Search

Recently, there has been increased interest in combining model-driven engineering and search-based software engineering. Such approaches use meta-heuristic search guided by search operators (model mutators and sometimes breeders) implemented as model transformations. The design of these operators can substantially impact the effectiveness and efficiency of the meta-heuristic search. Currently, designing search operators is left to the person specifying the optimisation problem. However, developing consistent and efficient search-operator rules requires not only domain expertise but also in-depth knowledge about optimisation, which makes the use of model-based meta-heuristic search challenging and expensive. In this paper, we propose a generalised approach to automatically generate atomic multiplicity-preserving search operators for a given optimisation problem. This reduces the effort required to specify an optimisation problem and shields optimisation users from the complexity of implementing efficient meta-heuristic search mutation operators. We evaluate our approach with a set of case studies and show that the automatically generated rules are comparable to, and in some cases better than, manually created rules at guiding evolutionary search towards near-optimal solutions.

The idea of hybrid algorithms is formed due to the functional and structural differences in optimization algorithms. The goal is to create hybrid algorithms that can combine the strengths of the optimization algorithms to perform better in solving different problems. The Emperor Penguins Colony (EPC) algorithm is a population-based and nature-inspired optimization algorithm. This algorithm is powerful in finding global optima. In this paper, the standard EPC is improved by combining with genetic operators to finding better global optima. The genetic crossover and mutation operators have been used for modifying the decision vectors. These operators can cause a balance between exploration and exploitation. The balance between exploration and exploitation is effective in achieving a better optimal solution. The proposed algorithm called Hybrid-EPC is compared with GA, PSO, standard EPC, and Hybrid-PSO and tested on 20 various benchmark test functions. Also as an application, the proposed Hybrid-EPC algorithm is used for community detection in complex networks. For this purpose, the algorithm is tested on four social datasets and is compared with other community detection algorithms. The results show that this hybridization improves the standard EPC algorithm and has been successful in community detection.

This paper considers a passive target localization problem based on the noisy time of arrival measurements obtained from multiple receivers and a single transmitter. The maximum likelihood (ML) estimator for this localization problem is formulated as a highly nonlinear and non-convex optimization problem, where conventional optimization methods are not suitable for solving such a problem. Consequently, this paper proposes an improved adaptive hybrid firefly differential evolution (AHFADE) algorithm, based on hybridization of firefly algorithm (FA) and differential evolution (DE) algorithm to estimate the unknown position of the target. The proposed AHFADE algorithm dynamically adjusts the control parameters, thus maintaining high population diversity during the evolution process. This paper aims to improve the accuracy of the global optimal solution by incorporating evolutionary operators of the DE in different searching stages of the FA. In this regard, an adaptive parameter is employed to select an appropriate mutation operator for achieving a proper balance between global exploration and local exploitation. In order to efficiently solve the ML estimation problem, this paper proposes the well-known semidefinite programming (SDP) method to convert the non-convex problem into a convex one. The simulation results obtained from the proposed AHFADE algorithm and well-known algorithms, such as SDP, DE and FA, are compared against Cramer–Rao lower bound (CRLB). The statistical analysis has been performed to compare the performance of the proposed AHFADE algorithm with several well-known algorithms on CEC2014 benchmark problems. The obtained simulation results show that the proposed AHFADE algorithm is more robust in high-noise environments compared to existing algorithms.

Effectiveness of any swarm based metaheuristic optimization algorithm focuses on perfect mishmash of operator’s castoff for exploration and exploitation. The absenteeism of balance between this two factors leads to deprived performance in terms of attaining global optimum by stagnating in local optimum and untimely convergence. Salp Swarm Algorithm (SSA) is a recently evolved optimization technique, intended to resolve continuous, non-linear and multifaceted real world optimization glitches. For solving complex day to day life problems the explorative strength of existing SSA is not adequate. So, this paper proposes a new improved algorithm termed as OBL-MO-SSA to enhance the performance of existing SSA. Two techniques such as normal distributed mutation operator and oppositional learning concept is embedded to achieve the purpose. Oppositional learning concept ensures the current as well as opposite candidate solutions in the search region simultaneously to evaluate the closer solutions during ongoing evolution process. Mutation operator avoids the arbitrary positions in the search region by choosing lesser and larger mutations for balanced motion in current and opposite directions. The proposed method OBL-MO-SSA improves the exploration and exploitation strength inside search region at the same time exhibiting better convergence speed by successfully avoiding local optima stagnation. To confirm the efficiency of proposed OBL-MO-SSA algorithm, the same is assessed by benchmark problems pertaining to IEEE-CEC-2017. The competence and strength of the proposed OBL-MO-SSA is characterised by using performance metrics, complexity analysis, convergence rate and statistical significance. Friedman and Holms test has been accomplished to substantiate its statistical significance. Furthermore to elucidate complex difficulties, the proposed method used to train higher order neural network (FLANN) by the help of 10 customary datasets preferred from UCI storehouse. The simulated outcomes reveals that the developed OBL-MO-SSA might be cast-off for resolving various optimization complications efficiently.

Genetic algorithm (GA) is used to solve a variety of optimization problems. Mutation operator also is responsible in GA for maintaining a desired level of diversity in the population. Here, a directional mutation operator is proposed for real-coded genetic algorithm (RGA) along with a directional crossover (DX) operator to improve its performance. These evolutionary operators use directional information to guide the search process in the most promising area of the variable space. The performance of an RGA with the proposed mutation operator and directional crossover (DX) is tested on six benchmark optimization problems of different complexities, and the results are compared to that of the RGAs with five other mutation schemes. The proposed IRGA is found to outperform other RGAs in terms of accuracy in the solutions, convergence rate, and computational time, which is established firmly through statistical analysis. Furthermore, the performance of the proposed IRGA is compared to that of a few recently proposed optimization algorithms. The proposed IRGA is seen to yield the superior results compared to that of the said techniques. It is also applied to solve five constrained engineering optimization problems, where again, it has proved its supremacy. The proposed mutation scheme using directional information leads to an efficient search, and consequently, a superior performance is obtained.

