A comparative study of local search within a surrogate-assisted multi-objective memetic algorithm framework for expensive problems

A comparative study of the impacts of various local search methodologies for the surrogate-assisted multi-objective memetic algorithm (MOMA) is presented in this paper. The base algorithm for the comparative study is the single surrogate-assisted MOMA (SS-MOMA) with the main aim being to solve expensive problems with a limited computational budget. In addition to the standard weighted sum (WS) method used in the original SS-MOMA, we studied the capabilities of other local search methods based on the achievement scalarizing function (ASF), Chebyshev function, and random mutation hill climber (RMHC) in various test problems. Several practical aspects, such as normalization and constraint handling, were also studied and implemented to deal with real-world problems. Results from the test problems showed that, in general, the SS-MOMA with ASF and Chebyshev functions was able to find higher-quality solutions that were more robust than those found with WS or RMHC; although on problems with more complicated Pareto sets SS-MOMA-WS appeared as the best. SS-MOMA-ASF in conjunction with the Chebyshev function was then tested on an airfoil-optimization problem and compared with SS-MOMA-WS and the non-dominated sorting based genetic algorithm-II (NSGA-II). The results from the airfoil problem clearly showed that SS-MOMA with an achievement-type function could find more diverse solutions than SS-MOMA-WS and NSGA-II. This suggested that for real-world applications, higher-quality solutions are more likely to be found when the surrogate-based memetic optimizer is equipped with ASF or a Chebyshev function than with other local search methods.     

电力系统经济负荷分配的混合粒子群优化算法

为解决电力系统中的经济负荷分配问题,提出一种将约束优化与粒子群优化算法相结合的混合算法,同时引入直接搜索方法。使得混合后的粒子群优化算法不但具有高效的全局搜索能力,而且具有较强的局部搜索能力,避免陷入局部最优,提高求解精度。对两个实例进行测试,与其他智能算法的结果比较,证明提出的算法可以有效找到可行解,避免陷入局部最优,实现问题的快速求解。     

Use of biased neighborhood structures in multiobjective memetic algorithms

In this paper, we examine the use of biased neighborhood structures for local search in multiobjective memetic algorithms. Under a biased neighborhood structure, each neighbor of the current solution has a different probability to be sampled in local search. In standard local search, all neighbors of the current solution usually have the same probability because they are randomly sampled. On the other hand, we assign larger probabilities to more promising neighbors in order to improve the search ability of multiobjective memetic algorithms. In this paper, we first explain our multiobjective memetic algorithm, which is a simple hybrid algorithm of NSGA-II and local search. Then we explain its variants with biased neighborhood structures for multiobjective 0/1 knapsack and flowshop scheduling problems. Finally we examine the performance of each variant through computational experiments. Experimental results show that the use of biased neighborhood structures clearly improves the performance of our multiobjective memetic algorithm.     

一种求解多目标优化问题的进化算法混合框架

为了提高多目标优化算法的求解性能,提出一种启发式的基于种群的全局搜索与局部搜索相结合的多目标进化算法混合框架.该框架采用模块化、系统化的设计思想,不同模块可以采用不同策略构成不同的算法.采用经典的改进非支配排序遗传算法(NSGA-II)和基于分解的多目标进化算法(MOEA/D)作为进化算法的模块算法来验证所提混合框架的有效性.数值实验表明,所提混合框架具有良好性能,可以兼顾算法求解的多样性和收敛性,有效提升现有多目标进化算法的求解性能.     

