution (DE) operator is constructed, which constitutes an operator pool with other DE operators. According to the search information of the current population, an adaptive dynamic selection strategy is proposed, which is used by MOEA/D-IMA to select a suitable DE operator to replace the simulated binary crossover (SBX) operator. Second, a parameter adaptive dynamic selection strategy is proposed to enhance the robustness of MOEA/D-IMA by using the information of population evolution state. Third, an elite archive strategy is introduced to improve the convergence and diversity of the population where mutual dominance of individuals and their aggregation distance is employed. Finally, the proposed MOEA/D-IMA is compared with several state-of-the-art algorithms on three suits of 18 test problems. Experimental results indicate that the proposed MOEA/D-IMA can significantly improve the optimization performance when coping with MOPs. [ABSTRACT FROM AUTHOR]

The challenge of solving nonlinear equation systems is how to locate multiple optimal solutions simultaneously in a single run. To address this issue, this paper proposes a novel algorithm by combining a diversity indicator, multi-objective optimization technique, and clustering technique. Firstly, a diversity indicator is designed to maintain the diversity of the population. Then, a K-means clustering-based selection strategy is introduced to locate the promising solutions. Finally, the local search is used to accelerate the convergence of population. The experimental results on 30 nonlinear equation systems show that the proposed algorithm is better than six state-of-the-art algorithms in terms of convergence rate and success rate. [ABSTRACT FROM AUTHOR]

Deep belief network (DBN) is an import deep learning model and restricted Boltzmann machine (RBM) is one of its basic models. The traditional DBN and RBM have numerous redundant features. Hence an improved strategy is required to perform sparse operations on them. Previously, we have proposed our own sparse DBN (SDBN): using a multi-objective optimization (MOP) algorithm to learn sparse features, which solves the contradiction between the reconstruction error and network sparsity of RBM. Due to the optimization algorithm and millions of parameters of the network itself, the training process is difficult. Therefore, in this paper, we propose an efficient parallel strategy to speed up the training of SDBN networks. Self-adaptive Quantum Multi-objectives Evolutionary algorithm based on Decomposition (SA-QMOEA/D) that we have proposed as the multi-objective optimization algorithm has the hidden parallelism of populations. Based on this, we not only parallelize the DBN network but also realize the parallelism of the multi-objective optimization algorithm. In order to further verify the advantages of our approach, we apply it to the problem of facial expression recognition (FER). The obtained experimental results demonstrate that our parallel algorithm achieves a significant speedup performance and a higher accuracy rate over previous CPU implementations and other conventional methods. [ABSTRACT FROM AUTHOR]

• The MCDM process is incorporated into the knee-guided evolutionary algorithm framework. • The knee and boundary regions are introduced to accelerate the convergence of the population. • Change detection in dynamic environment is analyzed and implemented. • A prediction method is implemented for tracking the moving locations of the knee point. Although dynamic multi-objective optimization problems dictate the evolutionary algorithms to quickly track the varying Pareto front when the environmental change occurs, the decision maker in the loop still needs to select a final optimal solution among a large number of candidate solutions before and after the environmental change. Most designs focus on searching for a well-distributed Pareto front which inadvertently demand excessive computational burden during the evolutionary process. In this paper, we propose a novel knee-guided prediction evolutionary algorithm (KPEA) which maintains non-dominated solutions near knee and boundary regions, in order to reduce the burden of maintaining a large and diversified population throughout the evolution process. When a change is detected, this design relocates the knee and boundary solutions based on the movement of the global knee solution in the new environment. In this way, this algorithm incurs a lower computational cost, allowing the evolutionary algorithm to converge quickly. In order to test the performance of the proposed algorithm, five popular dynamic multi-objective evolutionary algorithms (DMOEAs) are compared with KPEA based on two newly proposed metrics. The experimental results validate that the proposed algorithm effectively and efficiently converges to the global knee solution under the changing environments. [ABSTRACT FROM AUTHOR]

