A survey of symbiotic organisms search algorithms and applications

Nature-inspired algorithms take inspiration from living things and imitate their behaviours to accomplish robust systems in engineering and computer science discipline. Symbiotic organisms search (SOS) algorithm is a recent metaheuristic algorithm inspired by symbiotic interaction between organisms in an ecosystem. Organisms develop symbiotic relationships such as mutualism, commensalism, and parasitism for their survival in ecosystem. SOS was introduced to solve continuous benchmark and engineering problems. The SOS has been shown to be robust and has faster convergence speed when compared with genetic algorithm, particle swarm optimization, differential evolution, and artificial bee colony which are the traditional metaheuristic algorithms. The interests of researchers in using SOS for handling optimization problems are increasing day by day, due to its successful application in solving optimization problems in science and engineering fields. Therefore, this paper presents a comprehensive survey of SOS advances and its applications, and this will be of benefit to the researchers engaged in the study of SOS algorithm.

     

基于协同进化的约束多目标优化算法

针对约束多目标优化算法存在难以有效地兼顾收敛性和多样性的问题,提出一种基于协同进化的约束多目标优化算法。第一阶段,通过基于稳态演化的可行解搜索方式得到一个具有一定数量可行解的种群;第二阶段,将这个种群拆分为两个子种群,并通过双子种群协同进化的方式实现对收敛性和多样性的兼顾;最后采用标准约束多目标优化问题CF1~CF7、DOC1~DOC7和实际工程问题进行仿真实验,以测试所提算法的求解性能。实验结果表明,与基于约束支配准则的非支配排序遗传算法（NSGA-Ⅱ-CDP）、两阶段算法（ToP）、推拉搜索算法（PPS）和约束多目标优化的双存档进化算法（C-TAEA）相比,所提算法在反向世代距离（IGD）和超体积（HV）两个指标上均取得了良好的结果,说明所提算法可以有效地兼顾收敛性和多样性。     

Discrete symbiotic organisms search algorithm for travelling salesman problem

A Discrete Symbiotic Organisms Search (DSOS) algorithm for finding a near optimal solution for the Travelling Salesman Problem (TSP) is proposed. The SOS is a metaheuristic search optimization algorithm, inspired by the symbiotic interaction strategies often adopted by organisms in the ecosystem for survival and propagation. This new optimization algorithm has been proven to be very effective and robust in solving numerical optimization and engineering design problems. In this paper, the SOS is improved and extended by using three mutation-based local search operators to reconstruct its population, improve its exploration and exploitation capability, and accelerate the convergence speed. To prove that the proposed solution approach of the DSOS is a promising technique for solving combinatorial problems like the TSPs, a set of benchmarks of symmetric TSP instances selected from the TSPLIB library are used to evaluate its performance against other heuristic algorithms. Numerical results obtained show that the proposed optimization method can achieve results close to the theoretical best known solutions within a reasonable time frame.     

修正免疫克隆约束多目标优化算法

针对约束多目标优化问题,提出修正免疫克隆约束多目标优化算法.该算法通过引进一个约束处理策略,用一个修正算法对个体的目标函数值进行修正,并对修正后的目标函数值采用免疫克隆算法进行优化,用一个精英种群对可行非支配解进行存储.该算法在优化过程中,既保留了非支配可行解,也充分利用了约束偏离值小的非可行解,同时引进整体克隆策略来提高解分布的多样性.通过对约束多目标问题的各项性能指标的测试以及和对比算法的比较可以看出:该算法在处理约束多目标优化测试问题时,所得解的多样性得到了一定的提高.同时,解的收敛性和均匀性也得到了一定的改进.     

A surrogate-assisted evolution strategy for constrained multi-objective optimization