基于多点非均匀变异的多目标极值优化算法研究

多目标进化算法因其在解决含有多个矛盾目标函数的多目标优化问题中的强大处理能力,正受到越来越多的关注与研究。极值优化作为一种新型的进化算法,已在各种离散优化、连续优化测试函数以及工程优化问题中得到了较为成功的应用,但有关多目标EO算法的研究却十分有限。本文将采用Pareto优化的基本原理引入到极值优化算法中,提出一种求解连续多目标优化问题的基于多点非均匀变异的多目标极值优化算法。通过对六个国际公认的连续多目标优化测试函数的仿真实验结果表明：本文提出算法相比NSGA-II、 PAES、SPEA和SPEA2等经典多目标优化算法在收敛性和分布性方面均具有优势。     

Stopping criteria for MAPLS-AW,a hybrid multi-objective evolutionary algorithm

Evolutionary algorithms are widely used to solve multi-objective optimization problems effectively by performing global search over the solution space to find better solutions. Hybrid evolutionary algorithms have been introduced to enhance the quality of solutions obtained. One such hybrid algorithm is memetic algorithm with preferential local search using adaptive weights (MAPLS-AW) (Bhuvana and Aravindan in Soft Comput, doi: 10.1007/s00500-015-1593-9, 2015). MAPLS-AW, a variant of NSGA-II algorithm, recognizes the elite solutions of the population and preferences are given to them for local search during the evolution. This paper proposes a termination scheme derived from the features of MAPLS-AW. The objective of the proposed scheme is to detect convergence of population without compromising quality of solutions generated by MAPLS-AW. The proposed termination scheme consists of five stopping measures, among which two are newly proposed in this paper to predict the convergence of the population. Experimental study has been carried out to analyze the performance of the proposed termination scheme and to compare with existing termination schemes. Several constrained and unconstrained multi-objective benchmark test problems are used for this comparison. Additionally, a real-time application economic emission and load dispatch has also been used to check the performance of the proposed scheme. The results show that the proposed scheme identifies convergence of population much earlier than the existing stopping schemes without compromising the quality of solutions.     

A multi-objective hyper-heuristic based on choice function

Hyper-heuristics are emerging methodologies that perform a search over the space of heuristics in an attempt to solve difficult computational optimization problems. We present a learning selection choice function based hyper-heuristic to solve multi-objective optimization problems. This high level approach controls and combines the strengths of three well-known multi-objective evolutionary algorithms (i.e. NSGAII, SPEA2 and MOGA), utilizing them as the low level heuristics. The performance of the proposed learning hyper-heuristic is investigated on the Walking Fish Group test suite which is a common benchmark for multi-objective optimization. Additionally, the proposed hyper-heuristic is applied to the vehicle crashworthiness design problem as a real-world multi-objective problem. The experimental results demonstrate the effectiveness of the hyper-heuristic approach when compared to the performance of each low level heuristic run on its own, as well as being compared to other approaches including an adaptive multi-method search, namely AMALGAM.     

Zen-ReqOptimizer: a search-based approach for requirements assignment optimization

At early phases of a product development lifecycle of large scale Cyber-Physical Systems (CPSs), a large number of requirements need to be assigned to stakeholders from different organizations or departments of the same organization for review, clarification and checking their conformance to standards and regulations. These requirements have various characteristics such as extents of importance to the organization, complexity, and dependencies between each other, thereby requiring different effort (workload) to review and clarify. While working with our industrial partners in the domain of CPSs, we discovered an optimization problem, where an optimal solution is required for assigning requirements to various stakeholders by maximizing their familiarity to assigned requirements, meanwhile balancing the overall workload of each stakeholder. In this direction, we propose a fitness function that takes into account all the above-mentioned factors to guide a search algorithm to find an optimal solution. As a pilot experiment, we first investigated four commonly applied search algorithms (i.e., GA, (1 + 1) EA, AVM, RS) together with the proposed fitness function and results show that (1 + 1) EA performs significantly better than the other algorithms. Since our optimization problem is multi-objective, we further empirically evaluated the performance of the fitness function with six multi-objective search algorithms (CellDE, MOCell, NSGA-II, PAES, SMPSO, SPEA2) together with (1 + 1) EA (the best in the pilot study) and RS (as the baseline) in terms of finding an optimal solution using an real-world case study and 120 artificial problems of varying complexity. Results show that both for the real-world case study and the artificial problems (1 + 1) EA achieved the best performance for each single objective and NSGA-II achieved the best performance for the overall fitness. NSGA-II has the ability to solve a wide range of problems without having their performance degraded significantly and (1 + 1) EA is not fit for problems with less than 250 requirements Therefore we recommend that, if a project manager is interested in a particular objective then (1 + 1) EA should be used; otherwise, NSGA-II should be applied to obtain optimal solutions when putting the overall fitness as the first priority.     