Intuitively, the main novelties of the proposed Tk-MaOEA can be presented as follows. • In the global space optimization level, a new transfer learning approach is developed to reduce a large number of objectives while the original property of the problem is kept well. The proposed approach uses a specific transfer matrix to compress the search space, which is simple yet effective to handle with the curse of dimensionality in MaOPs. • In the objective optimization level, the Kriging model is devised for each objective to further reduce its computational cost. This Bayesian based surrogate model is to measure not only the objective value itself but also stochastic error of the approximation, which is essentially conductive to improve the accuracy of the optimization. • The multi-scale normalization approach is employed so as to avoid the distortion caused by conventional normalization in the high-dimensional objective space. This is a significant operation for the MaOEA to keep unchanged spatial distribution when the original population are normalized. • The FCS approach is incorporated instead of the traditional crowding distance method in the environmental selection. This approach is more effective to select a set of representative non-dominated solutions in a single run. Due to the curse of dimensionality caused by the increasing number of objectives, it is very challenging to tackle many-objective optimization problems (MaOPs). Aiming at this issue, this paper proposes a novel many-objective evolutionary algorithm, called Tk-MaOEA, based on transfer matrix assisted by Kriging model. In this approach, for the global space optimization, a transfer matrix is used as a map tool to reduce the number of objectives, which can simplify the optimization process. For the objective optimization, the Kriging model is incorporated to further reduce the computation cost. In addition, the fast non-dominated sorting and farthest-candidate selection (FCS) methods are used to guarantee the diversity of solutions. Comprehensive experiments on a set of benchmark functions have been conducted. Experimental results show that Tk-MaOEA is effective for solving complex MaOPs. [ABSTRACT FROM AUTHOR]

Compared with domination-based methods, the multi-objective evolutionary algorithm based on decomposition (MOEA/D) is less prone to the difficulty caused by an increase in the number of objectives. It is a promising algorithmic framework for solving many-objective optimization problems (MaOPs). In MOEA/D, the target MaOP is decomposed into a set of single-objective problems by using a scalarizing function with evenly specified weight vectors. Among the available scalarizing functions, penalty-based boundary intersection (PBI) with an appropriate penalty parameter is known to perform well. However, its performance is heavily influenced by the setting of the penalty factor (θ), which can take a value from zero to +∞. A limited amount of work has thus far considered the choice of an appropriate value of θ. This paper presents a comprehensive experimental study on WFG and WFG-extend problems featuring two to 15 objectives. A range of values of θ is investigated to understand its influence on the performance of the PBI-based MOEA/D (MOEA/D-PBI). Based on the observations, the range of values of θ are divided into three sub-regions, and a two-stage adaptive penalty scheme is proposed to adaptively choose an appropriate value from 0.001 to 8000 during an optimization run. The results of experiments show that, the robustness of MOEA/D-PBI can be significantly enhanced using the proposed scheme. [ABSTRACT FROM AUTHOR]

It is known that Pareto dominance encounters difficulties in many-objective optimization. This strict criterion could make most individuals of a population incomparable in a high-dimensional space. A straightforward approach to tackle this issue is modify the Pareto dominance criterion. This is typically done by relaxing the dominance region. However, this modification is often associated with one or more parameters of determining the relaxation degree, and the performance of the corresponding algorithm could be sensitive to such parameters. In this paper, we propose a new dominance criterion, angle dominance, to deal with many-objective optimization problems. This angle dominance criterion can provide sufficient selection pressure towards the Pareto front and be exempt from the parameter tuning. In addition, an interesting property of the proposed dominance criterion, in contrast to existing dominance criteria, lies in its capability to reflect an individual's extensity in the population. The angle dominance is integrated into NSGA-II (instead of Pareto dominance) and has demonstrated high competitiveness in many-objective optimization in comparison with a range of peer algorithms. [ABSTRACT FROM AUTHOR]