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.

Based on the algorithm structure, each metaheuristic algorithm may have its pros and cons, which may result in high performance in some problems and low functionality in some others. The idea is to hybridize two or more algorithms to cover each other’s weaknesses. In this study, particle swarm optimization (PSO), simulated annealing (SA) and differential evolution (DE) are combined to develop a more powerful search algorithm. First, the temperature concept of SA is applied to balance the exploration/exploitation capability of the hybridized algorithm. Then, the DE’s mutation operator is used to improve the exploration capability of the algorithm to escape the local minimums. Next, DE’s mutation operator has been modified so that past experiences can be used for smarter mutations. Finally, the PSO particles’ tendency to their local optimums or the global optimum, which balances the algorithm’s random and greedy search, is affected by the temperature. The temperature influences the algorithm’s behavior so that the random search is more significant at the beginning, and the greedy search becomes more important as the temperature is reduced. The results are compared with the basic PSO, SA, DE, cuckoo search (CS), and hybridized CS-PSO algorithm on 20 benchmark problems. The comparison reveals that, in most cases, the new algorithm outperforms others.

Constrained multi-objective optimization problems (CMOPs) are common in engineering design fields. To solve such problems effectively, this paper proposes a new differential evolution variant named IMDE with infeasible-guiding mutation operators and a multistrategy technique. In IMDE, an infeasible solution with lower objective values is maintained for each individual in the main population, and this infeasible solution is then incorporated into some common differential evolution’s mutation operators to guide the search toward the region with promising objective values. Moreover, multiple mutation strategies and control parameters are adopted during the trial vector generation procedure to enhance both the convergence and the diversity of differential evolution. The superior performance of IMDE is validated via comparisons with some state-of-the-art constrained multi-objective evolutionary algorithms over 3 sets of artificial benchmarks and 4 widely used engineering design problems. The experiments show that IMDE outperforms other algorithms or obtains similar results. It is an effective approach for solving CMOPs, basically due to the use of infeasible-guiding mutation operators and multiple strategies.

Moth-Flame Optimization (MFO) algorithm is a new population-based meta-heuristic algorithm for solving global optimization problems. Flames generation and spiral search are two key components that affect the performance of MFO. To improve the diversity of flames and the searching ability of moths, an improved Moth-Flame Optimization (IMFO) algorithm is proposed. The main features of the IMFO are: the flames are generated by orthogonal opposition-based learning (OOBL); the modified position updating mechanism of moths with linear search and mutation operator. To evaluate the performance of IMFO, the IMFO algorithm is compared with other 20 algorithms on 23 benchmark functions and IEEE (Institute of Electrical and Electronics Engineers) CEC (Congress on Evolutionary Computation) 2014 benchmark test set. The comparative results show that the IMFO is effective and has good performance in terms of jumping out of local optimum, balancing exploitation ability and exploration ability. Moreover, the IMFO is also used to solve three engineering optimization problems, and it is compared with other well-known algorithms. The comparison results show that the IMFO algorithm can improve the global search ability of MFO and effectively solve the practical engineering optimization problems.

The moth search algorithm (MS) is a novel intelligent optimization algorithm based on moth population behavior, which can solve many problems in different fields. However, the algorithm is easy to fall into local optimization when solving complex optimization problems. This study develops a new hybrid moth search-fireworks algorithm (MSFWA) to solve numerical and constrained engineering optimization problems. The explosion and mutation operators from the fireworks algorithm are introduced into the MS, which not only preserves the advantages of fast convergence and strong exploitation capability of the algorithm, but also significantly enhances the exploration capability. The performance of the MSFWA is tested using 23 benchmark functions. The hybrid algorithm is superior to other highly advanced metaheuristic algorithms for most benchmark functions, demonstrating the characteristics of fast convergence and high stability. Finally, the ability of the MSFWA to solve practical constrained problems is evaluated on six well-known engineering application problems. Compared with other optimization algorithms, the MSFWA is very competitive in its solution of these complex and constrained practical problems.

Feature selection is one of the hottest machine learning topics in recent years. The main purposes of it are to simplify the original model, improve the readability of the model, and prevent over-fitting by searching for a suitable subset of features. There are many methods for this problem, including evolutionary algorithms and particle swarm optimization. Among them, the competitive swarm optimizer is a new optimization algorithm proposed in recent years, which is based on particle swarm optimization algorithm, and has achieved good results in high-dimensional feature selection problems, but it also has the problems of high computation time cost and easily being premature. Aiming at these problems, this paper proposes to add the crossover operator and mutation operator in the genetic algorithm to the competitive swarm optimization, so as to improve the generation speed of new individuals in the algorithm and prevent premature population. After testing on UC Irvine Machine Learning Repository, the new algorithm not only improves the computational efficiency, but also avoids the problem that the competitive swarm optimization algorithm is easy to fall into the local optimum, which greatly improves the calculation effect.

Arising from the need of all time for optimization of irrigation systems, distribution network and cable network, Clustered Shortest-Path Tree Problem (CluSPT) has been attracting a lot of attention and interest from the research community. On the other hand, the Multifactorial Evolutionary Algorithm (MFEA) is one of the most recently exploited realms of Evolutionary Algorithms (EAs) and its performance in solving optimization problems has been very promising. Considering these characteristics, this paper describes a new approach using the MFEA for solving the CluSPT. The MFEA has two tasks: the goal of the first task is to determine the best tree (w.r.t. cost minimization) which envelops all vertices of the CluSPT while the goal of the second task is to find the fittest solution possible for the problem. The purpose of the second task is to find good materials for implicit genetic transfer process in MFEA to improve the quality of CluSPT. To apply this new algorithm, a decoding scheme for deriving individual solutions from the unified representation in the MFEA is also introduced in this paper. Furthermore, evolutionary operators such as population initialization, crossover and mutation operators are also proposed. These operators are applicable for constructing valid solution from both sparse and complete graph. Although the proposed algorithm is slightly complicated for implementation, it can enhance ability to explore and exploit the Unified Search Space (USS). To prove this increment in performance i.e, to assess the effectiveness of the proposed algorithm and methods, the authors implemented them on both Euclidean and Non-Euclidean instances. Experiment results show that the proposed MFEA outperformed existing heuristic algorithms in most of the test cases. The impact of the proposed MFEA was analyzed and a possible influential factor that may be useful for further study was also pointed out.