嵌入式系统动态数据结构优化的并行进化算法

为了更好地解决现代多媒体嵌入式系统动态数据结构优化问题,结合NSGA-II和SPEA2两个多目标进化算法,引入岛屿模型和多线程机制,提出了一种并行多目标进化算法--PMOEA-NS。基于多核计算机系统,使用PMOEA-NS具体的3个不同并行算法和串行NSGA-II、SPEA2,对一个实际动态嵌入式应用程序进行优化实验和计算,结果表明:与串行算法NSGA-II和SPEA2相比,并行算法不但提高了优化过程的速度,而且改善了解的质量和多样性。     

基于新型拥挤度距离的多目标麻雀搜索算法

现实中的多目标问题日益复杂,解决这类问题需要高效的优化算法。基于麻雀搜索算法,提出多目标麻雀搜索算法（Multi-objective Sparrow Search Algorithm,MSSA）,对多目标优化问题进行求解。依据外部存档收敛性动态调整麻雀种群比例因子,以达到全局探索能力和局部开发能力的最佳平衡,确保收敛性;对麻雀种群进行非支配排序;对麻雀种群的发现者引入多项式变异因子,增强算法跳出局部最优的能力;设计一种新型拥挤度距离计算策略,利用外部存档解的拥挤度大小剔除相似个体的方法对种群进行裁剪,使个体不超过存档上限的同时维持种群的多样性。分别使用多目标函数和盘式制动器设计测试算法性能。MSSA与MOPSO、MOGWO、NSGA-II和SPEA2在多目标测试函数上进行对比实验,结果表明MSSA算法在收敛性和均匀性两项指标上有显著的优势。盘式制动器仿真结果表明,MSSA可以快速地找到问题的非支配解,证明了该方法的有效性。     

一种基于云模型的多目标进化算法

在多目标进化算法的基础上,提出了一种基于云模型的多目标进化算法(CMOEA).算法设计了一种新的变异算子来自适应地调整变异概率,使得算法具有良好的局部搜索能力.算法采用小生境技术,其半径按X条件云发生器非线性动态地调整以便于保持解的多样性,同时动态计算个体的拥挤距离并采用云模型参数来估计个体的拥挤度,逐个删除种群中超出的非劣解以保持解的分布性.将该算法用于多目标0/1背包问题来测试CMOEA的性能,并与目前最流行且有效的多目标进化算法NSGA-II及SPEA2进行了比较.结果表明,CMOEA具有良好的搜索性能,并能很好地维持种群的多样性,快速收敛到Pareto前沿,所获得的Pareto最优解集具有更好的收敛性与分布性.     

ADAPTIVE MULTI-OBJECTIVE OPTIMIZATION BASED ON NONDOMINATED SOLUTIONS

An adaptive hybrid model (AHM) based on nondominated solutions is presented in this study for multi-objective optimization problems (MOPs). In this model, three search phases are devised according to the number of nondominated solutions in the current population: 1) emphasizing the dominated solutions when the population contains very few nondominated solutions; 2) maintaining the balance between nondominated and dominated solutions when nondominated ones become more; 3) when the population consists of adequate nondominated solutions, dominated ones could be ignored and the isolated nondominated ones are allocated more computational budget by their crowding distance values for heuristic search. To exploit local information efficiently, a local incremental search algorithm, LISA, is proposed and merged into the model. This model maintains the adaptive mechanism between the optimization process by the online discovered nondominated solutions. The proposed model is validated using five ZDT and five DTLZ problems. Compared with three other state-of-the-art multi-objective algorithms, namely NSGA-II, SPEA2, and PESA-II, AHM achieves comparable results in terms of convergence and diversity metrics. Finally, the sensitivity of introduced parameters and scalability to the number of objectives are investigated.     

