自适应偏好半径划分区域的多目标进化方法

偏好多目标进化算法是一类帮助决策者找到感兴趣的Pareto最优解的算法.目前,在以参考点位置作为偏好信息载体的偏好多目标进化算法中,不合适的参考点位置往往会严重影响算法的收敛性能,偏好区域的大小难以控制,在高维问题上效果较差.针对以上问题,通过计算基于种群的自适应偏好半径,利用自适应偏好半径构造一种新的偏好关系模型,通过对偏好区域进行划分,提出基于偏好区域划分的偏好多目标进化算法.将所提算法与4种常用的以参考点为偏好信息载体的多目标进化算法g-NSGA-II、r-NSGA-II、角度偏好算法、MOEA/D-PRE进行对比实验,结果表明,所提算法具有较好的收敛性能和分布性能,决策者可以控制偏好区域大小,在高维问题上也具有较好的收敛效果.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

On decomposition methods in interactive user-preference based optimization

Evolutionary multi-objective optimization (EMO) methodologies have been widely applied to find a well-distributed trade-off solutions approximating to the Pareto-optimal front in the past decades. However, integrating the user-preference into the optimization to find the region of interest (ROI) [1] or preferred Pareto-optimal solutions could be more efficient and effective for the decision maker (DM) straightforwardly. In this paper, we propose several methods by combining preference-based strategy (like the reference points) with the decomposition-based multi-objective evolutionary algorithm (MOEA/D) [2], and demonstrate how preferred sets or ROIs near the different reference points specified by the DM can be found simultaneously and interactively. The study is based on the experiments conducted on a set of test problems with objectives ranging from two to fifteen objectives. Experiments have proved that the proposed approaches are more efficient and effective especially on many-objective problems to provide a set of solutions to the DM's preference, so that a better and a more reliable decision can be made.     

Multi-objective topology optimization through GA-based hybridization of partial solutions

In a recent project the authors have developed an approach to assist the identification of the optimal topology of a technical system, capable of overcoming geometrical contradictions that arise from conflicting design requirements. The method is based on the hybridization of partial solutions obtained from mono-objective topology optimization tasks. In order to investigate efficiency, effectiveness and potentialities of the developed hybridization algorithm, a comparison among the proposed approach and traditional topology optimization techniques such as Genetic Algorithms (GAs) and gradient-based methods is presented here. The benchmark has been performed by applying the hybridization algorithm to several case studies of multi-objective optimization problems available in literature. The obtained results demonstrate that the proposed approach is definitely less expensive in terms of computational requirements, than the conventional application of GAs to topology optimization tasks, still keeping the same effectiveness in terms of searching the global optimum solution. Moreover, the comparison among the hybridized solutions and the solutions obtained through GAs and gradient-based optimization methods, shows that the proposed algorithm often leads to very different topologies having better performances.     

Elite-guided multi-objective artificial bee colony algorithm

Multi-objective optimization has been a difficult problem and a research focus in the field of science and engineering. This paper presents a novel multi-objective optimization algorithm called elite-guided multi-objective artificial bee colony (EMOABC) algorithm. In our proposal, the fast non-dominated sorting and population selection strategy are applied to measure the quality of the solution and select the better ones. The elite-guided solution generation strategy is designed to exploit the neighborhood of the existing solutions based on the guidance of the elite. Furthermore, a novel fitness calculation method is presented to calculate the selecting probability for onlookers. The proposed algorithm is validated on benchmark functions in terms of four indicators: GD, ER, SPR, and TI. The experimental results show that the proposed approach can find solutions with competitive convergence and diversity within a shorter period of time, compared with the traditional multi-objective algorithms. Consequently, it can be considered as a viable alternative to solve the multi-objective optimization problems.     

三种基于偏好的区间多目标进化算法及应用

区间参数多目标优化问题是普遍存在且非常重要的。目前直接求解该类问题的进化优化方法非常少,且已有方法的目的是找到收敛性好且分布均匀的Pareto最优解集。为得到符合决策者偏好的最满意解,本文综述3种基于偏好的区间多目标进化算法,并将其应用于特定环境下机器人路径规划问题,比较3种算法的性能。研究结果可丰富特定环境下机器人路径规划的求解方法,提高机器人路径优化效果。     