Recently, the ear biometric has received much attention for human recognition due to its unique shape and rich local features. However, extracting discriminative features from ear images is a crucial task in presence of illumination changes, low contrast, noise, and pose variations. With the aim of neutralizing the effect of these factors, this paper proposes an automatic enhancement technique using meta-heuristic optimization to enhance the ear images. Here, we modified a recent and simple yet meta-heuristic optimization technique known as Jaya algorithm by introducing a mutation operator to enhance the ear images in few iterations and the proposed approach is named as enhanced Jaya algorithm. Then, we employed a pose-invariant local feature extractor, SURF to extract local features. Finally, the k-NN classifier has used to evaluate the rate of correct identification. Extensive experiments are conducted on four standard datasets and the performance evaluation is carried out by qualitative and quantitative measures. Experimental results clearly indicate the proposed enhancement approach is competitive as compared to two classical methods HE, CLAHE, and two meta-heuristic algorithms PSO and DE-based image enhancement techniques.

In conventional differential evolutionary (DE) algorithm, mutation operator has significant influence on generating new vectors by mixing existing target vectors randomly selected from the current population. Recently, many mutation operators, which usually employ the best individual or some high-quality individuals randomly chosen, have been proposed to improve searching capability. However, such designs may easily suffer from premature convergence trapped by local optima. To make a trade-off between exploration and exploitation capability, this paper proposes a novel collective intelligence (CI)-based mutation operator, which is named as “current-to-sa-ci-best.” In the presented mutation operator, the evolutionary information of m best target vectors is linearly combined to generate new mutant vectors. Besides, m is designed as an exponential-distributed random number which could be self-adapted based on successful records of m values alongside evolution. Moreover, this mutation operator could be applied to any DE algorithm without destroying existing search capability by adding a greedy selection operator. To verify its effectiveness, the proposed CI-based mutation strategy, which is named as SaCI, was embedded into some state-of-the-art DE variants on 28 CEC2013 benchmark functions. Numerical results have confirmed that the SaCI operator may be beneficial to DEs to some extent.

Differential search (DSA) is a recently proposed evolutionary algorithm mimicking the Brownian motion-like random movement existing in living beings. Though it has displayed promise for global optimization, the original DSA suffers from relatively poor search capability, especially for exploitation. In this study, an augmented DSA (ADSA) is proposed by integrating memetic framework with multiple strategies. In ADSA, a sub-gradient strategy is combined to improve local exploitation, and the dynamic Levy flight technique is developed to strengthen the global exploration. Moreover, a mutation operator based on differential search is used to increase swarm diversity. An intelligent selection method is implemented to adaptively adjust the strategies based on historical performance. To fully benchmark the proposed algorithm, 35 test functions of various properties in 30-D and 100-D are adopted in numerical experiments. Seven canonical optimization algorithms are involved for experimental comparison. In addition, two real-world problems are also tested to verify ADSA’s practical applicability. Numerical results reveal the efficiency and effectiveness of ADSA.

To improve the disassembly efficiency, cooperative disassembly is essential for complex products. Operator task allocation is a significant challenge for cooperative disassembly sequence planning; however, it has not been studied previously to the best of our knowledge. To deal with this problem, a novel cooperative disassembly sequence and task planning (CDS&TP) method was proposed based on the genetic algorithm. A mathematical model of the CDS&TP problem was constructed based on the product’s disassembly hybrid graph model (DHGM). Focusing on the characteristics of the CDS&TP, a multi-layer chromosome coding method was proposed to describe the node layer and operator constraint layer. Thus, the initial population could be deduced through the node layer and operator constraints relationship rule model, which was proposed to construct the operator constraint and node layers. To obtain the task sequence of each operator and the disassembly time of each sequence, a chromosome fitness calculation formula was presented based on the disassembly set, which is the collection of all of the detachable nodes with a disassembly priority higher than the node. The chromosome evolution rules, such as the selection, crossover, and mutation operators, were redesigned to obtain the (approximate) optimal multiplayer cooperative disassembly sequences and task planning. Finally, a case study was proposed to validate the method.

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.

The problem of bi-level optimization has always been a hot topic due to its extensive application. Increasing size and complexity have prompted theoretical and practical interest in the design of effective algorithm. This paper adopts particle swarm algorithm (PSO) at both level. First, given the nested nature of bi-level problem, we introduce a hyper-sphere search into PSO as mutation operator to maintain the swarms diversity. Second, for complex constraints processing, the proposed algorithm adopts a dynamic constraint handling strategy, which makes the solution located on the constraint boundary easier to be obtained. Third, a quadratic approximation mutation is introduced into PSO, which guides particles to a better search area. Finally, the convergence is proved and the simulation results show that the proposed algorithm is effective.

A decomposition-based multi-objective evolutionary algorithm with a differential evolution variation operator (MOEA/D-DE) shows high performance on challenging multi-objective problems (MOPs). The DE mutation consists of three key components: a mutation strategy, an index selection method for parent individuals, and a bound-handling method. However, the configuration of the DE mutation operator that should be used for MOEA/D-DE has not been thoroughly investigated in the literature. This configuration choice confuses researchers and users of MOEA/D-DE. To address this issue, we present a review of the existing configurations of the DE mutation operator in MOEA/D-DE and systematically examine the influence of each component on the performance of MOEA/D-DE. Our review reveals that the configuration of the DE mutation operator differs depending on the source code of MOEA/D-DE. In our analysis, a total of 30 configurations (three index selection methods, two mutation strategies, and five bound handling methods) are investigated on 16 MOPs with up to five objectives. Results show that each component significantly affects the performance of MOEA/D-DE. We also present the most suitable configuration of the DE mutation operator, which maximizes the effectiveness of MOEA/D-DE., This is an accepted version of a paper published in Soft Computing

Due to the lack of global search capacity, most evolutionary or swarm intelligence based algorithms show their inefficiency when optimizing multi-modal problems. In this paper, we propose a grouping particle swarm optimizer (GPSO) to solve this kind of problem. In the proposed algorithm, the swarm consists of several groups. For every several iterations, an elite group is constructed and used to replace the worst one. The thought of grouping is helpful for improving the diversity of the solutions, and then enhancing the global search ability of the algorithm. In addition, we apply a simple mutation operator to the best solution so as to help it escape from local optima. The GPSO is compared with several variants of particle swarm optimizer (PSO) and some state-of-the-art evolutionary algorithms on CEC15 benchmark functions and three practical engineering problems. As demonstrated by the experimental results, the proposed GPSO outperforms its competitors in most cases.

