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A biomedical application of a novel metaheuristic optimizer is proposed in this paper by constructing an enhanced arithmetic optimization algorithm (AOA). The latter algorithm was constructed using the logarithmic spiral (Ls) search mechanism from the whale optimization algorithm and the greedy selection scheme from the differential evolution algorithm. The proposed algorithm (Ls-AOA) was tested against unimodal and multimodal benchmark functions and demonstrated better capability comparatively using other efficient metaheuristic algorithms reported in the literature. The constructed Ls-AOA algorithm was then proposed to design a proportional-integral-derivative (PID) controller employed in a functional electrical stimulation (FES) system for the first time. The initial statistical and convergence profile assessment showed better performance of the proposed algorithm. The comparative analyses for transient and frequency responses were performed for the PID-controlled FES system using the original AOA, sine–cosine and particle swarm optimization algorithms and the traditional Ziegler-Nichols tuning scheme. Similarly, the FES system tuned with the latter methods was also assessed for disturbance rejection and noise elimination. All the comparative analyses demonstrated that the proposed Ls-AOA has the greater capability for the challenging biomedical FES system. [ABSTRACT FROM AUTHOR]

Most production scheduling problems, including standard flexible job shop scheduling problems, assume that machines are continuously available. However, in most cases, due to preventive maintenance activities, machines may not be available for a certain time. Meanwhile, in the entire workshop production process, the transportation process of workpieces cannot be ignored. Therefore, the impact of transportation on the production planning should be considered in the scheduling process. To consider both preventive maintenance and transportation processes in the flexible job shop scheduling problem, this paper proposes a flexible job shop scheduling problem considering preventive maintenance activities and transportation processes and establishes a multi-objective flexible job shop scheduling model optimizing the total energy consumption and total makespan. Furthermore, a multi-region division sampling strategy-based multi-objective optimization algorithm integrated with a genetic algorithm and a differential evolution algorithm (MDSS-MOGA-DE) is proposed to solve the model. In the proposed algorithm, a multi-region division sampling strategy and two evaluation functions are utilized to improve the diversity of solutions. In addition, this paper combines a genetic operation and a differential operation to further enhance the search ability of the algorithm. The validity of the algorithm is verified by a real case. The computational results reveal that the proposed model and algorithm obtain appropriate results and have the potential to be applied to other similar problems. [ABSTRACT FROM AUTHOR]

Reentry trajectory optimization is a critical optimal control problem for reusable launch vehicle (RLV) with highly nonlinear dynamic characteristics and complex constraints. In this paper, a hybrid parallel Harris hawks optimization (HPHHO) algorithm is proposed to address the problem. HPHHO aims to enhance the performance of existing Harris hawks optimization (HHO) algorithm by three strategies including oppositional learning, smoothing technique and parallel optimization mechanism. At the beginning of each iteration, the opposite population is calculated from the current population by the oppositional learning strategy. Following that, the individuals in the two populations are arranged in ascending order on the basis of the fitness function values, and the top half of the resulting population is selected as the initial population. The selected initial population is divided into two equal subpopulations which are assigned to the differential evolution and the HHO algorithm, respectively. The both algorithms operate in parallel to search and update the solutions of each subpopulation simultaneously. Then the solutions are smoothed for each iteration by the smoothing technique to reduce fluctuations. As a result, the optimal solution obtained by the parallel optimization mechanism avoids falling into local optima. The performance of HPHHO is evaluated by 4 CEC 2005 benchmark functions and 3 constrained continuous optimal control problems, showing better efficiency and robustness in terms of performance metrics, convergence rate and stability. Finally, the simulation results show that the proposed algorithm is very effective, practical and feasible in solving the RLV reentry trajectory optimization problem. [ABSTRACT FROM AUTHOR]

In a textile mill, ring and rotor spinning processes are the main technologies employed to convert cotton fibres into yarns with desirable qualities. It has been observed that in order to produce yarns having satisfactory quality characteristics, those spinning processes need to be run while setting different input variables (control parameters) at their optimal operating levels. In this paper, the optimal parametric combinations of back and front zone variables in a ring frame, and input variables in a rotor spinning process are determined based on teaching-learning-based optimization algorithm. The optimization performance of this algorithm is also compared with four other techniques, e.g., firefly algorithm, differential evolution algorithm, cuckoo search algorithm and quantum particle swarm optimization algorithm with respect to accuracy and consistency of the derived solutions. This optimization technique can thus be effectively applied to any of the intermediate processes in a textile mill to obtain the best combinations of different input variables so as to achieve the target quality characteristics. [ABSTRACT FROM AUTHOR]