• A new multi-layer interaction preference based multi-objective optimization algorithm through decomposition (MLIP-MOEA/D) is proposed. • A fast way to get preference region is established, during the selection process, the preference weight vector is redefined using the angle-based method. • A novel multi-layer interaction strategy for searching the accurate solutions is proposed. During evolution, the preferred region is reduced gradually, making it easier for user to get the final preferred solution(s). • Besides ZDT problems with two objectives, the proposed algorithm shows its potentiality for solving many-objective problems, i.e., DTLZ problems with 3, 5, 8, 10 objectives. Many problems in real world have not only one objective to be met. In the majority of cases, a set of trade-off solutions which spread evenly along the entire Pareto optimal front are generated by multi-objective evolutionary algorithms (MOEAs). Taking the preference of decision maker (DM) into consideration, some specified solutions can be obtained, which is of great interest in practical applications. In this paper, a novel multi-layer interaction preference based multi-objective evolutionary algorithm through decomposition (denoted as MLIP-MOEA/D) is proposed. In MLIP-MOEA/D, a multi-layer interactive strategy is developed during evolution, in the first-layer interaction, the DM will provide a reference vector and an initial radius to determine a preference range, then all solutions in this range will be updated. The algorithm will stop if the DM is satisfied with the first output result, otherwise it will go on to the second-layer interaction. In this step, the most preferred solution generated from the first-layer interaction will be chosen as the new preference direction, and the weight vector is redefined by the angle-based method, and the range of preferred region is reduced gradually, until the closest solution that meet the DM's need is found. The algorithm is tested on a set of benchmark problems including DTLZ problems with more than three objectives, the experimental studies show that the proposed algorithm can effectively search the preferred solutions with the preference information and successfully deal with many-objective optimization problems. [ABSTRACT FROM AUTHOR]

This paper develops a multi-population evolutionary algorithm with single-objective guide to tackle many-objective optimization problems. It exploits the merits of both multiple populations and single-objective optimization to balance diversity and convergence of the evolution process. Specifically, the single-objective guide process helps to construct the better ideal point and reference points. A novel objective space partitioning mechanism is developed to transform a many-objective optimization problem into multiple subproblems, each of which is tackled by a subpopulation. A novel information sharing mechanism between subpopulations is proposed to balance diversity and convergence. Finally the subpopulations are merged together and deal with many-objective optimization problems to further enhance the convergence. We have compared the performance of the proposed algorithm with nine state-of-the-art algorithms on 85 test instances of 21 benchmark problems with up to 15 objectives. Experimental results show that the proposed algorithm has the superior performance in solving multi- and many-objective optimization problems. [ABSTRACT FROM AUTHOR]

Multi-objective evolutionary algorithms based on decomposition (MOEA/D) decomposes a multi-objective optimization problem (MOP) into a set of simple scalar objective optimization sub-problems and solves them in a collaborative way. Since the sub-problems are different in optimization difficulty and computational resource demanding, it is critical to reasonably allocate computational resources among them, which can optimize the usage of resources and improve the performance of an algorithm. This paper proposes a new resource allocation strategy based on the relationship between sub-problems for MOEA/D. A probability vector is maintained based on the relationship between sub-problems, which is used to guide the selection of sub-problems for optimization. In the optimization process, we explored the role of priority optimization of boundary sub-problems and used it to assist in the update of probability vector in the early optimization phase. A steady-state algorithm is designed and tested experimentally. The results suggest that the designed algorithms have some advantages over existing state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

The tradeoff between exploration and exploitation is critical to the performance of an evolutionary algorithm. Different levels of exploration-exploitation tradeoff are required at different evolutionary stages for achieving a satisfactory performance of an evolutionary algorithm. In this paper, we propose a novel survival analysis method to intelligently guide the maintenance of the exploration-exploitation tradeoff in multiobjective evolutionary algorithms. The survival analysis stems from a deep understanding of the evolutionary search procedure. Through survival analysis, an indicator is derived, which is used to guide the adoption of appropriate recombination operators, based on the assumption that the roles of these operators in terms of their capabilities on exploration-exploitation can be asserted. In the developed algorithm, a differential evolution recombination operator and a new sampling strategy are hybridized. Empirical comparison with five well-known multiobjective evolutionary algorithms on a number of test instances with complex Pareto sets and Pareto fronts indicates the effectiveness and superiority of the developed algorithm in terms of commonly-used performance metrics on these test instances. [ABSTRACT FROM AUTHOR]