改进果蝇优化算法在多目标搜索的应用

在实际工程优化问题中多数问题是多目标优化问题,多目标优化问题一直以来就是智能算法的研究热点。提出一种改进的果蝇优化算法,将其应用在多目标搜索领域,并成功使用该算法解决了一种多目标背包问题。算法在基本果蝇优化算法的基础上采用分群策略和动态半径,在群A中从种群位置开始以动态半径探索新的可行解,在群B中则通过非支配个体之间的交叉操作进行密集搜索。果蝇种群的位置在每一轮迭代产生的非劣解集中进行选取,提高了算法的收敛速度。通过在多个数据集下进行测试,并和粒子群算法、NSGA-2做了对比实验,最终结果显示使用该算法在特定条件下能取得较好的搜索效果,证明了使用果蝇优化算法解决多目标问题的可行性。     

Design optimization of laminar flow machine rotors based on the topological derivative concept

Flow machines are very important to industry, being widely used on various processes. Thus, performance improvements are relevant and can be achieved by using topology optimization methods. In particular, this work aims to develop a topological derivative formulation to design radial flow machine rotors by considering laminar flow. Based on the concept of traditional topology optimization approaches, in the adopted topological derivative formulation, solid or fluid material is distributed at each point of the domain. This is achieved by combining Navier–Stokes equations on a rotary referential with Darcy’s law equations. This strategy allows for working in a fixed computational domain, which leads to a topology design algorithm of remarkably simple computational implementation. In the optimization problem formulation, a multi-objective function is defined, aiming to minimize the energy dissipation, vorticity and power considering a volume constraint. The constrained optimization problem is rewritten in the form of an unconstrained optimization problem by using the Augmented Lagrangian formalism. The resulting multi-objective shape functional is then minimized with help of the topological derivative concept. In the context of this article, the topological derivative represents the exact sensitivity with respect to the nucleation of an inclusion within the design domain and the obtained analytical (closed) formula can be evaluated through a simple post processing of the solutions to the direct and adjoints problems. Both mentioned features allow for obtaining the optimized designs in few iterations by using a minimal number of user defined algorithm parameters. All equations and the derived continuous adjoint equations are solved through finite element method. As a result, two-dimensional designs of flow machine rotors are obtained by using this methodology. Their performance is analyzed by evaluating velocity and pressure distributions inside rotor.     

基于分解的多目标花朵授粉算法

在过去几十年里，许多多目标进化算法被广泛应用于解决多目标优化问题，其中一种比较流行的多目标进化算法是基于分解的多目标进化算法(MOEA/D)。花朵授粉算法是一种启发式优化算法，但迄今为止，花朵授粉算法在基于分解的多目标进化算法领域的研究还非常少。本文在基于分解的多目标进化算法的框架下，将花朵授粉算法拓展至多目标优化领域，提出一种基于分解的多目标花朵授粉算法(MOFPA/D)。此外，为了保证非支配解的多样性，本文提出一种基于网格的目标空间分割法，该方法从找到的Pareto最优解集中筛选出一定数量且分布均匀的Pareto最优解。实验结果表明，基于分解的多目标花朵授粉算法在收敛性与多样性方面均优于基于分解的多目标进化算法。     

含区间参数多目标系统的微粒群优化算法

参数不确定优化问题是实践中经常遇到的复杂优化问题, 现有方法多针对单目标函数的情况. 本文利用微粒群优化算法解决含区间参数多目标优化问题, 提出一种基于概率支配的多目标微粒群优化算法. 该算法通过定义概率支配关系, 比较所得解的优劣; 基于 σ 区间值, 选择微粒的全局极值点, 并给出新的微粒个体极值点及外部储备集的更新策略. 与传统多目标微粒群优化算法比较, 仿真结果表明本文所提算法的有效性.     

Perturbed Decomposition Algorithm applied to the multi-objective Traveling Salesman Problem

Dealing with multi-objective combinatorial optimization, this article proposes a new multi-objective set-based meta-heuristic named Perturbed Decomposition Algorithm (PDA). Combining ideas from decomposition methods, local search and data perturbation, PDA provides a 2-phase modular framework for finding an approximation of the Pareto front. The first phase decomposes the search into a number of linearly aggregated problems of the original multi-objective problem. The second phase conducts an iterative process: aggregated problems are first perturbed then selected and optimized by an efficient single-objective local search solver. Resulting solutions will serve as a starting point of a multi-objective local search procedure, called Pareto Local Search. After presenting a literature review of meta-heuristics on the multi-objective symmetric Traveling Salesman Problem (TSP), we conduct experiments on several instances of the bi-objective and tri-objective TSP. The experiments show that our proposed algorithm outperforms the best current methods on this problem.     