Artificial immune system is a class of computational intelligence methods drawing inspiration from biological immune system. As one type of popular artificial immune computing model, clonal selection algorithm (CSA) has been widely used for many optimization problems. When dealing with complex optimization problems, such as the characteristics of multimodal, high-dimension, rotational, the traditional CSA often suffers from diversity loss, poor search ability, premature convergence and stagnation. To address the problems, a modified combinatorial recombination is introduced to bring diversity to the population and avoid the premature convergence. Moreover, the success-history based adaptive mutation strategy is introduced to form a success-history based adaptive mutation based clonal selection algorithm to improve the search ability. The mutation operator is also modified and analyzed through experimental comparison. To further improve the precision and cope with the stagnation, the gene knockout strategy is proposed. The proposed algorithm is tested on CEC 2014 benchmarks and compared with state-of-the-art evolutionary algorithms. The experimental results show that MSHCSA is quite competitive.

Aiming at improving the performance of the endmember extraction problem in hyperspectral images, a new extraction method based on discrete hybrid artificial bee colony algorithm and genetic algorithm (DABC_GA) is proposed. By analyzing the characteristic of the problem, each dimension of candidate solution is a discrete and exclusive integer. Then we employ an optimization method with integral coding. By inheriting the strong exploration ability of the traditional artificial bee colony algorithm (ABC), we propose a discrete ABC which could quickly obtain more valuable endmembers combinations in the early stage. Then we select some outstanding results of DABC as the potential solutions of GA, which is adopted as another optimization tool in the later stage of iteration. The concept of complementary sets is proposed in the cross and mutation operators to guarantee the diversity and completeness of solutions. Meanwhile, the greedy strategy is adopted to ensure that the favorable potential solutions are not discarded. Compared with conventional extraction algorithms in simulated and real hyperspectral remote sensing data, the experimental results show the validity of our proposed algorithm.

In data mining, feature selection is an important part in data preprocessing, therefore selecting the optimal feature subset can effectively reduce the data dimension and computing cost of the learning algorithm. In this paper, Binary Particle Swarm Optimization is used to optimize the feature selection process. Firstly, a population initialization strategy based on chaos theory is proposed to reduce information redundancy and improve the quality of the initial population. Secondly, a chaos clonal operator, chaos mutation operator, and immune selection operator are proposed to improve the convergence speed and population diversity of the algorithm. Finally, three representative optimization algorithms were selected and compared in eight UCI datasets. The experimental results showed that the improved IBPSOCC algorithm is superior to other contrast algorithms in reducing the number of features and improving the classification accuracy.

Monarch butterfly optimization algorithm (MBO) has recently been proposed as a robust metaheuristic optimization algorithm for solving numerical global optimization problems. To enhance the performance of MBO algorithm, harmony search (HS) is introduced as a mutation operator during the adjusting operator of MBO. A novel hybrid metaheuristic optimization method, the so-called HMBO, is introduced to find the best solution for the global optimization problems. HMBO combines HS exploration with MBO exploitation, and therefore, it produces potential candidate solutions. The implementation process for enhancing MBO method is also presented. To evaluate the effectiveness of this improvement, fourteen standard benchmark functions are used. The mean and the best performance of these benchmark functions in 20, 50, and 100 dimensions demonstrated that HMBO often performs better than the original MBO and other population-based optimization algorithms such as ACO, BBO, DE, ES, GAPBIL, PSO and SGA. Moreover, the t-test result proved that the performance differences between the enhanced HMBO and the original MBO as well as the other optimization methods are statistically significant.

Differential evolution (DE) has been widely applied to complex global optimization problems. Different search strategies have been designed to find the optimum conditions in a fitness landscape. However, none of these strategies works well over all possible fitness landscapes. Since the fitness landscape associated with a complex global optimization problem usually consists of various local landscapes, each search strategy is efficient in a particular type of fitness landscape. A reasonable approach is to combine several search strategies and integrate their advantages to solve global optimization problems. This paper presents a new self-feedback strategy differential evolution (SFSDE) algorithm based on fitness landscape analysis of single-objective optimization problem. In the SFSDE algorithm, in the analysis of the fitness landscape features of fitness-distance correlation, a self-feedback operation is used to iteratively select and evaluate the mutation operators of the new SFSDE algorithm. Moreover, mixed strategies and self-feedback transfer are combined to design a more efficient DE algorithm and enhance the search range, convergence rate and solution accuracy. Finally, the proposed SFSDE algorithm is implemented to optimize soil water textures, and the experimental results show that the proposed SFSDE algorithm reduces the difficulty in estimating parameters, simplifies the solution process and provides a novel approach to calculate the parameters of the Van Genuchten equation. In addition, the proposed algorithm exhibits high accuracy and rapid convergence and can be widely used in the parameter estimation of such nonlinear optimization models.