In evolutionary multi-objective optimization, it is crucial for the evolutionary algorithm to maintain a good balance between convergence and diversity. The recently proposed Two_Arch2 algorithm provides a new perspective to solve this problem. However, due to the properties of the mating mechanism and the limitations of the distance-based diversity maintenance scheme, both the computational complexity and the diversity face great challenges as the number of objectives increases. In this paper, we propose an improved Two-Archive algorithm for both multi- and many-objective optimization, aiming at further promoting the balance between convergence and diversity. In the proposed algorithm, we introduce a decomposition idea into the mating pool of the convergence archive, which increases the number of favorable solutions and reduces the computational complexity. At the same time, we apply a penalty angle-based selection scheme to the diversity archive, which effectively maintains the population diversity. The effectiveness of the proposed algorithm is compared with five state-of-the-art multi-objective evolutionary algorithms on a variety of benchmark problems. The experimental results demonstrate that the proposed algorithm has highly competitive performance on both multi- and many-objective optimization problems—in particular, remedying problems of Two_Arch2. • A decomposition-based two-archive algorithm is proposed to promote the balance between convergence and diversity in many-objective optimization. • A penalty angle-based selection scheme is proposed to maintain the diversity of the population. • The solutions in the diversity archive are merged to the convergence archive to achieve a more uniform distribution of the solutions. • Only two solutions are considered in the mating selection of each sub-region, which makes the behavior resemble that of a steady-state algorithm. [ABSTRACT FROM AUTHOR]

Estimation of Distribution Algorithms (EDAs) constitutes a class of evolutionary algorithms that can extract and exploit knowledge acquired throughout the optimization process. The most critical step in the EDAs is the estimation of the joint probability distribution associated to the variables from the most promising solutions determined by the evaluation function. Recently, a new approach to EDAs has been developed, based on copula theory, to improve the estimation of the joint probability distribution function. However, most copula-based EDAs still present two major drawbacks: focus on copulas with constant parameters, and premature convergence. This paper presents a new copula-based estimation of distribution algorithm for numerical optimization problems, named EDA based on Multivariate Elliptical Copulas (EDA-MEC). This model uses multivariate copulas to estimate the probability distribution for generating a population of individuals. The EDA-MEC differs from other copula-based EDAs in several aspects: the copula parameter is dynamically estimated, using dependence measures; it uses a variation of the learned probability distribution to generate individuals that help to avoid premature convergence; and uses a heuristic to reinitialize the population as an additional technique to preserve the diversity of solutions. The paper shows, by means of a set of parametric tests, that this approach improves the overall performance of the optimization process when compared with other copula-based EDAs and with other efficient heuristics such as the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). [ABSTRACT FROM AUTHOR]

This paper puts forward a comprehensive study of the design of global stopping criteria for multi-objective optimization. In this study we propose a global stopping criterion, which is terms as MGBM after the authors surnames. MGBM combines a novel progress indicator, called mutual domination rate (MDR) indicator, with a simplified Kalman filter, which is used for evidence-gathering purposes. The MDR indicator, which is also introduced, is a special-purpose progress indicator designed for the purpose of stopping a multi-objective optimization. As part of the paper we describe the criterion from a theoretical perspective and examine its performance on a number of test problems. We also compare this method with similar approaches to the issue. The results of these experiments suggest that MGBM is a valid and accurate approach. [ABSTRACT FROM AUTHOR]

Penalty boundary intersection (PBI) is one popular method in decomposition based evolutionary multi-objective algorithms, where the penalty factor is crucial for striking a balance between convergence and diversity in a high-dimensional objective space. Meanwhile, the distribution of the obtained solutions highly depends on the setting of the weight vectors. This paper proposes an adaptive decomposition-based evolutionary algorithm for many-objective optimization, which introduces one adaptation mechanism for PBI-based decomposition and the other for adjusting the weight vector. The former assigns a specific penalty factor for each subproblem by using the distribution information of both population and the weight vectors, while the latter adjusts the weight vectors based on the objective ranges to handle problems with different scales on the objectives. We have compared the proposed algorithm with seven state-of-the-art many-objective evolutionary algorithms on a number of benchmark problems. The empirical results demonstrate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Abstract Achieving a balance between convergence and diversity in many-objective optimization is a great challenge. This paper suggests an evolutionary algorithm based on a region search strategy to deal with different kinds of benchmark problems. In the proposed algorithm, each solution is associated with a region, and the region search strategy is applied to constrain the updating process; this strategy will enhance the diversity of population without losing convergence. A new normalization procedure is used for dealing with scaled problems. Moreover, the comparison of two solutions is based on both dominance relation and perpendicular distance; the result shows the algorithm's reliability for solving both convex and concave problems. The performance of the proposed algorithm is validated by several well-known benchmark problems with different properties. Seven state-of-the-art algorithms are compared and the experimental results demonstrate that the introduced algorithm performs the best on almost all benchmark problems. Furthermore, the proposed strategy depicts a high computational efficiency for solving the problems with a high dimension of objectives. [ABSTRACT FROM AUTHOR]

