A hybrid shuffled complex evolution approach based on differential evolution for unconstrained optimization

Numerous optimization methods have been proposed for the solution of the unconstrained optimization problems, such as mathematical programming methods, stochastic global optimization approaches, and metaheuristics. In this paper, a metaheuristic algorithm called Modified Shuffled Complex Evolution (MSCE) is proposed, where an adaptation of the Downhill Simplex search strategy combined with the differential evolution method is proposed. The efficiency of the new method is analyzed in terms of the mean performance and computational time, in comparison with the genetic algorithm using floating-point representation (GAF) and the classical shuffled complex evolution (SCE-UA) algorithm using six benchmark optimization functions. Simulation results and the comparisons with SCE-UA and GAF indicate that the MSCE improves the search performance on the five benchmark functions of six tested functions.     

A differential evolution algorithm with cooperative coevolutionary selection operation for high-dimensional optimization

Although different kinds of evolutionary algorithms (EAs) have been designed and achieved great success on many optimization problems, they are usually limited to some small-scale problems, e.g. with less than 100 decision variables, which may be quite small comparing to the requirements of real-world applications. Therefore, scaling EAs to large size problems have attracted more and more interest. Conventional EAs mimic the seemingly random natural processes by which species evolve. These evolution processes are slow or inefficient. Now, genetic engineering has enabled man to increase both the yields and quality of some crops fast by modifying some part of their genome precisely. In this paper, inspired by the ideas of the genetic engineering, we designed a local selection operator by decomposing the high-dimensional problem into some subcomponents and assigning a local fitness function to evaluate each subcomponent. Then a new differential evolution (DE) is proposed by inserting the local selection operator into the framework of DE. Numerical experiments were carried out to evaluate the performance of the new algorithm on a large number of benchmark functions. The results show that the new algorithm is effective and efficient for high-dimensional optimization.     

Self-adaptive differential evolution incorporating a heuristic mixing of operators

A considerable number of differential evolution variants have been proposed in the last few decades. However, no variant was able to consistently perform over a wide range of test problems. In this paper, propose two novel differential evolution based algorithms are proposed for solving constrained optimization problems. Both algorithms utilize the strengths of multiple mutation and crossover operators. The appropriate mix of the mutation and crossover operators, for any given problem, is determined through an adaptive learning process. In addition, to further accelerate the convergence of the algorithm, a local search technique is applied to a few selected individuals in each generation. The resulting algorithms are named as Self-Adaptive Differential Evolution Incorporating a Heuristic Mixing of Operators. The algorithms have been tested by solving 60 constrained optimization test instances. The results showed that the proposed algorithms have a competitive, if not better, performance in comparison to the-state-of-the-art algorithms.     

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.     

Interval differential evolution with dimension-reduction interval analysis method for uncertain optimization problems

A constrained nonlinear interval optimization method under the framework of differential evolution algorithm is developed to solve the uncertain structural optimization problems with interval uncertainties. The proposed method is a direct optimization method based on the interval differential evolution and dimension-reduction interval analysis. The interval preferential rule based on the satisfaction value of interval possibility degree model is used to realize the direct interval ranking of different design vectors. At each evolutionary generation, the outer optimizer by differential evolution optimizer searches for the best solution within the design space. The dimension-reduction interval analysis is employed to calculate the intervals of objective and constraints for each design vector in the inner layer. This operation transforms the original nesting optimization problem into a single loop one which improves the computational efficiency of the proposed method. Finally, the effectiveness of the presented direct method is verified by two numerical examples and an engineering application.     

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.     

Parameter identification of Rossler’s chaotic system by an evolutionary algorithm

In this paper, a differential evolution (DE) algorithm is applied to parameter identification of Rossler’s chaotic system. The differential evolution has been shown to possess a powerful searching capability for finding the solutions for a given optimization problem, and it allows for parameter solution to appear directly in the form of floating point without further numerical coding or decoding. Three unknown parameters of Rossler’s Chaotic system are optimally estimated by using the DE algorithm. Finally, a numerical example is given to verify the effectiveness of the proposed method.     

A surrogate based multi-fidelity approach for robust design optimization

Robust design optimization (RDO) is a field of optimization in which certain measure of robustness is sought against uncertainty. Unlike conventional optimization, the number of function evaluations in RDO is significantly more which often renders it time consuming and computationally cumbersome. This paper presents two new methods for solving the RDO problems. The proposed methods couple differential evolution algorithm (DEA) with polynomial correlated function expansion (PCFE). While DEA is utilized for solving the optimization problem, PCFE is utilized for calculating the statistical moments. Three examples have been presented to illustrate the performance of the proposed approaches. Results obtained indicate that the proposed approaches provide accurate and computationally efficient estimates of the RDO problems. Moreover, the proposed approaches outperforms popular RDO techniques such as tensor product quadrature, Taylor’s series and Kriging. Finally, the proposed approaches have been utilized for robust hydroelectric flow optimization, demonstrating its capability in solving large scale problems.     