Monarch butterfly optimization (MBO) is a recently developed evolutionary algorithm which has been used in many optimization problems. Migration and adjusting operators of MBO have a significant effect on the performance of it. These two operators change candidate variables of each individual independently. So, they are rotationally variant and this is one of the limitations of MBO which can degrade its performance on non-separable problems. There are interactions among variables in non-separable problems and MBO’s operators have not any consideration to it. In this paper, we propose a linearized version of MBO to overcome the above-mentioned limitation of MBO. In other words, migration and adjusting operators of MBO are linearized. Moreover, DE’s mutation operator is integrated in our proposed algorithm to improve exploration of MBO. Our proposed algorithm which is a linearized and hybrid version of MBO (LMBO-DE) is validated by 18 benchmark functions in different dimensionality and is compared with original MBO, one of recently MBO’s improvements, and three other evolutionary algorithms (jDE, JADE, and CLPSO). Experimental results show that our proposed algorithm significantly outperforms the original MBO and its improvement in terms of solution quality and convergence rate. In comparison with the other three algorithms, LMBO-DE can find more accurate solutions.

Open-shop scheduling problem (OSSP) is a well-known topic with vast industrial applications which belongs to one of the most important issues in the field of engineering. OSSP is a kind of NP problems and has a wider solution space than other basic scheduling problems, i.e., Job-shop and flow-shop scheduling. Due to this fact, this problem has attracted many researchers over the past decades and numerous algorithms have been proposed for that. This paper investigates the effects of crossover and mutation operator selection in Genetic Algorithms (GA) for solving OSSP. The proposed algorithm, which is called EGA_OS, is evaluated and compared with other existing algorithms. Computational results show that selection of genetic operation type has a great influence on the quality of solutions, and the proposed algorithm could generate better solutions compared to other developed algorithms in terms of computational times and objective values.

In order to improve the optimization efficiency of the biogeography-based optimization (BBO) algorithm, this study proposes a novel BBO algorithm, namely an efficient and merged biogeography-based optimization (EMBBO) algorithm. Firstly, BBO’s mutation operator is got rid of. Then, a differential mutation operator and a sharing operator are merged into BBO’s migration operator to obtain an improved migration operator. In the improved migration operator, the emigration habitats are selected by a new example learning approach. The above improvements can enhance the optimization performance and reduce the computation complexity. Thirdly, a new single-dimensional and all-dimensional alternating strategy is combined with the improved migration operator to balance exploration and exploitation and reduce more computation complexity. Fourthly, the opposition-based learning approach is merged to prevent the algorithm from falling into the local optima. Finally, the greedy selection method is used instead of the elitist strategy to avoid setting the elitist parameter and to get rid of one sorting step. We make a large number of experiments on a set of classic benchmark functions and CEC2017 test set and apply EMBBO to clustering optimization. Experiment results verify that EMBBO can obtain the highest optimization efficiency compared with quite a few state-of-the-art algorithms.

Clustering is a technique which is used to group the data into different subgroups or subsets to retrieve meaningful information from the available huge dataset. The trending swarm based intelligent system replaces the conventional clustering algorithm with the objective of increased performance. Ant lion optimization (ALO) technique is the swarm based intelligence that exhibits the hunting mechanism of the ant lions in the natural environment. Ant colony optimization (ACO) algorithm is a swarm based intelligence technique which inherits the behaviour of natural ant. In this paper new hybrid ACO–ALO algorithm was proposed to solve the data clustering problem. Additionally Cauchy’s mutation operator is added with this proposed algorithm to avoid the local minima trapping problem. The main objective is to reduce the intra cluster distance in clustering problem. From the experimental analysis, it evidences the proposed ACO–ALO algorithm outperforms the traditional algorithms of data clustering.

Dynamic optimization problems challenge the evolutionary algorithms, owing to the diversity loss or the low search efficiency of the algorithms, especially when the problems change frequently. This paper presents a novel differential evolution algorithm to address the dynamic optimization problems. Unlike the most used “DE/rand/1” mutation operator, in this paper, the “DE/best/1” mutation is employed to generate a mutant individual. In order to enhance the search efficiency of differential evolution, the classical differential evolution algorithm is modified by a novel replacement operator, in which the worst individual in the whole population is replaced by the newly generated trial vector as a “steady-state” manner. During optimizing, some newly generated solutions are stored into a memory set, in which these stored solutions are located around the current best solution. When the environmental change is detected, the stored solutions are expected to guide the reinitialized solutions to track the new location of global optimum as soon as possible. The performance of the proposed algorithm is compared with six state-of-the-art dynamic evolutionary algorithms over some benchmark problems. The experimental results show that the proposed algorithm clearly outperforms the competitors.

Constrained optimization problems (COPs) are most commonly encountered problems in science and engineering design field. To solve such kind of problem effectively, in this paper, we put forward a new approach named CAMDE which integrates adaptive differential evolution (DE) with new multi-population-based mutation operators. In CAMDE, some inferior solutions with low objective values are maintained in an external population. During mutation process, this external population is combined with main population to generate promising progress directions toward optimal region. Furthermore, DE’s control parameters F and CR are adaptively adjusted according to the statistical information learnt from the previous searches in generating improved solutions. The advantageous performance of CAMDE is validated by comparisons with some representatives of state of the art in constrained optimization over 24 test instances. Moreover, four widely used constrained mechanical engineering problems are selected to validate the search ability of CAMDE for real-world problems. The performance results show that CAMDE is an effective approach to solving COPs, which is basically enabled by the integration of multi-population-based mutation operators and adaptive control strategy for DE’s control parameters.

Differential evolution (DE) is a very simple, but effective technique for solving various optimization problems. However, the performance of DE remarkably relies on its control parameter settings, and enormous adaptive or self-adaptive mechanisms for DE have been proposed to improve the robustness of DE. In this paper, we put forward an enhanced parameter adaptation technique for DE, which exploits the previous successful experience to compress the parameter space by using the dichotomy (called DPADE, i.e., dichotomy-based parameter adaptation DE). In this way, the control parameters are able to approach the suitable values for the given problems. The proposed technique is integrated with three classic mutation operators and one state-of-the-art mutation operator. The experimental results on 59 problems derived from the CEC2014 benchmark set and CEC2017 benchmark set show that our proposed method is able to improve the performance of DE and it is more effective than other state-of-the-art parameter control techniques.