Abstract Environmental changes are traditionally considered intrinsic in evolutionary dynamic optimization. However, by ignoring that changes can instead be induced, we are ignoring that environmental changes can be eventually beneficial. To investigate the impact of artificial changes on the optimization speed up, we propose a framework for inducing artificial changes in any pseudo-Boolean or continuous optimization in this paper. Seven types of changes can be induced. Knowing when and how the changes occur allows us to design new strategies for evolutionary algorithms. Through computational experiments and illustrative examples, the impact of introducing changes in the optimization process is investigated. Experimental results indicate that changing the environments according to the proposed framework can lead to higher speed up, but not for all problems and change types. The best performance was obtained by change types that introduce plateaus and/or modify the gradient of regions of the fitness landscape around the current best solution. By doing this, the evolutionary dynamics is modified, eventually allowing the population to escape faster from local optima and reach new zones of the fitness landscape. Given a pseudo-Boolean or continuous optimization static problem, the proposed framework can be used to dynamically change the problem to speed up the optimization. [ABSTRACT FROM AUTHOR]

Abstract Evolutionary algorithms (EAs) have shown to be efficient in dealing with many-objective optimization problems (MaOPs) due to their ability to obtain a set of compromising solutions which not only converge toward the Pareto front (PF), but also distribute well. The Pareto-based multi-objective evolutionary algorithms are valid for solving optimization problems with two and three objectives. Nevertheless, when they encounter many-objective problems, they lose their effectiveness due to the weakening of selection pressure based on the Pareto dominance relation. Our major purpose is to develop more effective diversity maintenance mechanisms which cover convergence besides dominance in order to enhance the Pareto-based many-objective evolutionary algorithms. In this paper, we propose a Pareto-based many-objective evolutionary algorithm using space partitioning selection and angle-based truncation, abbreviated as SPSAT. The space partitioning selection increases selection pressure and maintains diversity simultaneously, which we realize through firstly dividing the normalized objective space into many subspaces and then selecting only one individual with the best proximity estimation value in each subspace. To further enhance convergence and diversity, the angle-based truncation calculates the angle values of any pair of individuals in the critical layer and then gradually removes the individuals with the minimum angle values. From the comparative experimental results with six state-of-the-art algorithms on a series of well-defined optimization problems with up to 20 objectives, the proposed algorithm shows its competitiveness in solving many-objective optimization problems. [ABSTRACT FROM AUTHOR]

Abstract As a new evolutionary computation method, the structure of backtracking search optimization algorithm (BSA) is simple and the exploration capability of it is strong. However, the global performance of the BSA is significantly affected by mutation strategies and control parameters. Designing appropriate mutation strategies and control parameters is important to improve the global performance of the BSA. In this paper, an adaptive BSA with knowledge learning (KLBSA) is developed to improve the global performance of the BSA. In the method, an adaptive control parameter based on the global and local information of the swarms in the current iteration is designed to adjust the search step length of individuals, which helps to balance the exploration and exploitation abilities of the algorithm. Moreover, a new mutation strategy based on the guidance of different information is designed to improve the optimization ability of the algorithm. In addition, a multi-population strategy is implemented to thoroughly improve the searching ability of the algorithm for different searching areas. To this end, experiments on three groups of benchmark functions and three real-world problems are implemented to verify the performance of the proposed KLBSA algorithm. The results indicate that the proposed algorithm performs competitively and effectively when compared to some other evolutionary algorithms. [ABSTRACT FROM AUTHOR]