A multi-objective differential evolutionary algorithm for constrained multi-objective optimization problems with low feasible ratio

Most current evolutionary multi-objective optimization (EMO) algorithms perform well on multi-objective optimization problems without constraints, but they encounter difficulties in their ability for constrained multi-objective optimization problems (CMOPs) with low feasible ratio. To tackle this problem, this paper proposes a multi-objective differential evolutionary algorithm named MODE-SaE based on an improved epsilon constraint-handling method. Firstly, MODE-SaE self-adaptively adjusts the epsilon level in line with the maximum and minimum constraint violation values of infeasible individuals. It can prevent epsilon level setting from being unreasonable. Then, the feasible solutions are saved to the external archive and take part in the population evolution by a co-evolution strategy. Finally, MODE-SaE switches the global search and local search by self-switching parameters of search engine to balance the convergence and distribution. With the aim of evaluating the performance of MODE-SaE, a real-world problem with low feasible ratio in decision space and fourteen bench-mark test problems, are used to test MODE-SaE and five other state-of-the-art constrained multi-objective evolution algorithms. The experimental results fully demonstrate the superiority of MODE-SaE on all mentioned test problems, which indicates the effectiveness of the proposed algorithm for CMOPs which have low feasible ratio in search space.     

Achieving super-linear performance in parallel multi-objective evolutionary algorithms by means of cooperative coevolution

This article introduces three new multi-objective cooperative coevolutionary variants of three state-of-the-art multi-objective evolutionary algorithms, namely, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Multi-objective Cellular Genetic Algorithm (MOCell). In such a coevolutionary architecture, the population is split into several subpopulations or islands, each of them being in charge of optimizing a subset of the global solution by using the original multi-objective algorithm. Evaluation of complete solutions is achieved through cooperation, i.e., all subpopulations share a subset of their current partial solutions. Our purpose is to study how the performance of the cooperative coevolutionary multi-objective approaches can be drastically increased with respect to their corresponding original versions. This is specially interesting for solving complex problems involving a large number of variables, since the problem decomposition performed by the model at the island level allows for much faster executions (the number of variables to handle in every island is divided by the number of islands). We conduct a study on a real-world problem related to grid computing, the bi-objective robust scheduling problem of independent tasks. The goal in this problem is to minimize makespan (i.e., the time when the latest machine finishes its assigned tasks) and to maximize the robustness of the schedule (i.e., its tolerance to unexpected changes on the estimated time to complete the tasks). We propose a parallel, multithreaded implementation of the coevolutionary algorithms and we have analyzed the results obtained in terms of both the quality of the Pareto front approximations yielded by the techniques as well as the resulting speedups when running them on a multicore machine.     

基于全组合策略的多目标阴阳对算法

基于前沿的阴阳对优化算法（Front-based Yin-Yang-Pair Optimization,F-YYPO）是一种新颖的轻量级多目标优化算法,其利用两点--局部开发点[Pi1]和全局探索点[Pi2]在搜索过程中的迭代交换实现搜索。基于F-YYPO提出了一种改进的多目标优化算法F-ACYYPO。新算法对F-YYPO做了以下三方面的改进：（1）对多个目标函数进行全组合,以增强优化个体分布的均匀性;（2）引入已在YYPO算法中被证明有明显性能提高效果的缩放因子[α]自适应措施;（3）改进F-YYPO存档操作的更新方式。采用在2009年进化计算大会多目标优化算法竞赛中使用的UF测试套件以及PlatEMO平台下的DTLZ测试套件进行算法的性能评估,将F-ACYYPO与F-YYPO以及其他多种已知性能优良的多目标优化算法NSGA2、SPEA2、MOPSO、MOGWO、gamultiobj、MOEA\D、GDE3进行性能测试及比较,并通过两个综合性指标（反转世代距离IGD、超体积HV）和一个收敛性指标（世代距离GD）进行性能评价。实验结果表明,F-ACYYPO比F-YYPO具有更高的计算精度以及更快的收敛速度,并且与其他高性能多目标算法相比,F-ACYYPO表现出了很强的竞争性,在综合性能指标下有将近超1/2的测试用例占优。     