This paper considers the multi-skill resource-constrained project scheduling problem in which the processing time of each task is modeled as a step-function of its starting time and a specific deteriorating date. For solving the complex problem, four neighborhood structures and two mutation operators based on problem characteristics are proposed to form an improved tabu search algorithm (ITS). Computational experiments are performed on a set of test instances from the recent literature. The proposed algorithm improved the currently best-known results for most instances in a reasonable time. Furthermore, the dataset is revised to integrate the step-deteriorating effect. Numerical results demonstrate the proposed algorithm is a powerful solution methodology for solving the studied problem in terms of solutions quality and show that the mutation phase in ITS has a direct benefit over the solving ability of the ITS.

Evolutionary algorithms have long been quite successfully applied to solve multi-objective optimization problems. However, theoretical analysis of multi-objective evolutionary algorithms (MOEAs) is mainly restricted to the simple evolutionary multi-objective optimizer (SEMO). The Pareto archived evolution strategy (PAES) is a simple but important multi-objective evolutionary algorithm which is come from the study of telecommunication problems, and it has been successfully applied to many optimization problems, such as image processing and signal processing. In this paper, we make a first step toward studying the rigorous running time analysis for PAES. We show that the PAES outperforms the SEMO on function PATH when the PAES uses a simple mutation operator. However, it can not find the whole Pareto front with overwhelming probability on the well-studied function LOTZ. Additional experiments show that the experimental results are in agreement with the theoretical results.

Many-objective optimization problems (MaOPs) are vital and challenging in real-world applications. Existing evolutionary algorithms mostly produce an approximate Pareto-optimal set using new dominance relations, dimensionality reduction, objective decomposition, and set-based evolution. In this paper, we propose a mutation operator guided by preferred regions to improve an existing set-based evolutionary many-objective optimization algorithm that integrates preferences. In the proposed mutation operator, optimal solutions in a preferred region are first chosen to form a reference set; then for each solution within the individual to be mutated, an optimal solution from the reference set is specified as its reference point; finally, the solution is mutated towards the preferred region via an adaptive Gaussian disturbance to accelerate the evolution, and thus an approximate Pareto-optimal set with high performances is obtained. We apply the proposed method to 21 instances of seven benchmark MaOPs, and the experimental results empirically demonstrate its superiority.

The problem in software cost estimation revolves around accuracy. To improve the accuracy, heuristic/meta-heuristic algorithms have been known to yield better results when it is applied in the domain of software cost estimation. For the sake of accuracy in results, we are still modifying these algorithms. Here we have proposed a new meta-heuristic algorithm based on Differential Evolution (DE) by Homeostasis mutation operator. Software development requires high prediction and low Root Mean Squared Error (RMSE) and mean magnitude relative error(MMRE). The problem in software cost estimation relates to accurate prediction and minimization of RMSE and MMRE, which are used to solve multiobjective optimization. Many versions of DE were proposed, however multi-objective versions where the concept of Pareto optimality is used, are most popular. Pareto-Based Differential Evolution (PBDE) is one of them. Although the performance of this algorithm is very good, its convergence rate can be further improved by minimizing the time complexity of nondominated sorting, and by improving the diversity of solutions. This has been implemented by using efficient nondominated algorithm whose time complexity is better than the previous one and a new mutation scheme is implemented in DE which can provide more diversity among solutions. The proposed variant multiplies the Homeostasis value with one more vector, named the Homeostasis mutation vector, in the existing mutation vector to provide more bandwidth for selecting effective mutant solutions. The proposed approach provides more promising solutions to guide the evolution and helps DE escape the situation of stagnation. The performance of the proposed algorithm is evaluated on twelve benchmark test functions (bi-objective and tri-objective) on the Pareto-optimal front. The performance of the proposed algorithm is compared with other state-of-the-art algorithms on five multi-objective evolutionary algorithms (MOEAs). The result verifies that our proposed Homeostasis mutation strategy performs better than other state-of-the-art algorithms. Finally, application of MODE-HBM is applied to solve in terms of Pareto front, representing the trade-off between development RMSE, MMRE, and prediction for COCOMO model.

Multi-model techniques have shown an outstanding effectiveness in the cooperative task assignment and path planning of the unmanned combat aerial vehicle(UCAV) formation. With cooperative decision making and control, the cooperative combat of the UCAV formation are described and the mathematical model of the UCAV formation is built. Then, the task assignment model of the UCAV formation is developed according to flight characteristics of the UCAV formation and constraints in battlefield. The cooperative task assignment problem is solved using the improved particle swarm optimization(IPSO), ant colony algorithm(ACA) and genetic algorithm(GA) respectively. The comparative analysis is conducted in the aspects of the precision and the search speed. The path planning model of the UCAV formation is constructed considering the oil cost, threat cost, crash cost and time cost. The cooperative path planning problem is solved based on the evolution algorithm(EA), in which unique coding scheme of chromosomes is designed, and the crossover operator and mutation operator are redefined. Simulation results demonstrate that the UCAV formation can choose the best algorithm according to the real battlefield environment, which can solve the cooperative task assignment and path planning problems quickly and effectively to meet the demand of the cooperative combat.

This paper investigates the Google machine reassignment problem (GMRP). GMRP is a real world optimisation problem which is to maximise the usage of cloud machines. Since GMRP is computationally challenging problem and exact methods are only advisable for small instances, meta-heuristic algorithms have been used to address medium and large instances. This paper proposes a cooperative evolutionary heterogeneous simulated annealing (CHSA) algorithm for GMRP. The proposed algorithm consists of several components devised to generate high quality solutions. Firstly, a population of solutions is used to effectively explore the solution space. Secondly, CHSA uses a pool of heterogeneous simulated annealing algorithms in which each one starts from a different initial solution and has its own configuration. Thirdly, a cooperative mechanism is designed to allow parallel searches to share their best solutions. Finally, a restart strategy based on mutation operators is proposed to improve the search performance and diversification. The evaluation on 30 diverse real-world instances shows that the proposed CHSA performs better compared to cooperative homogeneous SA and heterogeneous SA with no cooperation. In addition, CHSA outperformed the current state-of-the-art algorithms, providing new best solutions for eleven instances. The analysis on algorithm behaviour clearly shows the benefits of the cooperative heterogeneous approach on search performance.