Abstract Differential evolution (DE) is a simple yet powerful evolutionary algorithm that has been used to solve various complex optimization problems in numerous engineering fields. However, DE has some problems, such as premature convergence and sensitivity to parameter settings. To improve the performance of DE and extend its application, an adaptive differential evolution with the Lagrange interpolation argument algorithm (ADELI) is proposed in this paper. To accelerate the convergence speed of DE, a local search with Lagrange interpolation (LSLI) is introduced into DE. LSLI performs a local search in the neighborhood of the best individual in the current generation to enhance the exploitation capability of DE. Meanwhile, an adaptive argument strategy is presented to adaptively determine whether to use LSLI in terms of its performance in the previous generation, which can balance the global exploration capability and the local exploitation capability of ADELI. To verify the feasibility and effectiveness of ADELI, 30 test functions in the CEC 2014 benchmark sets with different dimensions were simulated. Moreover, a path synthesis problem was also optimized. The results demonstrated that ADELI considerably outperforms other EAs in most functions and obtains the most accurate solution among the compared algorithms in the application of path generation. [ABSTRACT FROM AUTHOR]

To be efficient and reach the best solution, evolutionary algorithms (EAs) are composed of three evolutionary operators: selection, crossover and mutation. Nevertheless, there is no established rule to choose them from a large panel of operators available in the literature. In this paper, a Maximum A Posteriori (MAP) principle based rule is proposed to palliate the operators’ selection problem for solving different kinds of continuous optimization problems. This learning based approach allows switching between different strategies during the optimization. This algorithm is called Maximum a posteriori based Evolutionary Algorithm (MEA). Experimental analysis was performed and proved its efficiency and robustness on a large set of 34 problems. [ABSTRACT FROM AUTHOR]

In this paper we present a novel universal metaheuristic, Discrete Bacterial Memetic Evolutionary Algorithm (DBMEA), which is based on the combination of the Bacterial Evolutionary Algorithm and local search techniques, used for solving NP-hard optimization problems. The algorithm was tested on a series of symmetric Traveling Salesman Problems (TSP) and Traveling Salesman Problem with time windows (TSPTW) benchmarks. The size of the symmetric TSP benchmarks went up to 5 000 cities. In all cases the DBMEA algorithm produced optimal or near-optimal solutions and the difference from the known best values was within 0.16%. While for large size problems it was much faster than the Concorde solver, it was found to be slower compared to the Helsgaun-Lin-Kernighan heuristic, which is the most efficient TSP solver method. With some slight modifications the same algorithm was also tested on TSP with time windows (TSPTW) benchmark instances. In most cases the DBMEA procedure found the known best solutions, and it was again the second fastest method compared with the state-of-the-art techniques for the TSPTW. DBMEA is called efficacious because it is a universal method. It can be efficiently applied to various NP-hard optimization problems and, as in all cases, it results in the optimal or a very near-optimal solutions, while its runtime is very predictable in terms of the size of the problem, and the topology of the instance does not affect its runtime significantly. Even though heuristics developed for a particular type of problem might perform better for that restricted class, our novel method proposed here is universally applicable and may be deployed successfully for optimizing other discreet NP-hard graph search and optimization problems as well. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to propose an effective evolutionary method for solving the problem of working paths optimization in survivable MPLS network. The paper focuses on existing network, in which only network flow can be optimized to provide network survivability using the local repair strategy. The problem is NP-complete, the solution space of the test cases is large and many genes are required to code the potential solution. Recently, the MuPPetS method (Multi-Population Pattern Searching Algorithm for Flow Assignment) was proposed and seems to be a promising tool for tackling high-dimensional, hard optimization problems. The MuPPetS is a linkage learning method that minimizes the negative effects of typical EA bottlenecks, e.g., preconvergence and significant effectiveness dropdown caused by an increasing number of genes in the chromosome. In comparison to other evolutionary methods, the MuPPetS was shown to be effective and capable of solving GA-hard problems. Therefore, the proposed MuPPetS-FuN method (Multi-Population Pattern Searching Algorithm for Flow Assignment in Non-bifurcated Commodity Flow) is based on MuPPetS. The additional objective of this paper is to propose changes to general MuPPetS framework to increase its effectiveness via better subpopulation number control strategy. [ABSTRACT FROM AUTHOR]