Multi-objective shape optimization using ant colony coupled computational fluid dynamics solver

An adaptation of a parametric ant colony optimization (ACO) to multi-objective optimization (MOO) is presented in this paper. In this algorithm (here onwards called MACO) the concept of MOO is achieved using the reference point (or goal vector) optimization strategy by applying scalarization. This method translates the multi-objective optimization problem to a single objective optimization problem. The ranking is done using ?-dominance with modified L_p metric strategy. The minimization of the maximum distance from the goal vector drives the solution close to the goal vector. A few validation test cases with multi-objectives have been demonstrated. MACO was found to out perform R-NSGA-II for the test cases considered. This algorithm was then integrated with a meshless computational fluid dynamics (CFD) solver to perform aerodynamic shape optimization of an airfoil. The algorithm was successful in reaching the optimum solutions near to the goal vector on one hand. On the other hand the algorithm converged to an optimum outside the boundary specified by the user for the control variables. These make MACO a good contender for multi-objective shape optimization problems.     

Evolutionary multi-objective blocking lot-streaming flow shop scheduling with interval processing time

A blocking lot-streaming flow shop scheduling problem with interval processing time has a wide range of applications in various industrial systems, however, not yet been well studied. In this paper, the problem is formulated as a multi-objective optimization problem, where each interval objective is converted into a real-valued one using a dynamically weighted sum of its midpoint and radius. A novel evolutionary multi-objective optimization algorithm is then proposed to solve the re-formulated multi-objective optimization problem, in which non-dominated solutions and differences among parents are taken advantage of when designing the crossover operator, and an ideal-point assisted local search strategy for multi-objective optimization is employed to improve the exploitation capability of the algorithm. To empirically evaluate the performance of the proposed algorithm, a series of comparative experiments are conducted on 24 scheduling instances. The experimental results show that the proposed algorithm outperforms the compared algorithms in convergence, and is more capable of tackling uncertainties.     

Multi-objective colonial competitive algorithm for hybrid flowshop problem

This study analyses the multi-objective optimization in hybrid flowshop problem, in which two conflicting objectives, makespan and total weighted tardiness, are considered to be minimized simultaneously. The multi-objective version of Colonial Competitive Algorithm (CCA) for real world optimization problem is introduced and investigated. In contrast to multi-objective problems solved by CCA, presented in the literature, which used the combination of the objectives as single objective, the proposed algorithm is established on Pareto solutions concepts. Another novelty of this paper is estimating the power of each imperialist by a probabilistic criterion for this multi objective algorithm. Besides that, the variable neighborhood search is implemented as an assimilation strategy. Performance of the algorithm is finally compared with a famous algorithm for scheduling problem, NSGA-II, and the multi-objective form of CCA [28].     

Multi-objective optimization of machining and micro-machining processes using non-dominated sorting teaching–learning-based optimization algorithm

Selection of optimum machining parameters is vital to the machining processes in order to ensure the quality of the product, reduce the machining cost, increasing the productivity and conserve resources for sustainability. Hence, in this work a posteriori multi-objective optimization algorithm named as Non-dominated Sorting Teaching–Learning-Based Optimization (NSTLBO) is applied to solve the multi-objective optimization problems of three machining processes namely, turning, wire-electric-discharge machining and laser cutting process and two micro-machining processes namely, focused ion beam micro-milling and micro wire-electric-discharge machining. The NSTLBO algorithm is incorporated with non-dominated sorting approach and crowding distance computation mechanism to maintain a diverse set of solutions in order to provide a Pareto-optimal set of solutions in a single simulation run. The results of the NSTLBO algorithm are compared with the results obtained using GA, NSGA-II, PSO, iterative search method and MOTLBO and are found to be competitive. The Pareto-optimal set of solutions for each optimization problem is obtained and reported. These Pareto-optimal set of solutions will help the decision maker in volatile scenarios and are useful for real production systems.     

A study of interval metric and its application in multi-objective optimization with interval objectives

The aim of this paper is to discuss the optimality of interval multi-objective optimization problems with the help of different interval metric. For this purpose, we have proposed the new definitions of interval order relations by modifying the existing definitions and also modified different definitions of interval mathematics. Using the definitions of interval order relations and interval metric, the multi-objective optimization problem is converted into single objective optimization problem by different techniques. Then the corresponding problems have been solved by hybrid Tournament Genetic Algorithm with whole arithmetic crossover and double mutation (combination of non-uniform and boundary mutations). To illustrate the methodology, five numerical examples have been solved and the computational results have been compared. Finally, to test the efficiency of the proposed hybrid Tournament Genetic Algorithm, sensitivity analyses have been carried out graphically with respect to genetic algorithm parameters.     