In many real-world optimization problems, several conflicting objectives must be achieved and optimized simultaneously and the solutions are often required to satisfy certain restrictions or constraints. Moreover, in some applications, the numerical values of the objectives and constraints are obtained from computationally expensive simulations. Many multi-objective optimization algorithms for continuous optimization have been proposed in the literature and some have been incorporated or used in conjunction with expert and intelligent systems. However, relatively few of these multi-objective algorithms handle constraints, and even fewer, use surrogates to approximate the objective or constraint functions when these functions are computationally expensive. This paper proposes a surrogate-assisted evolution strategy (ES) that can be used for constrained multi-objective optimization of expensive black-box objective functions subject to expensive black-box inequality constraints. Such an algorithm can be incorporated into an intelligent system that finds approximate Pareto optimal solutions to simulation-based constrained multi-objective optimization problems in various applications including engineering design optimization, production management and manufacturing. The main idea in the proposed algorithm is to generate a large number of trial offspring in each generation and use the surrogates to predict the objective and constraint function values of these trial offspring. Then the algorithm performs an approximate non-dominated sort of the trial offspring based on the predicted objective and constraint function values, and then it selects the most promising offspring (those with the smallest predicted ranks from the non-dominated sort) to become the actual offspring for the current generation that will be evaluated using the expensive objective and constraint functions. The proposed method is implemented using cubic radial basis function (RBF) surrogate models to assist the ES. The resulting RBF-assisted ES is compared with the original ES and to NSGA-II on 20 test problems involving 2–15 decision variables, 2–5 objectives and up to 13 inequality constraints. These problems include well-known benchmark problems and application problems in manufacturing and robotics. The numerical results showed that the RBF-assisted ES generally outperformed the original ES and NSGA-II on the problems used when the computational budget is relatively limited. These results suggest that the proposed surrogate-assisted ES is promising for computationally expensive constrained multi-objective optimization.     

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。     

改进的约束优化多目标遗传算法及工程应用

利用多目标法处理约束条件,提出一种改进的基于多目标优化的遗传算法用于求解约束优化问题。该算法将约束优化问题转化为两个目标的多目标优化问题; 利用庄家法构造非劣个体,将种群分为支配子种群和非支配子种群,以一定概率分别从支配子种群和非支配子种群中选择个体进行算术交叉操作,引导个体逐步向极值点靠近,增强算法的局部搜索能力,对非支配子种群进行多样性变异操作。8个标准测试函数和3个工程应用的仿真实验结果表明了该算法的有效性。     

ε constrained differential evolution with pre-estimated comparison using gradient-based approximation for constrained optimization problems

Many real-world problems can be categorized as constrained optimization problems. So, designing effective algorithms for constrained optimization problems become more and more important. In designing algorithms, how to guide the individuals moving more efficiently towards the feasible region is one of the most important aspects on finding the optimum of constrained optimization problems. In this paper, we propose an improved ε constrained differential evolution, which combines with pre-estimated comparison gradient based approximation. The proposed algorithm uses gradient matrix to determine whether the trail vector generated by differential evolution algorithm is worth using the fitness function to evaluate it or not. Pre-estimated comparison gradient based approximation is used as a detector to find the promising offspring and in this way can we guide the individuals moving towards the feasible region. The proposed method is tested both on twenty-four benchmark functions and four well-known engineering optimization problems. Experimental results show that the proposed algorithm is highly competitive in comparing with other state-of-the-art algorithms. The proposed algorithm offers higher accuracy in engineering optimization problems for constrained optimization problems.     

Self-adaptive differential evolution algorithm with α-constrained-domination principle for constrained multi-objective optimization

Real-world problems are inherently constrained optimization problems often with multiple conflicting objectives. To solve such constrained multi-objective problems effectively, in this paper, we put forward a new approach which integrates self-adaptive differential evolution algorithm with α-constrained-domination principle, named SADE-αCD. In SADE-αCD, the trial vector generation strategies and the DE parameters are gradually self-adjusted adaptively based on the knowledge learnt from the previous searches in generating improved solutions. Furthermore, by incorporating domination principle into α-constrained method, α-constrained-domination principle is proposed to handle constraints in multi-objective problems. The advantageous performance of SADE-αCD is validated by comparisons with non-dominated sorting genetic algorithm-II, a representative of state-of-the-art in multi-objective evolutionary algorithms, and constrained multi-objective differential evolution, over fourteen test problems and four well-known constrained multi-objective engineering design problems. The performance indicators show that SADE-αCD is an effective approach to solving constrained multi-objective problems, which is basically enabled by the integration of self-adaptive strategies and α-constrained-domination principle.     

BSTBGA: A hybrid genetic algorithm for constrained multi-objective optimization problems

Most of the existing multi-objective genetic algorithms were developed for unconstrained problems, even though most real-world problems are constrained. Based on the boundary simulation method and trie-tree data structure, this paper proposes a hybrid genetic algorithm to solve constrained multi-objective optimization problems (CMOPs). To validate our approach, a series of constrained multi-objective optimization problems are examined, and we compare the test results with those of the well-known NSGA-II algorithm, which is representative of the state of the art in this area. The numerical experiments indicate that the proposed method can clearly simulate the Pareto front for the problems under consideration.     