The cuckoo search (CS) algorithm is an effective optimization algorithm, but it is prone to stagnation in suboptimality because of some limitations in its exploration mechanisms. This paper introduces a variation of CS called exploratory CS (ECS), which incorporates three modifications to the original CS algorithm to enhance its exploration capabilities. First, ECS uses a special type of opposition-based learning called refraction learning to improve the ability of CS to jump out of suboptimality. Second, ECS uses the Gaussian perturbation to optimize the worst candidate solutions in the population before the discard step in CS. Third, in addition to the Lévy flight mutation method used in CS, ECS employs two mutation methods, namely highly disruptive polynomial mutation and Jaya mutation, to generate new improved candidate solutions. A set of 14 widely used benchmark functions was used to evaluate and compare ECS to three variations of CS:CS with Lévy flight (CS), CS with highly disruptive polynomial mutation (CS10) and CS with pitch adjustment mutation (CS11). The overall experimental and statistical results indicate that ECS exhibits better performance than all of the tested CS variations. Besides, the single-objective IEEE CEC 2014 functions were used to evaluate and compare the performance of ECS to six well-known swarm optimization algorithms: CS with Lévy flight, Grey wolf optimizer (GWO), distributed Grey wolf optimizer (DGWO), distributed adaptive differential evolution with linear population size reduction evolution (L-SHADE), memory-based hybrid Dragonfly algorithm and Fireworks algorithm with differential mutation. Interestingly, the results indicate that ECS provides competitive performance compared to the tested six well-known swarm optimization algorithms. [ABSTRACT FROM AUTHOR]

The selection of the mutation strategy for differential evolution (DE) algorithm plays an important role in the optimization performance, such as exploration ability, convergence accuracy and convergence speed. To improve these performances, an improved differential evolution algorithm with neighborhood mutation operators and opposition-based learning, namely NBOLDE, is developed in this paper. In the proposed NBOLDE, the new evaluation parameters and weight factors are introduced into the neighborhood model to propose a new neighborhood strategy. On this basis, a new neighborhood mutation strategy based on DE/current-to-best/1, namely DE/neighbor-to-neighbor/1, is designed in order to replace large-scale global mutation by local neighborhood mutation with high search efficiency. Then, a generalized opposition-based learning is employed to optimize the initial population and select the better solution between the current solution and reverse solution in order to approximate global optimal solution, which can amend the convergence direction, accelerate convergence, improve efficiency, enhance the stability and avoid premature convergence. Finally, the proposed NBOLDE is compared with four state-of-the-art DE variants by 12 benchmark functions with low-dimension and high-dimension. The experiment results indicate that the proposed NBOLDE has a faster convergence speed, higher convergence accuracy, and better optimization capabilities in solving high-dimensional complex functions. [ABSTRACT FROM AUTHOR]

Harmony search (HS) is a type of population-based optimization algorithm that is introduced based on the idea of musical instruments being tuned to obtain the best harmony state. Several versions of HS have been presented, with global harmony search (GHS) considered one of the most popular. Although GHS is efficient in solving various optimization problems, a new position updating mechanism has been added to improve its efficiency and help it avoid getting stuck in local minima. The novel algorithm proposed in this paper is called the intersect mutation global harmony search algorithm (IMGHSA), which has been tested and evaluated on a set of well-known benchmark functions. The IMGHSA is compared with several improved variants of the HS algorithm, such as the basic version of harmony search (HS), improved differential harmony search, generalized opposition-based learning with global harmony search , and novel global harmony search. The experimental results show that the proposed IMGHSA performs better than the state-of-the-art HS variants and has a more robust convergence when optimizing objective functions in terms of the solution accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In this paper, a new population-based stochastic optimization algorithm called Hybrid Self-Adaptive Differential Evolution (HSADE) is proposed. The algorithm addresses unconstrained global optimization problems, exploring and combining the best features of some Differential Evolution (DE), obtaining a good balance between exploration and exploitation. These approaches are important for increasing the accuracy and efficiency of a population-based stochastic algorithm and for adapting the control parameter values during the optimization process. Further, they are crucial for increasing the convergence speed and reducing the risk of search stagnation. To verify the performance of the HSADE, 25 benchmark functions were tested presenting an optimal performance when compared to some state-of-the-art DEs algorithms. Furthermore, an experimental problem in an automotive sector, related to automatic internal combustion engine calibration, was used adjusting 300 decision variables. The HSADE achieved a reliable calibration, reducing the time required to perform approximately 90% when comparing to other optimization algorithms. [ABSTRACT FROM AUTHOR]