This article introduces a new variation of a known metaheuristic method for solving global optimization problems. The proposed algorithm is based on the Bat algorithm (BA), which is inspired by the micro-bat echolocation phenomenon, and addresses the problems of local-optima trapping using a special mutation operator that enhances the diversity of the standard BA, hence the name enhanced Bat algorithm (EBat). The design of EBat is introduced and its performance is evaluated against 24 of the standard benchmark functions, and compared to that of the standard BA, as well as to several well-established metaheuristic techniques. We also analyze the impact of different parameters on the EBat algorithm and determine the best combination of parameter values in the context of numerical optimization. The obtained results show that the new EBat method is indeed a promising addition to the arsenal of metaheuristic algorithms and can outperform several existing ones, including the original BA algorithm.

The aim of the study was to propose a new metaheuristic algorithm that combines parts of the well-known artificial bee colony (ABC) optimization with elements from the recent monarch butterfly optimization (MBO) algorithm. The idea is to improve the balance between the characteristics of exploration and exploitation in those algorithms in order to address the issues of trapping in local optimal solution, slow convergence, and low accuracy in numerical optimization problems. This article introduces a new hybrid approach by modifying the butterfly adjusting operator in MBO algorithm and uses that as a mutation operator to replace employee phase of the ABC algorithm. The new algorithm is called Hybrid ABC/MBO (HAM). The HAM algorithm is basically employed to boost the exploration versus exploitation balance of the original algorithms, by increasing the diversity of the ABC search process using a modified operator from MBO algorithm. The resultant design contains three components: The first and third component implements global search, while the second one performs local search. The proposed algorithm was evaluated using 13 benchmark functions and compared with the performance of nine metaheuristic methods from swarm intelligence and evolutionary computing: ABC, MBO, ACO, PSO, GA, DE, ES, PBIL, and STUDGA. The experimental results show that the HAM algorithm is clearly superior to the standard ABC and MBO algorithms, as well as to other well-known algorithms, in terms of achieving the best optimal value and convergence speed. The proposed HAM algorithm is a promising metaheuristic technique to be added to the repertory of optimization techniques at the disposal of researchers. The next step is to look into application fields for HAM.

Parameters identification of permanent magnetic synchronous motor (PMSM), which significantly influences the control performance of the drive system, is an important and challenging task of power electronic system. The problem requires both high solution quality and fast convergence speed due to the constraints of hardware. This paper presents a self-adaptive differential evolution algorithm with hybrid mutation operator (SHDE) for parameters identification problem. In this method, a novel mutation operator, called “current-to-archive-best,” is developed by mixing the best solutions randomly selected from archive set and current population. Thus, the algorithm could use the best searching memories so far to generate promising solutions, yielding a faster evolving procedure. Besides, the corresponding control parameters of SHDE are also self-adapted without tedious trial-and-error progress to get appropriate values. Moreover, the parameters estimation program is inserted into the PMSM simulation that is solved by using Newton–Raphson method without any pre-assumption and simplification. This framework, which may be used under any working conditions with large disturbance, is different from other publications, resulting in wider applications. The proposed method applied to parameters identification of PMSM is evaluated on a PMSM drive system with two different operations. The comprehensive results and statistical analyses, compared with other state-of-the-art algorithms, show that SHDE could find high-quality solutions with higher convergence speed and probability.

An improved hybrid immune algorithm (HIA) with parallelism and adaptability is proposed to solve the flexible job shop scheduling problem. In order to represent the actual characteristics of the problem’s solution, in the algorithm the author uses a hybrid encoding method of piece—machine. Firstly, adaptive crossover operator and mutation operator are designed based on the encoding antibody method and the affinity calculation based on group matching is adopted. Secondly, the algorithm uses adaptive crossover probability and mutation probability in the operation of immune for the antibody population. The new antibody after crossing can automatically meet the constraints of the problem. Next, a hybrid algorithm based on simulated annealing algorithm is introduced to avoid the local optimization in this paper. Finally, it is demonstrated the effectiveness of the proposed algorithm through the simulation and comparison with some existing algorithms.

A method of generating assembly sequences is developed in this paper, which can be used in the satellites assembly. The method must take into account the assumptions specific for assembly processes of large number of connections, multi-stage and parallel assembly. Setting priority relations between connections is involved. The assembly sequence is presented as a directed acyclic graph, whose vertices are mutually uniquely assigned to the connections. The minimization of the number of violated priority precedence of performing connections has been proposed as a criterion of optimization. In this article, a new way of coding the acyclic serial-parallel sequence was designed. The proposed method allows analyzing the sequence using the graph theory. Original, two-part crossover and mutation operators for assembling sequence were proposed. Examples of calculations are performed on an actual structure of a local structure of a satellite.

Differential Evolution (DE) is one of the most successful and powerful evolutionary algorithms for global optimization problem. The most important operator in this algorithm is mutation operator which parents are selected randomly to participate in it. Recently, numerous papers are tried to make this operator more intelligent by selection of parents for mutation intelligently. The intelligent selection for mutation vectors is performed by applying design space (also known as decision space) criterion or fitness space criterion, however, in both cases, half of valuable information of the problem space is disregarded. In this article, a Universal Differential Evolution (UDE) is proposed which takes advantage of both design and fitness spaces criteria for intelligent selection of mutation vectors. The experimental analysis on UDE are performed on CEC2005 benchmarks and the results stated that UDE significantly improved the performance of differential evolution in comparison with other methods that only use one criterion for intelligent selection.