Novel Evolutionary Algorithms are usually tested on sets of artificially-constructed benchmark problems. Such problems are often created to make the search of one global extremum (usually minimum) tricky. In this paper it is shown that benchmarking heuristics on either minimization or maximization of the same set of artificially-created functions (with equal bounds and number of allowed function calls) may lead to very different ranking of tested algorithms. As Evolutionary Algorithms and other heuristic optimizers are developed in order to be applicable to real-world problems, such result may raise doubts on the practical meaning of benchmarking them on artificial functions, as there is little reason that searching for the minimum of such functions should be more important than searching for their maximum. Thirty optimization heuristics, including a number of variants of Differential Evolution, as well as other kinds of Evolutionary Algorithms, Particle Swarm Optimization, Direct Search methods and – following the idea borrowed from No Free Lunch – pure random search are tested in the paper. Some discussion regarding the choice of the mean or the median performance for comparison is addressed and a short debate on the overall performance of particular methods is given. [ABSTRACT FROM AUTHOR]

Harmony search is a powerful metaheuristic algorithm with excellent exploitation capabilities but suffers a very serious limitation of premature convergence if one or more initially generated solutions/harmonies are in the vicinity of local optimal. In order to remove this limitation this paper proposes a novel algorithm based on hybridization of Harmony search and Simulated Annealing called HS-SA to inherit their advantages in a complementary way. Taking the inspiration from Simulated Annealing the proposed HS-SA algorithm accepts even the inferior harmonies with a probability determined by parameter called Temperature. The Temperature parameter is initially kept high to favor exploration of search space and is linearly decreased to gradually shift focus to exploitation of promising search areas. The performance of HS-SA is tested on IEEE CEC 2014 benchmark functions and real life problem from computer vision called Camera Calibration problem. The numerical results demonstrate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The many-objective optimization problem (MaOP) is a common problem in the fields of engineering and scientific computing. It requires the optimization of multiple conflicting objectives. Due to the complexity of the MaOP, its optimization requires considerable amounts of time and computation resources to execute. Moreover, demand for a general optimization method for different types of MaOPs is becoming increasingly urgent. In this paper, the reference-vector-guided evolutionary algorithm (RVEA) is modified to accelerate the optimization speed and to improve its adaptability. To achieve more rapid convergence, a sub-problem optimal solution updating direction-guided variation strategy is developed to replace the original variation strategy of the RVEA. A comparative experiment on the typical test suites verifies that the proposed method offers preferable performance. Our experiment shows that the performance of the OD-RVEA declines when optimizing MaOPs with irregular Pareto fronts (PFs). To address this issue, an adaptive reference vector adjustment strategy is designed as a means of enhancing the optimization capabilities of MaOPs with irregular PFs by adjusting the distribution of reference vectors. Our comparative experiment on test cases that involve irregular PFs shows that the algorithm that applies this strategy outperforms the algorithm that applies fixed reference vectors. [ABSTRACT FROM AUTHOR]

Constrained optimization problems (COPs) are common in many fields. To solve such problems effectively, in this paper, we propose a new constrained optimization evolutionary algorithm (COEA) named CACDE that combines an adaptive trial vector generation strategy-based differential evolution (DE) algorithm with a cluster-replacement-based feasibility rule. In CACDE, some potential mutation strategies, scale factors and crossover rates are stored in candidate pools, and each element in the pools is assigned a selection probability. During the trial vector generation stage, the mutation strategy, scale factor and crossover rate for each target vector are competitively determined based on these selection probabilities. Meanwhile, the selection probabilities are dynamically updated based on statistical information learned from previous searches in generating improved solutions. Moreover, to alleviate the greediness of the feasibility rule, the main population is divided into several clusters, and one vector in each cluster is conditionally replaced with an archived infeasible vector with a low objective value. The superior performance of CACDE is validated via comparisons with some state-of-the-art COEAs over 2 sets of artificial problems and 5 widely used mechanical design problems. The results show that CACDE is an effective approach for solving COPs, basically due to the use of adaptive DE and cluster-replacement-based feasibility rule. [ABSTRACT FROM AUTHOR]