A partial enumeration algorithm for pure nonlinear integer programming

In this paper, a partial enumeration algorithm is developed for a class of pure IP problems. Then, a computational algorithm, named PE_SPEEDUP (partial enumeration speedup), has been developed to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to understand and implement, yet very effective in dealing with many pure IP problems, including knapsack problems, reliability optimization, and spare allocation problems. The algorithm is based on monotonicity properties of the problem functions, and uses function values only; it does not require continuity or differentiability of the problem functions. This allows its use on problems whose functions cannot be expressed in closed algebraic form. The reliability and efficiency of the proposed algorithm and the PE_SPEEDUP algorithm has been demonstrated on some integer optimization problems taken from the literature.     

A Trigonometric Mutation Operation to Differential Evolution

Previous studies have shown that differential evolution is an efficient, effective and robust evolutionary optimization method. However, the convergence rate of differential evolution in optimizing a computationally expensive objective function still does not meet all our requirements, and attempting to speed up DE is considered necessary. In this paper, a new local search operation, trigonometric mutation, is proposed and embedded into the differential evolution algorithm. This modification enables the algorithm to get a better trade-off between the convergence rate and the robustness. Thus it can be possible to increase the convergence velocity of the differential evolution algorithm and thereby obtain an acceptable solution with a lower number of objective function evaluations. Such an improvement can be advantageous in many real-world problems where the evaluation of a candidate solution is a computationally expensive operation and consequently finding the global optimum or a good sub-optimal solution with the original differential evolution algorithm is too time-consuming, or even impossible within the time available. In this article, the mechanism of the trigonometric mutation operation is presented and analyzed. The modified differential evolution algorithm is demonstrated in cases of two well-known test functions, and is further examined with two practical training problems of neural networks. The obtained numerical simulation results are providing empirical evidences on the efficiency and effectiveness of the proposed modified differential evolution algorithm.     

基于种群自适应调整的多目标差分进化算法

为提高已有多目标进化算法在求解复杂多目标优化问题上的收敛性和解集分布性,提出一种基于种群自适应调整的多目标差分进化算法。该算法设计一个种群扩增策略,它在决策空间生成一些新个体帮助搜索更优的非支配解;设计了一个种群收缩策略,它依据对非支配解集的贡献程度淘汰较差的个体以减少计算负荷,并预留一些空间给新的带有种群多样性的扰动个体;引入精英学习策略,防止算法陷入局部收敛。通过典型的多目标优化函数对算法进行测试验证,结果表明所提算法相对于其他算法具有明显的优势,其性能优越,能够在保证良好收敛性的同时,使获得的Pareto最优解集具有更均匀的分布性和更广的覆盖范围,尤其适合于高维复杂多目标优化问题的求解。     

A multi-objective memetic algorithm based on decomposition for big optimization problems

When solving multi-objective optimization problems (MOPs) with big data, traditional multi-objective evolutionary algorithms (MOEAs) meet challenges because they demand high computational costs that cannot satisfy the demands of online data processing involving optimization. The gradient heuristic optimization methods show great potential in solving large scale numerical optimization problems with acceptable computational costs. However, some intrinsic limitations make them unsuitable for searching for the Pareto fronts. It is believed that the combination of these two types of methods can deal with big MOPs with less computational cost. The main contribution of this paper is that a multi-objective memetic algorithm based on decomposition for big optimization problems (MOMA/D-BigOpt) is proposed and a gradient-based local search operator is embedded in MOMA/D-BigOpt. In the experiments, MOMA/D-BigOpt is tested on the multi-objective big optimization problems with thousands of variables. We also combine the local search operator with other widely used MOEAs to verify its effectiveness. The experimental results show that the proposed algorithm outperforms MOEAs without the gradient heuristic local search operator.     

A new multi-threshold image segmentation approach using state transition algorithm

Thresholding plays an important role in image segmentation and image analysis. In this paper, the normalized histogram of an image is fitted by a linear combined normal distribution functions and each normal distribution function represents a class of pixels, whereas the parameters like the mean, the variance and the weights in the fitting function are undetermined. By transforming the fitting problem into a nonlinear and non-convex optimization problem, the state transition algorithm (STA) which is a new global optimization method is used to choose the optimal parameters of the fitting function. The effectiveness of proposed approach in multilevel thresholding problems is tested by several experimental results. By comparing with OTSU, particle swarm optimization (PSO), genetic algorithm (GA) and differential evolution (DE) algorithm, it has shown that STA has competitive performance in terms of both optimization results and thresholding segmentation.     