带拥塞控制的多种群二元蚁群算法

二元蚁群算法在函数优化中有着良好的表现, 但仍存在易陷入局部最优和在多峰函数求解中无法同时得到多个解的缺陷. 使用拥塞控制策略改善算法的全局寻优能力, 同时引入多种群的思想, 提出了带拥塞控制多种群二元蚁群算法. 通过对几个不同函数(包括单峰与多峰)的测试, 实验结果表明该改进算法在保证较好的全局搜索能力的基础上, 拥有很好的多目标求解能力.     

A Multi-Objective Integer Melody Search Algorithm

There are a number of algorithms for the solution of continuous optimization problems. However, many practical design optimization problems use integer design variables instead of continuous. These types of problems cannot be handled by using continuous design variables-based algorithms. In this paper, we present a multi-objective integer melody search optimization algorithm (MO-IMS) for solving multi-objective integer optimization problems, which take design variables as integers. The proposed algorithm is a modified version of single-objective melody search (MS) algorithm, which is an innovative optimization algorithm, inspired by basic concepts applied in harmony search (HS) algorithm. Results show that MO-IMS has better performance in solving multi-objective integer problems than the existing multi-objective integer harmony search algorithm (MO-IHS). Performance of proposed algorithm is evaluated by using various performance metrics on test functions. The simulation results show that the proposed MO-IMS can be a better technique for solving multi-objective problems having integer decision variables.     

Preference-based multi-objectivization applied to decision support for High-Pressure Thermal processes in food treatment

Food industry aims to provide healthy products that must satisfy the quality requirements of the considered legislation. To do so, food is treated by using some processing techniques, such as High-Pressure Thermal (HPT) treatments. In this work, we propose a preference-based multi-objectivization methodology to design HPT processes for food treatment. This approach is based on formulating a multi-objective optimization problem, instead of a constrained mono-objective problem, where the constraints are reformulated as separate objective functions. The multi-objective problem is then solved by using preference-based evolutionary optimization algorithms (PMOEAs). PMOEAs focus the search of a numerical solution inside a region of interest defined by the food engineer, avoiding exploring HPT designs that are out of interest. The proposed methodology is validated by considering several particular mono-objective and multi-objective optimization problems related to HPT processing. In particular, we compare the results obtained by two competitive state-of-the-art PMOEAs, called WASF-GA and R-NSGA-II, with the ones returned by a mono-objective algorithm called MLS-GA. As part of this study, the influence of the optimization algorithm parameters on the solutions, their quality and the computing time are discussed. Finally, the best solutions returned by the algorithm that shows a better performance for our problems, which is WASF-GA, are analyzed from a food engineering point of view and a sensitivity analysis regarding the impact of design parameters on the performances of those solutions is carried out.     

HMOSHSSA: a hybrid meta-heuristic approach for solving constrained optimization problems

This paper proposes a novel hybrid multi-objective optimization algorithm named HMOSHSSA by synthesizing the strengths of Multi-objective Spotted Hyena Optimizer (MOSHO) and Salp Swarm Algorithm (SSA). HMOSHSSA utilizes the exploration capability of MOSHO to explore the search space effectively and leader and follower selection mechanism of SSA to achieve global best solution with faster convergence. The proposed algorithm is evaluated on 24 benchmark test functions, and its performance is compared with seven well-known multi-objective optimization algorithms. The experimental results demonstrate that HMOSHSSA acquires very competitive results and outperforms other algorithms in terms of convergence speed, search-ability and accuracy. Additionally, HMOSHSSA is also applied on seven well-known engineering problems to further verify its efficacy. The results reveal the effectiveness of proposed algorithm toward solving real-life multi-objective optimization problems.

     

面向复杂约束优化问题的进化算法综述

约束优化是多数实际工程应用优化问题的呈现方式.进化算法由于其高效的表现,近年来被广泛应用于约束优化问题求解.但约束条件使得问题解空间离散、缩小、改变,给进化算法求解约束优化问题带来极大挑战.在此背景下,融合约束处理技术的进化算法成为研究热点.此外,随着研究的深入,近年来约束处理技术在复杂工程应用问题优化中得到了广泛发展,例如多目标、高维、等式优化等.根据复杂性的缘由,将面向复杂约束优化问题的进化优化分为面向复杂目标的进化约束优化算法和面向复杂约束场景的进化算法两种类别进行综述,其中,重点探讨了实际工程应用的复杂性对约束处理技术的挑战和目前研究的最新进展,并最后总结了未来的研究趋势与挑战.     