A machine-learning based memetic algorithm for the multi-objective permutation flowshop scheduling problem

In recent years, the historical data during the search process of evolutionary algorithms has received increasing attention from many researchers, and some hybrid evolutionary algorithms with machine-learning have been proposed. However, the majority of the literature is centered on continuous problems with a single optimization objective. There are still a lot of problems to be handled for multi-objective combinatorial optimization problems. Therefore, this paper proposes a machine-learning based multi-objective memetic algorithm (ML-MOMA) for the discrete permutation flowshop scheduling problem. There are two main features in the proposed ML-MOMA. First, each solution is assigned with an individual archive to store the non-dominated solutions found by it and based on these individual archives a new population update method is presented. Second, an adaptive multi-objective local search is developed, in which the analysis of historical data accumulated during the search process is used to adaptively determine which non-dominated solutions should be selected for local search and how the local search should be applied. Computational results based on benchmark problems show that the cooperation of the above two features can help to achieve a balance between evolutionary global search and local search. In addition, many of the best known Pareto fronts for these benchmark problems in the literature can be improved by the proposed ML-MOMA.     

Real-coded memetic algorithms with crossover hill-climbing

This paper presents a real-coded memetic algorithm that applies a crossover hill-climbing to solutions produced by the genetic operators. On the one hand, the memetic algorithm provides global search (reliability) by means of the promotion of high levels of population diversity. On the other, the crossover hill-climbing exploits the self-adaptive capacity of real-parameter crossover operators with the aim of producing an effective local tuning on the solutions (accuracy). An important aspect of the memetic algorithm proposed is that it adaptively assigns different local search probabilities to individuals. It was observed that the algorithm adjusts the global/local search balance according to the particularities of each problem instance. Experimental results show that, for a wide range of problems, the method we propose here consistently outperforms other real-coded memetic algorithms which appeared in the literature.     

一种双链结构的多目标进化算法DCMOEA

提出一种双链结构的多目标进化算法(DCMOEA).该算法采用双链结构表示个体,执行过程中无需设置外部归档集合,并采用ε支配策略保持解群的多样性.DCMOEA与MOEA/D、NSGA-II、SPEA2和PAES一同在4个2-目标ZDT函数和4个3-目标DTLZ问题上进行实验,并从算法所获解集的收敛性、分布均匀性和宽广性3个方面进行比较,仿真实验结果表明了DCMOEA的综合性能最好,是一种颇具竞争力的多目标进化算法.     

A hybrid intelligent model for order allocation planning in make-to-order manufacturing

This paper investigated a multi-objective order allocation planning problem in make-to-order manufacturing with the consideration of various real-world production features. A novel hybrid intelligent optimization model, integrating a multi-objective memetic optimization (MOMO) process, a Monte Carlo simulation technique and a heuristic pruning technique, is developed to tackle this problem. The MOMO process, combining a NSGA-II optimization process with a tabu search, is proposed to provide Pareto optimal solutions. Extensive experiments based on industrial data are conducted to validate the proposed model. Results show that (1) the proposed model can effectively solve the investigated problem by providing effective production decision-making solutions; (2) the MOMO process has better capability of seeking global optimum than an NSGA-II-based optimization process and an industrial method.     

A Comparison of three evolutionary strategies for multiobjective genetic programming

We report what we believe to be the first comparative study of multi-objective genetic programming (GP) algorithms on benchmark symbolic regression and machine learning problems. We compare the Strength Pareto Evolutionary Algorithm (SPEA2), the Non-dominated Sorting Genetic Algorithm (NSGA-II) and the Pareto Converging Genetic Algorithm (PCGA) evolutionary paradigms. As well as comparing the quality of the final solutions, we also examine the speed of convergence of the three evolutionary algorithms. Based on our observations, the SPEA2-based algorithm appears to have problems controlling tree bloat—that is, the uncontrolled growth in the size of the chromosomal tree structures. The NSGA-II-based algorithm on the other hand seems to experience difficulties in locating low error solutions. Overall, the PCGA-based algorithm gives solutions with the lowest errors and the lowest mean complexity.