Differential evolution framework for big data optimization

During the last two decades, dealing with big data problems has become a major issue for many industries. Although, in recent years, differential evolution has been successful in solving many complex optimization problems, there has been research gaps on using it to solve big data problems. As a real-time big data problem may not be known in advance, determining the appropriate differential evolution operators and parameters to use is a combinatorial optimization problem. Therefore, in this paper, a general differential evolution framework is proposed, in which the most suitable differential evolution algorithm for a problem on hand is adaptively configured. A local search is also employed to increase the exploitation capability of the proposed algorithm. The algorithm is tested on the 2015 big data optimization competition problems (six single objective problems and six multi-objective problems). The results show the superiority of the proposed algorithm to several state-of-the-art algorithms.     

Novel biogeography-based optimization algorithm with hybrid migration and global-best Gaussian mutation

The Biogeography-Based Optimization algorithm and its variants have been used widely for optimization problems. To get better performance, a novel Biogeography-Based Optimization algorithm with Hybrid migration and global-best Gaussian mutation is proposed in this paper. Firstly, a linearly dynamic random heuristic crossover strategy and an exponentially dynamic random differential mutation one are presented to form a hybrid migration operator, and the former is used to get stronger local search ability and the latter strengthen the global search ability. Secondly, a new global-best Gaussian mutation operator is put forward to balance exploration and exploitation better. Finally, a random opposition learning strategy is merged to avoid getting stuck in local optima. The experiments on the classical benchmark functions and the complexity functions from CEC-2013 and CEC-2017 test sets, and the Wilcoxon, Bonferroni-Holm and Friedman statistical tests are used to evaluate our algorithm. The results show that our algorithm obtains better performance and faster running speed compared with quite a few state-of-the-art competitive algorithms. In addition, experimental results on Minimum Spanning Tree and K-means clustering optimization show that our algorithm can cope with these two problems better than the comparison algorithms.     

A real coded genetic algorithm for solving integer and mixed integer optimization problems

In this paper, a real coded genetic algorithm named MI-LXPM is proposed for solving integer and mixed integer constrained optimization problems. The proposed algorithm is a suitably modified and extended version of the real coded genetic algorithm, LXPM, of Deep and Thakur [K. Deep, M. Thakur, A new crossover operator for real coded genetic algorithms, Applied Mathematics and Computation 188 (2007) 895-912; K. Deep, M. Thakur, A new mutation operator for real coded genetic algorithms, Applied Mathematics and Computation 193 (2007) 211-230]. The algorithm incorporates a special truncation procedure to handle integer restrictions on decision variables along with a parameter free penalty approach for handling constraints. Performance of the algorithm is tested on a set of twenty test problems selected from different sources in literature, and compared with the performance of an earlier application of genetic algorithm and also with random search based algorithm, RST2ANU, incorporating annealing concept. The proposed MI-LXPM outperforms both the algorithms in most of the cases which are considered.     

Particle swarm optimization: Hybridization perspectives and experimental illustrations

Metaheuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods. In the present study an attempt is made to review the hybrid optimization techniques in which one main algorithm is a well known metaheuristic; particle swarm optimization or PSO. Hybridization is a method of combining two (or more) techniques in a judicious manner such that the resulting algorithm contains the positive features of both (or all) the algorithms. Depending on the algorithm/s used we made three classifications as (i) Hybridization of PSO and genetic algorithms (ii) Hybridization of PSO with differential evolution and (iii) Hybridization of PSO with other techniques. Where, other techniques include various local and global search methods. Besides giving the review we also show a comparison of three hybrid PSO algorithms; hybrid differential evolution particle swarm optimization (DE-PSO), adaptive mutation particle swarm optimization (AMPSO) and hybrid genetic algorithm particle swarm optimization (GA-PSO) on a test suite of nine conventional benchmark problems.     

Balancing exploration and exploitation with adaptive variation for evolutionary multi-objective optimization

Although recent studies have shown that evolutionary algorithms are effective tools for solving multi-objective optimization problems, their performances are often bottlenecked by the suitability of the evolutionary operators with respect to the optimization problem at hand and their corresponding parametric settings. To adapt the search dynamic of evolutionary operation in multi-objective optimization, this paper proposes an adaptive variation operator that exploits the chromosomal structure of binary representation and synergizes the function of crossover and mutation. The overall search ability is deterministically tuned online to maintain a balance between extensive exploration and local fine-tuning at different stages of the evolutionary search. Also, the coordination between the two variation operators is achieved by means of an adaptive control that ensures an efficient exchange of information between the different chromosomal sub-structures throughout the evolutionary search. Extensive comparative studies with several representative variation operators are performed on different benchmark problems and significant algorithmic performance improvements in terms of proximity, uniformity and diversity are obtained with the incorporation of the proposed adaptive variation operator into the evolutionary multi-objective optimization process.     