求解一类不可微多目标优化问题的社会认知算法*

针对一类不可微多目标优化问题,给出了一个新的算法——极大熵社会认知算法。利用极大熵方法将带有约束的不可微多目标优化问题转化为无约束单目标优化问题,然后利用社会认知算法对其进行求解。该算法是基于社会认知理论,通过一系列的学习代理来模拟人类的社会性和智能性从而完成对目标的优化。利用两个测试算例对其进行测试并与其他算法进行比较,计算结果表明,该算法在求解的准确性和有效性方面均优于其他算法。     

A particle swarm optimization for a fuzzy multi-objective unrelated parallel machines scheduling problem

This paper proposes a novel multi-objective model for an unrelated parallel machine scheduling problem considering inherent uncertainty in processing times and due dates. The problem is characterized by non-zero ready times, sequence and machine-dependent setup times, and secondary resource constraints for jobs. Each job can be processed only if its required machine and secondary resource (if any) are available at the same time. Finding optimal solution for this complex problem in a reasonable time using exact optimization tools is prohibitive. This paper presents an effective multi-objective particle swarm optimization (MOPSO) algorithm to find a good approximation of Pareto frontier where total weighted flow time, total weighted tardiness, and total machine load variation are to be minimized simultaneously. The proposed MOPSO exploits new selection regimes for preserving global as well as personal best solutions. Moreover, a generalized dominance concept in a fuzzy environment is employed to find locally Pareto-optimal frontier. Performance of the proposed MOPSO is compared against a conventional multi-objective particle swarm optimization (CMOPSO) algorithm over a number of randomly generated test problems. Statistical analyses based on the effect of each algorithm on each objective space show that the proposed MOPSO outperforms the CMOPSO in terms of quality, diversity and spacing metrics.     

Development and correlation analysis of non-dominated sorting buffalo optimization NSBUF II using Taguchi’s design coupled gray relational analysis and ANN

African Buffalo Optimization (ABO) is a latest bio-inspired optimization technique in the domain of evolutionary optimization, which mimics the migratory behaviour of the buffalo foraging for food across the African plains and forests. The ABO is, by now, recognized as a single-objective optimization algorithm, comprising the ability to solve both, the continuous and discrete optimization problems. However, a multi-objective version of ABO could be more useful for industrial problems. An aim is made in this article to develop the multi-objective variant of ABO, namely NSBUF II, which incorporates Pareto search for non-dominated solutions in the state space and a local search module for faster convergence. Selection of parameters for the NSBUF II is extremely sensitive to the obtained Pareto fronts. Thus, a Grey Relational Analysis (GRA) coupled with Taguchi’s L₁₆ orthogonal array is adopted, which efficiently obtains the best set of parameters for the NSBUF II. Initially the proposed NSBUF II is tested using utilization based bi-objective production cell design problem and compared with published Multi-Objective Particle Swarm Optimization (MOPSO), and Non-dominated Sorting Genetic Algorithm (NSGA II) successfully. To analyse the performance of the NSBUF II, Self-Organizing Map (SOM) is applied, which is a powerful tool for visualizing the high-dimensional data in low dimensional maps. Applied SOM visually reveals the hidden correlational structure among the design parameters and the objective space. The performance of the NSBUF II is validated statistically NSBUF II is further verified with a real-world case obtained based on the Abrasive Water Jet Machining (AWJM) process. Validation test proves the competence of the proposed NSBUF II for real-world problem solving. The contribution of this paper is threefold. First, a novel multi-objective NSBUF II algorithm is developed. Second, a SOM based visual analysis is proposed to visualize the correlation among design parameters and Pareto fronts. Third, the NSBUF II is employed to solve a combinatorial production cell design problem followed by a real-world industrial problem.     

基于知识的污水生化处理过程智能优化方法

针对污水处理过程控制能耗过大和水质超标严重等问题,本文提出一种基于知识的污水生化处理过程智能优化控制方法.该方法通过记忆多目标智能优化算法的动态处理信息,建立环境变量参数与最优解之间的知识模型.优化算法利用知识库中非支配解的引导,结合定向局部区域寻优以及随机全局寻优策略,提高了算法的收敛性,获取了更高质量的解.最后基于国际通用平台BSM1进行实验验证.结果表明,与其他优化算法相比,该方法能够在保证出水水质的前提下产生更少的能量消耗.