This study presented a new multi-species binary coded algorithm, Mendelian evolutionary theory optimization (METO), inspired by the plant genetics. This framework mainly consists of three concepts: first, the "denaturation" of DNA's of two different species to produce the hybrid "offspring DNA". Second, the Mendelian evolutionary theory of genetic inheritance, which explains how the dominant and recessive traits appear in two successive generations. Third, the Epimutation, through which organism resist for natural mutation. The above concepts are reconfigured in order to design the binary meta-heuristic evolutionary search technique. Based on this framework, four evolutionary operators—(1) Flipper, (2) Pollination, (3) Breeding, and (4) Epimutation—are created in the binary domain. In this paper, METO is compared with well-known evolutionary and swarm optimizers: (1) binary hybrid GA, (2) bio-geography-based optimization, (3) invasive weed optimization, (4) shuffled frog leap algorithm, (5) teaching–learning-based optimization, (6) cuckoo search, (7) bat algorithm, (8) gravitational search algorithm, (9) covariance matrix adaptation evolution strategy, (10) differential evolution, (11) firefly algorithm and (12) social learning PSO. This comparison is evaluated on 30 and 100 variables benchmark test functions, including noisy, rotated, and hybrid composite functions. Kruskal–Wallis statistical rank-based nonparametric H-test is utilized to determine the statistically significant differences between the output distributions of the optimizer, which are the result of the 100 independent runs. The statistical analysis shows that METO is a significantly better algorithm for complex and multi-modal problems with many local extremes. [ABSTRACT FROM AUTHOR]

The design method of adaptive infinite impulse response (IIR) filter is a challenging problem. Its design principle is to determine the filter parameters by the iteration process of the adaptive algorithm, which is to obtain an optimal model for unknown plant based on minimizing mean square error (MSE). However, many adaptive algorithms cannot adjust the parameters of IIR filter to the minimum MSE. Therefore, a more efficient adaptive optimization algorithm is required to adjust the parameters of IIR filter. In this paper, we propose a selfish herd optimization algorithm based on chaotic strategy (CSHO) and apply it to solving IIR system identification problem. In CSHO, we add a chaotic search strategy, which is a better local optimization strategy. Its function is to search for better candidate solutions around the global optimal solution, which makes the local search of the algorithm more precise and finds out potential global optimal solutions. We use solving IIR system identification problem to verify the effectiveness of CSHO. Ten typical IIR filter models with the same order and reduced order are selected for experiments. The experimental results of CSHO compare with those of bat algorithm (BA), cellular particle swarm optimization and differential evolution (CPSO-DE), firefly algorithm (FFA), hybrid particle swarm optimization and gravitational search algorithm (HPSO-GSA), improved particle swarm optimization (IPSO) and opposition-based harmony search algorithm (OHS), respectively. The experimental results show that CSHO has better optimization accuracy, convergence speed and stability in solving most of the IIR system identification problems. At the same time, it also obtains better optimization parameters and achieves smaller difference between actual output and expected output in test samples. [ABSTRACT FROM AUTHOR]