Global and Local Search Algorithms for Concave Cost Transshipment Problems

Traditionally, the minimum cost transshipment problems have been simplified as linear cost problems, which are not practical in real applications. Recently, some advanced local search algorithms have been developed that can directly solve concave cost bipartite network problems. However, they are not applicable to general transshipment problems. Moreover, the effectiveness of these modified local search algorithms for solving general concave cost transshipment problems is doubtful. In this research, we propose a global search algorithm for solving concave cost transshipment problems. Effecient methods for encoding, generating initial populations, selection, crossover and mutation are proposed, according to the problem characteristics. To evaluate the effectiveness of the proposed global search algorithm, four advanced local search algorithms based on the threshold accepting algorithm, the great deluge algorithm, and the tabu search algorithm, are also developed and are used for comparison purpose. To assist with the comparison of the proposed algorithms, a randomized network generator is designed to produce test problems. All the tests are performed on a personal computer. The results indicate that the proposed global search algorithm is more effective than the four advanced local algorithms, for solving concave cost transshipment problems.     

蚁群遗传混合算法

将蚁群遗传混合算法分别求解离散空间的和连续空间优化问题.求解旅行商问题的混合算法是以遗传算法为整个算法的框架,利用了蚁群算法中的信息素特性的进行交叉操作;根据旅行商问题的特点,给出了4种变异策略;针对遗传算法存在的过早收敛问题,加入2-0pt方法对问题求解进行了局部优化.与模拟退火算法、标准遗传算法和标准蚁群算法进行比较,4种混合算法效果都比较好,策略D的混合算法效果最好.求解连续空间优化问题是以蚁群算法为整个算法的框架,加入遗传算法的交叉操作和变异操作,用测试函数验证了混合蚁群算法的正确性.     

Handling equality constraints in evolutionary optimization

Over the last few decades several methods have been proposed for handling functional constraints while solving optimization problems using evolutionary algorithms (EAs). However, the presence of equality constraints makes the feasible space very small compared to the entire search space. As a consequence, the handling of equality constraints has long been a difficult issue for evolutionary optimization methods. This paper presents a Hybrid Evolutionary Algorithm (HEA) for solving optimization problems with both equality and inequality constraints. In HEA, we propose a new local search technique with special emphasis on equality constraints. The basic concept of the new technique is to reach a point on the equality constraint from the current position of an individual solution, and then explore on the constraint landscape. We believe this new concept will influence the future research direction for constrained optimization using population based algorithms. The proposed algorithm is tested on a set of standard benchmark problems. The results show that the proposed technique works very well on those benchmark problems.     

基于种群分类排序的约束优化遗传算法

针对约束优化问题,提出了一类将种群中的个体分类排序的思想.算法的特点在于:先将种群中的解分为可行解和不可行解两类,然后分别按照不同的标准排序.由于很多约束优化问题的最优解位于可行域的边界上或附近,所以排序时并不认为可行解一定优于不可行解.基于此分类排队思想,特别设计了只允许同等级个体进行交叉的新的交叉算子,称之为同等级交叉算子,以及基于一维搜索的变异算子.算法同时采用了保证固定比例不可行解的自适应策略.4个标准测试函数的数值仿真结果验证了算法的有效性.     

Multi-strategy ensemble evolutionary algorithm for dynamic multi-objective optimization

Dynamic optimization and multi-objective optimization have separately gained increasing attention from the research community during the last decade. However, few studies have been reported on dynamic multi-objective optimization (dMO) and scarce effective dMO methods have been proposed. In this paper, we fulfill these gabs by developing new dMO test problems and new effective dMO algorithm. In the newly designed dMO problems, Pareto-optimal decision values (i.e., Pareto-optimal solutions: POS) or both POS and Pareto-optimal objective values (i.e., Pareto-optimal front: POF) change with time. A new multi-strategy ensemble multi-objective evolutionary algorithm (MS-MOEA) is proposed to tackle the challenges of dMO. In MS-MOEA, the convergence speed is accelerated by the new offspring creating mechanism powered by adaptive genetic and differential operators (GDM); a Gaussian mutation operator is employed to cope with premature convergence; a memory like strategy is proposed to achieve better starting population when a change takes place. In order to show the advantages of the proposed algorithm, we experimentally compare MS-MOEA with several algorithms equipped with traditional restart strategy. It is suggested that such a multi-strategy ensemble approach is promising for dealing with dMO problems.     