基于多目标飞蛾算法的电力系统无功优化研究

鉴于电力需求的日益增长与传统无功优化方法的桎梏,如何更加合理有效地解决电力系统的无功优化问题逐渐成为了研究的热点。提出一种多目标飞蛾扑火算法来解决电力系统多目标无功优化的问题,算法引入固定大小的外部储存机制、自适应的网格和筛选机制来有效存储和提升无功优化问题的帕累托最优解集,算法采用CEC2009标准多目标测试函数来进行仿真实验,并与两种经典算法进行性能的对比分析。此外,在电力系统IEEE 30节点上将该算法与MOPSO,NGSGA-II算法的求解结果进行比较分析的结果表明,多目标飞蛾算法具有良好的性能,并在解决电力系统多目标无功优化问题上具有良好的潜力。     

LADPSO: using fuzzy logic to conduct PSO algorithm

Optimization plays a critical role in human modern life. Nowadays, optimization is used in many aspects of human modern life including engineering, medicine, agriculture and economy. Due to the growing number of optimization problems and their growing complexity, we need to improve and develop theoretical and practical optimization methods. Stochastic population based optimization algorithms like genetic algorithms and particle swarm optimization are good candidates for solving complex problems efficiently. Particle swarm optimization (PSO) is an optimization algorithm that has received much attention in recent years. PSO is a simple and computationally inexpensive algorithm inspired by the social behavior of bird flocks and fish schools. However, PSO suffers from premature convergence, especially in high dimensional multi-modal functions. In this paper, a new method for improving PSO has been introduced. The Proposed method which has been named Light Adaptive Particle Swarm Optimization is a novel method that uses a fuzzy control system to conduct the standard algorithm. The suggested method uses two adjunct operators along with the fuzzy system in order to improve the base algorithm on global optimization problems. Our approach is validated using a number of common complex uni-modal/multi-modal benchmark functions and results have been compared with the results of Standard PSO (SPSO2011) and some other methods. The simulation results demonstrate that results of the proposed approach is promising for improving the standard PSO algorithm on global optimization problems and also improving performance of the algorithm.     

星型结构的多目标粒子群算法求解多模态多目标问题

首先,根据多目标粒子群算法中的粒子结构信息,利用非支配解集构造粒子个体邻域之间的拓扑结构,提出星型结构的多目标粒子群算法用于求解多模态多目标问题。其次,针对多目标粒子群中全局最优个体选择困难,提出一种非支配解集分布均匀程度的评价方法,评价结果用于确定当前粒子对应的全局最优个体。最后,结合2种方法提出带均匀计算方法的星型拓扑结构多目标粒子群优化算法STMOPSONCMIU。通过测试函数分析算法的收敛性,表明改进的算法比原来的算法收敛速度快。实验结果表明,该算法可以较好地兼顾问题的目标空间和决策空间的分布,有效解决多模态多目标问题。     

一种新型约束多目标帝国竞争算法

针对约束多目标优化问题，提出了一种基于约束违背程度和Pareto支配的有效约束处理策略，并设计了一种新型多目标帝国竞争算法（MOICA）.该算法采用一种简化的初始帝国构建过程，在同化过程引入了向外部档案内非劣解学习的机制，并基于帝国势力新定义的帝国竞争新方法以获取问题高质量的解.选用了7个测试问题CF1~CF7进行计算实验并和多种算法进行对比.计算结果表明， MOICA在求解约束多目标优化问题方面具有较强的搜索能力和优势.     

一类带约束动态多目标优化问题的进化算法

动态多目标约束优化问题是一类NP-Hard问题,定义了动态环境下进化种群中个体的序值和个体的约束度,结合这两个定义给出了一种选择算子.在一种环境变化判断算子下给出了求解环境变量取值于正整数集Z+的一类带约束动态多目标优化问题的进化算法.通过几个典型的Benchmark函数对算法的性能进行了测试,其结果表明新算法能够较好地求出带约束动态多目标优化问题在不同环境下质量较好、分布较均匀的Pareto最优解集.