This paper presents a new multi-objective discreet learnable evolution model (MODLEM) to address the vehicle routing problem with time windows (VRPTW). Learnable evolution model (LEM) includes a machine learning algorithm, like the decision trees, that can discover the correct directions of the evolution leading to significant improvements in the fitness of the individuals. We incorporate a robust strength Pareto evolutionary algorithm in the LEM presented here to govern the multi-objective property of this approach. A new priority-based encoding scheme for chromosome representation in the LEM as well as corresponding routing scheme is introduced. To improve the quality and the diversity of the initial population, we propose a novel heuristic manner which leads to a good approximation of the Pareto fronts within a reasonable computational time. Moreover, a new heuristic operator is employed in the instantiating process to confront incomplete chromosome formation. Our proposed MODLEM is tested on the problem instances of Solomon's VRPTW benchmark. The performance of this proposed MODLEM for the VRPTW is assessed against the state-of-the-art approaches in terms of both the quality of solutions and the computational time. Experimental results and comparisons indicate the effectiveness and efficiency of our proposed intelligent routing approach. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a simple yet powerful evolutionary algorithm for numerical optimization. However, the performance of DE significantly relies on its mutation operator and control parameters (scaling factor and crossover rate). In this paper, we propose a novel DE variant by introducing a series of combined strategies into DE, called CSDE. Specifically, in CSDE, to obtain a proper balance between global exploration ability and local exploitation ability, we adopt two mutation operators with different characteristics to produce the mutant vector, and provide a mechanism based on their own historical success rate to coordinate the two adopted mutation operators. Moreover, we combine a periodic function based on one modulo operation, an individual-independence macro-control function and an individual-dependence function based on individual's fitness value information to adaptively produce scaling factor and crossover rate. To verify the effectiveness of the proposed CSDE, comparison experiments contained seven other state-of-the-art DE variants are tested on a suite of 30 benchmark functions and four real-world problems. The simulation results demonstrate that CSDE achieves the best overall performance among the eight DE variants. [ABSTRACT FROM AUTHOR]

The set-union knapsack problem (SUKP) is a variation of the 0–1 knapsack problem (KP) in which each item is a set of elements, each item has a nonnegative value, and each element has a nonnegative weight. The weight of one item is given by the total weight of the elements in the union of the items' sets. The SUKP accommodates a number of real-life applications and is more complicated and computationally difficult than the 0–1 KP. In this paper, we propose a novel hybrid Jaya algorithm with double coding (DHJaya) to solve the SUKP. In the DHJaya, double coding is used to represent the individual, which includes the solutions for solving the SUKP by adopting a mapping function. The Jaya algorithm and differential evolution algorithm are combined to improve the exploration ability. To enhance the exploitation ability, the Cauchy mutation is performed on some individuals. Meanwhile, an improved repairing and optimization algorithm (MS-GROA) is proposed to repair the infeasible solutions and optimize the feasible solutions. We test the DHJaya using three sets of SUKP instances to demonstrate its efficiency, and the obtained results are compared with those in the previous study. Extensive experiments show a remarkable performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Multimodal optimization problem (MMOP) requires to find optima as many as possible for a single problem. Recently, many niching techniques have been proposed to tackle MMOPs. However, most of the niching techniques are either sensitive to the niching parameters or causing a waste of fitness evaluations. In this paper, we proposed a novel niching technique based on minimum spanning tree (MST) and applied it into differential evolution (DE), termed as MSTDE, to solve MMOPs. In every generation, an MST is built based on the distance information among the individuals. After that, we cut the M largest weighted edges of the MST to form some subtrees, so-called subpopulations. The DE operators are executed within the subpopulations. Besides, a dynamic pruning ratio (DPR) strategy is proposed to determine M with an attempt to reduce its sensitivity, so as to enhance the niching performance. Meanwhile, the DPR strategy can achieve a good balance between diversity and convergence. Besides, taking the advantage of fast availability in time from virtual machines (VMs), a distributed model is applied in MSTDE, where different subpopulations run concurrently on distributed VMs. Experiments have been conducted on the CEC2013 multimodal benchmark functions to test the performance of MSTDE, and the experimental results show that MSTDE can outperform many existed multimodal optimization algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we tackle a problem of frequency assignment in Wi-Fi networks with a novel evolutionary-type algorithm. In this version of the problem, we consider the interferences originated by the access points, and also by the clients and all the 11 available channels in the 2.4 GHz Wi-Fi frequency band. The proposed evolutionary-type algorithm is the Coral Reefs Optimization approach with substrate layer (CRO-SL). It is a recently proposed algorithm, which simulates the processes which occur in real coral reefs, including the reproduction and fight for the space of living corals. This version of the algorithm includes a layer of "substrates" which allows using different search patterns jointly in the algorithm. This way, the CRO-SL is able to apply search patterns such as harmony search, differential evolution, Gaussian-based mutations and other traditional and novel search procedures, including local search algorithms, within a single population of solutions. We show the good performance of the proposed approach in a real case study of Wi-Fi frequency assignment, in the Polytechnic School building of the Universidad de Alcalá (Spain), where different realistic scenarios of the problem have been simulated and successfully solved with the CRO-SL algorithm. [ABSTRACT FROM AUTHOR]