Advanced particle swarm assisted genetic algorithm for constrained optimization problems

A novel hybrid evolutionary algorithm is developed based on the particle swarm optimization (PSO) and genetic algorithms (GAs). The PSO phase involves the enhancement of worst solutions by using the global-local best inertia weight and acceleration coefficients to increase the efficiency. In the genetic algorithm phase, a new rank-based multi-parent crossover is used by modifying the crossover and mutation operators which favors both the local and global exploration simultaneously. In addition, the Euclidean distance-based niching is implemented in the replacement phase of the GA to maintain the population diversity. To avoid the local optimum solutions, the stagnation check is performed and the solution is randomized when needed. The constraints are handled using an effective feasible population based approach. The parameters are self-adaptive requiring no tuning based on the type of problems. Numerical simulations are performed first to evaluate the current algorithm for a set of 24 benchmark constrained nonlinear optimization problems. The results demonstrate reasonable correlation and high quality optimum solutions with significantly less function evaluations against other state-of-the-art heuristic-based optimization algorithms. The algorithm is also applied to various nonlinear engineering optimization problems and shown to be excellent in searching for the global optimal solutions.     

An innovative flower pollination algorithm for continuous optimization problem

The flower pollination algorithm (FPA) is a relatively new swarm optimization algorithm that inspired by the pollination phenomenon of natural phanerogam. Since its proposed, it has received widespread attention and been applied in various engineering fields. However, the FPA still has certain drawbacks, such as inadequate optimization precision and poor convergence. In this paper, an innovative flower pollination algorithm based on cloud mutation is proposed (CMFPA), which adds information of all dimensions in the global optimization stage and uses the designed cloud mutation method to redistribute the population center. To verify the performance of the CMFPA in solving continuous optimization problems, we test twenty-four well-known functions, composition functions of CEC2013 and all benchmark functions of CEC2017. The results demonstrate that the CMFPA has better performance compared with other state-of-the-art algorithms. In addition, the CMFPA is implemented for five constrained optimization problems in practical engineering, and the performance is compared with state-of-the-art algorithms to further prove the effectiveness and efficiency of the CMFPA.     

Grey prediction evolution algorithm for global optimization

This article uses the grey prediction theory to structure a new metaheuristic: grey prediction evolution algorithm based on the even grey model. The proposed algorithm considers the population series of evolutionary algorithms as a time series, and uses the even grey model as a reproduction operator to forecast the next population (without employing any mutation and crossover operators). It is theoretically proven that the reproduction operator based on the even grey model is adaptive. Additionally, the algorithmic search mechanism and its differences with other evolutionary algorithms are analyzed. The performance of the proposed algorithm is validated on CEC2005 benchmark functions and a test suite composed of six engineering constrained design problems. The comparison experiments show the effectiveness and superiority of the proposed algorithm.The proposed algorithm can be regarded as the first case of structuring metaheuristics by using the prediction theory. The novel algorithm is anticipated to influence two future works. The first is to propose more metaheuristics inspired by prediction theories (including some statistical algorithms). Another is that the theoretical results of these prediction systems can be used for this novel type of metaheuristics.     

A novel differential evolution algorithm for binary optimization

Differential evolution (DE) is one of the most powerful stochastic search methods which was introduced originally for continuous optimization. In this sense, it is of low efficiency in dealing with discrete problems. In this paper we try to cover this deficiency through introducing a new version of DE algorithm, particularly designed for binary optimization. It is well-known that in its original form, DE maintains a differential mutation, a crossover and a selection operator for optimizing non-linear continuous functions. Therefore, developing the new binary version of DE algorithm, calls for introducing operators having the major characteristics of the original ones and being respondent to the structure of binary optimization problems. Using a measure of dissimilarity between binary vectors, we propose a differential mutation operator that works in continuous space while its consequence is used in the construction of the complete solution in binary space. This approach essentially enables us to utilize the structural knowledge of the problem through heuristic procedures, during the construction of the new solution. To verify effectiveness of our approach, we choose the uncapacitated facility location problem (UFLP)—one of the most frequently encountered binary optimization problems—and solve benchmark suites collected from OR-Library. Extensive computational experiments are carried out to find out the behavior of our algorithm under various setting of the control parameters and also to measure how well it competes with other state of the art binary optimization algorithms. Beside UFLP, we also investigate the suitably of our approach for optimizing numerical functions. We select a number of well-known functions on which we compare the performance of our approach with different binary optimization algorithms. Results testify that our approach is very efficient and can be regarded as a promising method for solving wide class of binary optimization problems.     