Many laboratory scale biochemical processes, including clinical diagnostics are being revolutionized by Digital Microfluidic Biochips (DMFBs). This is owing to their high automation capability, low cost, portability, and efficiency. Central to the efficient operation of these devices is the droplet routing problem that aims to drive a set of droplets, each from its source to its target cells, without violating a given set of fluidic and timing constraints. The efficiency of the routing is measured by the amount of cells used and the arrival time of the latest droplet and both criteria are aimed to be minimized simultaneously. To solve this problem we propose an Evolutionary Multi-objective Optimization algorithm for the Droplet Routing problem (EMO-DR) based on the NSGA-II framework, where the crossover operator is not used. EMO-DR features new mutation operators and a biased random generator of initial solutions. Experimental results show that the proposed approach produces competitive results when compared with those obtained through state-of-the-art methods. The paper also highlights the main challenges that evolutionary approaches need to solve when dealing with this routing problem. [ABSTRACT FROM AUTHOR]

Artificial immune systems have been widely applied to a variety of complex real-world problems. However, theoretical studies on artificial immune system are still limited and there is a strong need for building a rigorous theoretical foundation to better understand these heuristics. This paper contributes to a theoretical runtime analysis of immune inspired hypermutations on some discrete optimization problems. In particular, we are interested in the performance comparison among somatic contiguous hypermutations (CHM), standard bit mutations (SBM) and local mutation. We reveal that the immune inspired hypermutations can significantly outperform the standard bit mutation most often used in evolutionary algorithms on some well-known pseudo-Boolean functions including Trap and Hierarchical-if-and-only-if functions and instances of two combinatorial optimization problems, namely the Max-Cut problem and the Minimum s-t-cut problem. The proofs give some insights into the relationships between the problem characteristics and algorithmic features. The results of the analysis help strengthen the usefulness of Artificial immune systems. [ABSTRACT FROM AUTHOR]

The artificial bee colony (ABC) algorithm is a new branch of evolutionary algorithms (EAs) that is inspired by the collective foraging behavior of real honey bee colonies. Due to its foraging model and its solution search equation, ABC generally performs well in exploration but badly in exploitation. To address this concerning issue and obtain a good balance between exploration and exploitation, in this paper, we mainly introduce into the ABC an adaptive method for the population size (AMPS). AMPS is inspired by the natural principle that the size of a population is affected by the availability of food resources. When food resources are abundant, a population tends to expand; otherwise, a decrease in the availability of food resources leads to a shrinkage in the population size. Specifically, when the algorithm performs well in exploration, AMPS will shrink the population to enhance exploitation by periodically removing some inferior solutions that have low success rates. In contrast, AMPS will enlarge the population to improve exploration by introducing some reserved solutions. Furthermore, to make AMPS perform better, we design a new solution search equation for employed bees and onlooker bees. Moreover, we also improve the probability model of the onlooker bees. By embedding our three proposed algorithmic components into ABC, we propose a novel ABC variant, called APABC. To demonstrate the performance of APABC, we compare APABC with some state-of-the-art ABC variants and some other non-ABC methods on 22 scalable benchmark functions and 30 CEC2014 test functions. The simulation results show that APABC is better than or at least competitive with the competitors in terms of its solution quality, robustness and convergence speed. [ABSTRACT FROM AUTHOR]

In this paper, a visual analysis methodology is proposed to perform comparative analysis of guided random algorithms such as evolutionary optimization algorithms and community detection algorithms. Proposed methodology is designed based on quantile-quantile plot and regression analysis to compare performance of one algorithm over other algorithms. The methodology is extrapolated as one-to-one comparison, one-to-many comparison and many-to-many comparison of solution quality and convergence rate. Most of the existing approaches utilize both solution quality and convergence rate to perform comparative analysis. However, the many-to-many comparison i.e. ranking of algorithms is done only with solution quality. On the contrary, with proposed methodology ranking of algorithms is done in terms of both solution quality and convergence rate. Proposed methodology is studied with four evolutionary optimization algorithms on 25 benchmark functions. A non-parametric statistical analysis called Wilcoxon signed-rank test is also performed to verify the indication of proposed methodology. Moreover, methodology is also applied to analyze four state-of-the-art community detection algorithms on 10 real-world networks. [ABSTRACT FROM AUTHOR]