Nature-inspired optimization algorithms are meta-heuristics that mimic nature for solving optimization problems. Many optimization problems are constrained and have a bounded search space from which some solution vectors leave when the variation operators are applied. Therefore, the use of boundary constraint-handling methods (BCHM) is necessary in order to repair the invalid vectors. This paper presents an adaptive scheme to handling boundary constraints in constrained numerical optimization problems. The proposed adaptive scheme operates in two stages: At the first one, when there are still no feasible solutions, a BCHM that benefits the exploration of the search space is employed, and in the second stage, one of several BCHMs, according to their associated probabilities, is selected. The methods' probabilities are updated every learning period so that the methods that generate the best repaired solutions will have a greater chance of being selected. The proposed scheme has been tested within two nature-inspired optimization algorithms: Particle Swarm Optimization and Differential Evolution employing their canonical version as well as one state-of-the-art version specialized in constrained optimization. A set of sixty single-objective constrained real-parameter optimization problems are solved. The results show that this adaptive scheme has a major impact on the algorithm's performance, and it is able to promote better final results mainly within high-dimensional problems. [ABSTRACT FROM AUTHOR]

Image matting is a fundamental operator in image editing and has significant influence on video production. This paper explores sampling-based image matting technology, with the aim to improve the accuracy of matting result. The result of sampling-based image matting technology is determined by the selected samples. Every undetermined pixel needs both a foreground and background pixel to estimate whether the undetermined one is in the foreground region of the image. These foreground pixels and background pixels are sampled from known regions, which form sample pairs. High-quality sample pairs can improve the accuracy of matting results. Therefore, how to search for the best sample pairs for all undetermined pixels is a key optimization problem of sampling-based image matting technology, termed 'sample optimization problem.' In this paper, in order to improve the efficiency of searching for high-quality sample pairs, we propose a cooperative coevolution differential evolution (DE) algorithm in solution to this optimization problem. Strong-correlate pixels are divided into a group to cooperatively search for the best sample pairs. In order to avoid premature convergence of DE algorithm, a scattered strategy is used to keep the diversity of population. Besides, a simple but effective evaluation function is proposed to distinguish the quality of various candidate solutions. The existing optimization method, original DE algorithm and a popular evolution algorithm are used for comparison. The experimental results demonstrate that the proposed cooperative coevolution DE algorithm can search for higher-quality sample pairs and improve the accuracy of sampling-based image matting. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is one of the most powerful and versatile evolutionary algorithms for efficiently solving complex real-world optimization problems in recent years. Since its introduction in 1995, the research focus in DE has mostly been on the variant side with so many new algorithms proposed based on the original DE algorithm. However, each new algorithm is only suitable for certain fitness landscapes, and, therefore, some types of optimization problems cannot be solved efficiently. To tackle this issue, this paper presents a new self-feedback DE algorithm, named the SFDE; its optimal variation strategy is selected by extracting the local fitness landscape characteristics in each generation population and combing the probability distributions of unimodality and multimodality in each local fitness landscape. The proposed algorithm is tested on a suite of 17 benchmark functions, and the experimental results demonstrated its advantages in a high search dimension in that it can ensure that the population moves to a better fitness landscape, then speeds up convergence to the global optimum, and avoids falling into local optima. [ABSTRACT FROM AUTHOR]

In this paper, a novel heuristic optimization algorithm called differential evolution (DE) technique has been proposed to solve the optimal location of FACTS devices in deregulated electricity market using contingency analysis. The proposed approach deals with the optimal injection of real and reactive power using FACTS devices with an aim to minimize the total system cost, the total number of overloads, excess power flow, the severity of overload and real power loss of the network. To enhance the search behavior of the DE approach, the scaling factor and crossover parameters are empirically selected. To show the superiority of the proposed DE approach and as a step ahead to prove its novelty, the same optimization problem is solved using evolutionary programming method, and the results are compared. The results indicate the proposed DE algorithm is superior in terms of final solution quality, efficiency, convergence rate and robustness. A sample four-bus system and 24-bus EHV southern region of Indian grid system has been considered to illustrate the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper presents differential evolution with Gaussian mutation to solve the complex non-smooth non-convex combined heat and power economic dispatch (CHPED) problem. Valve-point loading and prohibited operating zones of conventional thermal generators are taken into account. Differential evolution (DE) is a simple yet powerful global optimization technique. It exploits the differences of randomly sampled pairs of objective vectors for its mutation process. This mutation process is not suitable for complex multimodal optimization. This paper proposes Gaussian mutation in DE which improves search efficiency and guarantees a high probability of obtaining the global optimum without significantly impairing the simplicity of the structure of DE. The effectiveness of the proposed method has been verified on five test problems and three test systems. The results of the proposed approach are compared with those obtained by other evolutionary methods. It is found that the proposed differential evolution with Gaussian mutation-based approach is able to provide better solution. [ABSTRACT FROM AUTHOR]