Inspired grey wolf optimizer for solving large-scale function optimization problems

Grey wolf optimizer algorithm was recently presented as a new heuristic search algorithm with satisfactory results in real-valued and binary encoded optimization problems that are categorized in swarm intelligence optimization techniques. This algorithm is more effective than some conventional population-based algorithms, such as particle swarm optimization, differential evolution and gravitational search algorithm. Some grey wolf optimizer variants were developed by researchers to improve the performance of the basic grey wolf optimizer algorithm. Inspired by particle swarm optimization algorithm, this study investigates the performance of a new algorithm called Inspired grey wolf optimizer which extends the original grey wolf optimizer by adding two features, namely, a nonlinear adjustment strategy of the control parameter, and a modified position-updating equation based on the personal historical best position and the global best position. Experiments are performed on four classical high-dimensional benchmark functions, four test functions proposed in the IEEE Congress on Evolutionary Computation 2005 special session, three well-known engineering design problems, and one real-world problem. The results show that the proposed algorithm can find more accurate solutions and has higher convergence rate and less number of fitness function evaluations than the other compared techniques.     

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.     

基于混合果蝇优化算法的选址-库存-配送集成优化研究

本文面向企业运营管理实践,构建了一种基于联合补货策略的选址-库存-配送集成优化新模型。作为典型的NP-hard问题,传统算法难以高效稳定地求解,故本文设计了一种新的混合果蝇优化算法(Fruit Fly Optimization Algorithm, FOA),通过引入进化算法的信息交换、变异、选择操作来增强算法局部寻优能力,采取概率性飞行策略来平衡算法的全局寻优与局部寻优。算例结果表明,新混合FOA算法的准确性和稳定性较标准FOA有了明显的改善,与差分进化、自适应混合差分进化、粒子群优化相比也具有比较优势。     

次模函数最大化的流算法综述

次模函数优化在计算机科学、数学、经济学等学科得到广泛研究.大数据环境下的次模优化是相对较新的研究领域,受到更多关注.特别地,考虑基于流模型的次模最大化问题.在该问题中,数据以流的形式呈现,其目的是从数据流中抽取满足某些特性的稀疏子集,最大化次模收益函数值.介绍了基于流模型的次模最大化问题的阈值和优先权方法,同时也介绍了若干次模最大化变形的流算法进展.     

Scale factor local search in differential evolution

This paper proposes the scale factor local search differential evolution (SFLSDE). The SFLSDE is a differential evolution (DE) based memetic algorithm which employs, within a self-adaptive scheme, two local search algorithms. These local search algorithms aim at detecting a value of the scale factor corresponding to an offspring with a high performance, while the generation is executed. The local search algorithms thus assist in the global search and generate offspring with high performance which are subsequently supposed to promote the generation of enhanced solutions within the evolutionary framework. Despite its simplicity, the proposed algorithm seems to have very good performance on various test problems. Numerical results are shown in order to justify the use of a double local search instead of a single search. In addition, the SFLSDE has been compared with a standard DE and three other modern DE based metaheuristic for a large and varied set of test problems. Numerical results are given for relatively low and high dimensional cases. A statistical analysis of the optimization results has been included in order to compare the results in terms of final solution detected and convergence speed. The efficiency of the proposed algorithm seems to be very high especially for large scale problems and complex fitness landscapes.     

A Particle Swarm Optimization Algorithm with Path Relinking for the Location Routing Problem

This paper introduces a new hybrid algorithmic nature inspired approach based on particle swarm optimization, for solving successfully one of the most popular logistics management problems, the location routing problem (LRP). The proposed algorithm for the solution of the location routing problem, the hybrid particle swarm optimization (HybPSO-LRP), combines a particle swarm optimization (PSO) algorithm, the multiple phase neighborhood search – greedy randomized adaptive search procedure (MPNS-GRASP) algorithm, the expanding neighborhood search (ENS) strategy and a path relinking (PR) strategy. The algorithm is tested on a set of benchmark instances. The results of the algorithm are very satisfactory for these instances and for six of them a new best solution has been found.      

Differential evolution algorithms using hybrid mutation

Differential evolution (DE) has gained a lot of attention from the global optimization research community. It has proved to be a very robust algorithm for solving non-differentiable and non-convex global optimization problems. In this paper, we propose some modifications to the original algorithm. Specifically, we use the attraction-repulsion concept of electromagnetism-like (EM) algorithm to boost the mutation operation of the original differential evolution. We carried out a numerical study using a set of 50 test problems, many of which are inspired by practical applications. Results presented show the potential of this new approach.