A novel multi-population coevolution strategy for single objective immune optimization algorithm (MCIA) is proposed to solve numerical and engineering optimization problem in real world from the inspiration that how neuro-endocrine system affects T cells and B cells in immune system eliminate the danger. The main idea of MCIA is to promote three populations to coevolution through self-adjusted clone operator, the applied dislocation arithmetic crossover, cloud self-adapting mutation operator and local search operator to produce lymphocyte with high affinity, where several operators have the capability of broadening the elites search space, boosting the global and local search around elites in search space. The MCIA is population B, population T, and assistant population A carrying on parallel evolution in nature, which simulates the immune system more comprehensively and unique in the aspects: clone operator and selected elite elements in the memory population enable the search space be broadened and compressed, and with the help of the cloud model characterized with randomness and stable topotaxis and local search technique, the global and local search is integrated to find the global optima with high population diversity. The performance comparisons of MCIA with three known immune algorithms and three optimization algorithms in optimizing 12 benchmark functions indicate that MCIA is an effective algorithm for solving global optimization problems with high precision, good robustness and low time complexity.

Optimization is a classical issue and in many areas that are bound up with people’s daily life. In current decades, with the development of human civilization and industry society, many complicated optimization problems are raised. In the meantime, corresponding novel approaches are constantly proposed for solving these problems. One of them is meta-heuristics, which is inspired from natural phenomena and contains many kinds of algorithms. The classical meta-heuristic algorithms have exhibited their superiority in dealing optimization problems, especially for specific problems such as combinatorial optimization. As a novel meta-heuristic algorithm, biogeography-based optimization (BBO), inspired from the science of biogeography, has its own characteristics and exhibits a huge potential in computation and optimization. According to current investigations and analysis on this algorithm, it has not only achieved a great success in numerical optimization problems, but also been implemented in various kinds of applications, and drawn worldwide attentions. In this paper, we present a survey for this algorithm. First, we introduce the basic operators of BBO, including migration and mutation. For migration operator, it mimics species migration among islands, which provides a recombination way for candidate solutions to interact with each other so that the whole population can be improved. Besides linear migration model, several other popular migration models are also introduced and the corresponding performances are analyzed. For mutation operator, the design of BBO is different from other meta-heuristics. In standard BBO, different candidate solutions have different migration rates and the rate assignment is influential to BBO’s performance. Second, we summarized some popular variants of BBO and related hybrid algorithms that significantly enhance BBO’s performance. This part introduces the development of this algorithm and helps readers understand the way to choose a suitable version of BBO for a given problem. The way to improve algorithms’ performances helps readers design new variants of BBO for specific problems. Third, we present the evaluation of BBO’s performance for both numerical and practical problems. The results demonstrate BBO is competent to solve optimization problems. Despite so many achievements of BBO, some open issues that should be considered and solved in future work in order to make this algorithm more competitive in meta-heuristics.

© 2015, Springer Science+Business Media New York. This paper proposes a modified harmony search (MHS) algorithm with an intersect mutation operator and cellular local search for continuous function optimization problems. Instead of focusing on the intelligent tuning of the parameters during the searching process, the MHS algorithm divides all harmonies in harmony memory into a better part and a worse part according to their fitness. The novel intersect mutation operation has been developed to generate new -harmony vectors. Furthermore, a cellular local search also has been developed in MHS, that helps to improve the optimization performance by exploring a huge search space in the early run phase to avoid premature, and exploiting a small region in the later run phase to refine the final solutions. To obtain better parameter settings for the proposed MHS algorithm, the impacts of the parameters are analyzed by an orthogonal test and a range analysis method. Finally, two sets of famous benchmark functions have been used to test and evaluate the performance of the proposed MHS algorithm. Functions in these benchmark sets have different characteristics so they can give a comprehensive evaluation on the performance of MHS. The experimental results show that the proposed algorithm not only performs better than those state-of-the-art HS variants but is also competitive with other famous meta-heuristic algorithms in terms of the solution accuracy and efficiency.

In order to solve the non-linear and high-dimensional optimization problems more effectively, an improved self-adaptive membrane computing (ISMC) optimization algorithm was proposed. The proposed ISMC algorithm applied improved self-adaptive crossover and mutation formulae that can provide appropriate crossover operator and mutation operator based on different functions of the objects and the number of iterations. The performance of ISMC was tested by the benchmark functions. The simulation results for residue hydrogenating kinetics model parameter estimation show that the proposed method is superior to the traditional intelligent algorithms in terms of convergence accuracy and stability in solving the complex parameter optimization problems.

A novel multi-function rescue attachment with tonging, shearing and grasping capabilities is proposed to improve the rescue operation efficiency and save time when switching between different attachments during rescue operations. The tonging and shearing form, as well as the grasping form, of the rescue attachment, is analyzed. Furthermore, the tonging diameter, shearing diameter and grasping force are simultaneously chosen as objective functions, and respective mathematical models are established for estimating the attachment’s performance. The nondominated sorting genetic algorithm (NSGA-II) is used for multi-objective optimization of the attachment. To improve the population diversity and increase the search capability and uniformity of the distribution of Pareto fronts of NSGA-II, the elitist strategy, crossover operator and mutation operator are improved. The Pareto front is visualized in a specific polygon, and the best solution is then selected. More importantly, the simulation results indicate that the astringency, population diversity and search ability of the proposed algorithm can be improved. The uniformity of the Pareto front distribution can also be improved, which may lead to an increased number of available design schemes. The values of the three objectives of the best solution obtained via the improved algorithm are superior to those for other algorithms.

Reasonable scheduling of flexible job shop is key to improve production efficiency and economic benefits; in order to solve the problem in flexible job shop scheduling problem, a novel flexible job shop scheduling method based on improved artificial immune algorithm is proposed. Firstly, a mathematical model of the flexible job shop scheduling is established, and the total shortest processing time is taken as the objective function. Secondly, artificial immune algorithm is used to solve the problem, and particle swarm optimization algorithm is taken as the operator to embed into manual immune algorithm for maintaining the diversity of population and prevent obtaining local optimal solution. Finally, the performance of the algorithm is tested by simulation experiments on standard set. The results show that the proposed algorithm can obtain better flexible job shop scheduling scheme and especially has more significant advantages in solving large-scale problems in comparison with other algorithms.