Clustering Search ( *CS) has been proposed as a generic way of combining search metaheuristics with clustering to detect promising search areas before applying local search procedures. The clustering process may keep representative solutions associated with different search subspaces. In this paper, new approaches are proposed, based on *CS, as an Artificial Bee Colony-based one, which detects promising food sources alike *CS approaches. The other new *CS approach is based on Differential Evolution (DE) algorithm. The DE is just a CS component (the evolutionary algorithm), different from ABC-based approach, called Artificial Bee Clustering Search (ABCS). ABCS tries to find promising solutions using some concepts from CS. The proposed hybrid algorithms, performing a Hooke and Jeeves-based local, are compared to another hybrid approaches, exploring an elitist criteria to apply local search. The experiments show that the proposed ABCS and Differential Evolutionary Clustering Search (DECS) are competitive for the majority continuous optimization functions benckmarks selected in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes an improved memetic algorithm relying on ring neighborhood topology for constrained optimization problems based on our previous work in Cai et al. (Soft Comput (in press), ). The main motivation of using ring neighborhood topology is to provide a good balance between effective exploration and efficient exploitation, which is a very important design issue for memetic algorithms. More specifically, a novel variant of invasive weed optimization (IWO) as the local refinement procedure is proposed in this paper. The proposed IWO variant adopts a neighborhood-based dispersal operator to achieve more fine-grained local search through the estimation of neighborhood fitness information relying on the ring neighborhood topology. Furthermore, a modified version of differential evolution (DE), known as 'DE/current-to-best/1', is integrated into the improved memetic algorithm with the aim of providing a more effective exploration. Performance of the improved memetic algorithm has been comprehensively tested on 13 well-known benchmark test functions and four engineering constrained optimization problems. The experimental results show that the improved memetic algorithm obtains greater competitiveness when compared with the original memetic approach Cai et al. in (Soft Comput (in press), ) and other state-of-the-art algorithms. The effectiveness of the modification of each component in the proposed approach is also discussed in the paper. [ABSTRACT FROM AUTHOR]

Different mutation strategies and control parameters settings directly affect the performance of differential evolution (DE) algorithm. In this paper, a self-adaptive differential evolution algorithm with improved mutation strategy (IMSaDE) is proposed to improve optimization performance of DE. IMSaDE improves the “DE/rand/2” mutation strategy by incorporating elite archive strategy and control parameters adaptation strategy. Both strategies diversify the population and improve the convergence performance of the algorithm. IMSaDE was compared with eleven DE algorithms and six non-DE algorithms by using a set of 20 benchmark functions taken from the literature. Experimental results show that the overall performance of IMSaDE is better than the other competitors. In addition, the size of elite population has a significant impact on the performance of IMSaDE. [ABSTRACT FROM AUTHOR]

This paper presents enhanced fitness-adaptive differential evolution algorithm with novel mutation (EFADE) for solving global numerical optimization problems over continuous space. A new triangular mutation operator is introduced. It is based on the convex combination vector of the triplet defined by the three randomly chosen vectors and the difference vectors between the best, better and the worst individuals among the three randomly selected vectors. Triangular mutation operator helps the search for better balance between the global exploration ability and the local exploitation tendency as well as enhancing the convergence rate of the algorithm through the optimization process. Besides, two novel, effective adaptation schemes are used to update the control parameters to appropriate values without either extra parameters or prior knowledge of the characteristics of the optimization problem. In order to verify and analyze the performance of EFADE, numerical experiments on a set of 28 test problems from the CEC2013 benchmark for 10, 30 and 50 dimensions, including a comparison with 12 recent DE-based algorithms and six recent evolutionary algorithms, are executed. Experimental results indicate that in terms of robustness, stability and quality of the solution obtained, EFADE is significantly better than, or at least comparable to state-of-the-art approaches with outstanding performance. [ABSTRACT FROM AUTHOR]