Differential evolution using a superior–inferior crossover scheme

Differential evolution (DE) is a new population-based stochastic optimization, which has difficulties in solving large-scale and multimodal optimization problems. The reason is that the population diversity decreases rapidly, which leads to the failure of the clustered individuals to reproduce better individuals. In order to improve the population diversity of DE, this paper aims to present a superior–inferior (SI) crossover scheme based on DE. Specifically, when population diversity degree is small, the SI crossover is performed to improve the search space of population. Otherwise, the superior–superior crossover is used to enhance its exploitation ability. In order to test the effectiveness of our SI scheme, we combine the SI with adaptive differential evolution (JADE), which is a recently developed DE variant for numerical optimization. In addition, the theoretical analysis of SI scheme is provided to show how the population’s diversity can be improved. In order to make the selection of parameters in our scheme more intelligently, a self-adaptive SI crossover scheme is proposed. Finally, comparative comprehensive experiments are given to illustrate the advantages of our proposed method over various DEs on a suite of 24 numerical optimization problems.     

一种求解约束优化问题的改进差分进化算法

针对在处理约束优化问题时约束条件难以处理的问题,提出了一种求解约束优化问题的改进差分进化算法.即在每代进化前将群体分为可行个体和不可行个体两类,对不可行个体,用差量法将其逐个转化为可行个体,并保持种群规模不变,经过一序列的进化后,计算所有可行个体的适应度并找到问题的最优解.对5个经典函数进行了优化测试,测试结果表明提出的算法对求解约束优化问题是有效的.     

A Continuous Genetic Algorithm Designed for the Global Optimization of Multimodal Functions

Genetic algorithms are stochastic search approaches based on randomized operators, such as selection, crossover and mutation, inspired by the natural reproduction and evolution of the living creatures. However, few published works deal with their application to the global optimization of functions depending on continuous variables.A new algorithm called Continuous Genetic Algorithm (CGA) is proposed for the global optimization of multiminima functions. In order to cover a wide domain of possible solutions, our algorithm first takes care over the choice of the initial population. Then it locates the most promising area of the solution space, and continues the search through an intensification inside this area. The selection, the crossover and the mutation are performed by using the decimal code. The efficiency of CGA is tested in detail through a set of benchmark multimodal functions, of which global and local minima are known. CGA is compared to Tabu Search and Simulated Annealing, as alternative algorithms.     

Multiobjective big data optimization based on a hybrid salp swarm algorithm and differential evolution

This paper developed a multiobjective Big Data optimization approach based on a hybrid salp swarm algorithm and the differential evolution algorithm. The role of the differential evolution algorithm is to enhance the capability of the feature exploitation of the salp swarm algorithm because the operators of the differential evolution algorithm are used as local search operators. In general, the proposed method contains three stages. In the first stage, the population is generated, and the archive is initialized. The second stage updates the solutions using the hybrid salp swarm algorithm and the differential evolution algorithm, and the final stage determines the nondominated solutions and updates the archive. To assess the performance of the proposed approach, a series of experiments were performed. A set of single-objective and multiobjective problems from the 2015 Big Data optimization competition were tested; the dataset contained data with and without noise. The results of our experiments illustrated that the proposed approach outperformed other approaches, including the baseline nondominated sorting genetic algorithm, on all test problems. Moreover, for single-objective problems, the score value of the proposed method was better than that of the traditional multiobjective salp swarm algorithm. When compared with both algorithms, that is, the adaptive DE algorithm with external archive and the hybrid multiobjective firefly algorithm, its score was the largest. In contrast, for the multiobjective functions, the scores of the proposed algorithm were higher than that of the fireworks algorithm framework.     

A numerical study of some modified differential evolution algorithms

Modifications in mutation and localization in acceptance rule are suggested to the differential evolution algorithm for global optimization. Numerical experiments indicate that the resulting algorithms are considerably better than the original differential evolution algorithm. Therefore, they offer a reasonable alternative to many currently available stochastic algorithms, especially for problems requiring ‘direct search type’ methods. Numerical study is carried out using a set of 50 test problems many of which are inspired by practical applications.     

二层线性规划的自适应遗传算法

提出了一种自适应遗传算法来求解二层线性规划问题.该方法克服了难以确定合适的交叉概率和变异概率的困难.另外,在该方法中还采用了其它一些技巧不仅解决了在采用遗传算法经常出现的有些个体不可行的问题,而且还改进了算法的效率.