Many numerical methods applied on a Shishkin mesh are very popular in solving the singularly perturbed problems. However, few approaches are used to obtain the Shishkin mesh transition parameter. Thus, in this paper, we first use the cubic B-spline collocation method on a Shishkin mesh to solve the singularly perturbed convection-diffusion problem with two small parameters. Then, we transform the Shishkin mesh transition parameter selection problem into a nonlinear unconstrained optimization problem which is solved by using the self-adapting differential evolution (jDE) algorithm. To verify the performance of our presented method, a numerical example is employed. It is shown from the experiment results that our approach is efficient. Compared with other evolutionary algorithms, the jDE algorithm performs better and with more stability. [ABSTRACT FROM AUTHOR]

In real-time high-dimensional optimization problem, how to quickly find the optimal solution and give a timely response or decisive adjustment is very important. This paper suggests a self-adaptive differential evolution algorithm (abbreviation for APDDE), which introduces the corresponding detecting values (the values near the current parameter) for individual iteration during the differential evolution. Then, integrating the detecting values into two mutation strategies to produce offspring population and the corresponding parameter values of champion are retained. In addition, the whole populations are divided into a predefined number of groups. The individuals of each group are attracted by the best vector of their own group and implemented a new mutation strategy DE/Current-to-lbest/1 to keep balance of exploitation and exploration capabilities during the differential evolution. The proposed variant, APDDE, is examined on several widely used benchmark functions in the CEC 2015 Competition on Learning-based Real-Parameter Single Objective Optimization (13 global numerical optimization problems) and 7 well-known basic benchmark functions, and the experimental results show that the proposed APDDE algorithm improves the existing performance of other algorithms when dealing with the highdimensional and multimodal problems. [ABSTRACT FROM AUTHOR]

This paper proposes an adaptive neural network (ANN) model for modeling the nonlinear dynamic of a robot manipulator based on experimental input–output data from the system. The ANN model is created by combining the multilayer perceptron neural network structure and the nonlinear auto-regressive with eXogenous input model and is trained by the modified differential evolution (MDE) algorithm. The effectiveness of the proposed method is evaluated and compared with other algorithms such as the back-propagation algorithm, the traditional differential evolution and the hybrid differential evolution–back-propagation algorithm. The results prove that the proposed ANN model optimized by the MDE algorithm for the 5-DOF robot manipulator dynamic is successfully modeled and performed well. [ABSTRACT FROM AUTHOR]

This paper proposes a new stopping criterion for decomposition-based multi-objective evolutionary algorithms (MOEA/Ds) to reduce the unnecessary usage of computational resource. In MOEA/D, a multi-objective problem is decomposed into a number of single-objective subproblems using a Tchebycheff decomposition approach. Then, optimal Pareto front (PF) is obtained by optimizing the Tchebycheff objective of all the subproblems. The proposed stopping criterion monitors the variations of Tchebycheff objective at every generation using maximum Tchebycheff objective error (MTOE) of all the subproblems and stops the algorithm, when there is no significant improvement in MTOE. $$\chi ^{2}$$ test is used for statistically verifying the significant changes of MTOE for every $$\gamma $$ generations. The proposed stopping criterion is implemented in a recently constrained MOEA/D variant, namely CMOEA/D-CDP, and a simulation study is conducted with the constrained test instances for choosing a suitable tolerance value for the MTOE stopping criterion. A comparison with the recent stopping methods demonstrates that the proposed MTOE stopping criterion is simple and has minimum computational complexity. Moreover, the MTOE stopping criterion is tested on real-world application, namely multi-objective $$\hbox {H}_{\infty }$$ loop shaping PID controller design. Simulation results revealed that the MTOE stopping criterion reduces the unnecessary usage of computational resource significantly when solving the constrained test instances and multi-objective $$\hbox {H}_{\infty }$$ loop shaping PID controller design problems. [ABSTRACT FROM AUTHOR]

In this paper, a new multi-objective evolutionary algorithm (MOEA) named hybrid MOEA with adaptive multi-population strategy (HMOEA-AMP) is proposed for multi-objective optimization problems (MOPs).In the framework of HMOEA-AMP, the particle swarm optimization and differential evolution are hybridized to guide the exploitation of the Pareto optimal solutions and the exploration of the optimal distribution of the achieved solutions, respectively. Multiple subpopulations are constructed in an adaptive fashion according to a number of scalar subproblems, which are decomposed from a MOP through a set of predefined weight vectors. Comprehensive experiments using a set of benchmark are conducted to investigate the performance of HMOEA-AMP in comparison with several state-of-the-art MOEAs. The experimental results show the advantage of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The role of parent selection is to distinguish between individuals based on their quality. Parent selection has been a key component in the design of evolutionary algorithms, since it is partially responsible for improving the quality of the population. Stochastic ranking is quite a successful approach for evolutionary constrained optimization, and has usually been employed during the survival selection process. This paper provides the first insight into the use of the stochastic ranking procedure during the parent selection mechanism in the design of new evolutionary algorithms for constraint handling. We adopted differential evolution as the base algorithm, mainly because of its outstanding performance in continuous optimization found in literature. We undertake seven experiments in order to validate our proposal. The results indicate that our proposed approach is able to find solutions that are competitive with respect to other recently proposed approaches, but uses a fraction of the required computational effort. Furthermore, our proposal can easily be incorporated into any probabilistic evolutionary algorithm that is based on parent selection. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a simple yet efficient stochastic search approach for numerical optimization. However, it tends to suffer from slow convergence when tackling complicated problems. In addition, its search ability is significantly influenced by its control parameters. To improve the performance of the basic DE, this paper proposes a self-adaptive differential evolution with global neighborhood search (NSSDE). In the proposed NSSDE, its control parameters are self-adaptively tuned according to the feedback from the search process, while the global neighborhood search strategy is incorporated to accelerate the convergence speed. To evaluate the performance of the proposed NSSDE, we compare it with several DE variants on a set of benchmark test functions. The experimental results show that NSSDE can achieve better results than its competitors on the majority of the benchmark test functions. [ABSTRACT FROM AUTHOR]

In this work, we present an evolutionary omputation-based solution to the circle packing problem (ECPP). The circle packing problem consists of placing a set of circles into a larger containing circle without overlaps: a problem known to be NP-hard. Given the impossibility to solve this problem efficiently, traditional and heuristic methods have been proposed to solve it. A naïve representation for chromosomes in a population-based heuristic search leads to high probabilities of violation of the problem constraints, i.e., overlapping. To convert solutions that violate constraints into ones that do not (i.e., feasible solutions), in this paper we propose two repair mechanisms. The first one considers every circle as an elastic ring and overlaps create repulsion forces that lead the circles to positions where the overlaps are resolved. The second one forms a Delaunay triangulation with the circle centers and repairs the circles in each triangle at a time, making sure repaired triangles are not modified later on. Based on the proposed repair heuristics, we present the results of the solution to the CPP problem to a set of unit circle problems (whose exact optimal solutions are known). These benchmark problems are solved using genetic algorithms, evolutionary strategies, particle swarm optimization, and differential evolution. The performance of the solutions is compared to those known solutions based on the packing density. We then perform a series of experiments to determine the performance of ECPP with non-unitary circles. First, we compare ECPP's results to those of a public competition, which stand as the world record for that particular instance of the non-unitary CPP. On a second set of experiments, we control the variance of the size of the circles. In all experiments, ECPP yields satisfactory near-optimal solutions. [ABSTRACT FROM AUTHOR]

Biogeography-based optimization (BBO) is a relatively new heuristic method, where a population of habitats (solutions) are continuously evolved and improved mainly by migrating features from high-quality solutions to low-quality ones. In this paper we equip BBO with local topologies, which limit that the migration can only occur within the neighborhood zone of each habitat. We develop three versions of localized BBO algorithms, which use three different local topologies namely the ring topology, the square topology, and the random topology respectively. Our approach is quite easy to implement, but it can effectively improve the search capability and prevent the algorithm from being trapped in local optima. We demonstrate the effectiveness of our approach on a set of well-known benchmark problems. We also introduce the local topologies to a hybrid DE/BBO method, resulting in three localized DE/BBO algorithms, and show that our approach can improve the performance of the state-of-the-art algorithm as well. [ABSTRACT FROM AUTHOR]