A new multi-objective particle swarm optimizer using empirical movement and diversified search strategies

Most real-world optimization problems involve the optimization task of more than a single objective function and, therefore, require a great amount of computational effort as the solution procedure is designed to anchor multiple compromised optimal solutions. Abundant multi-objective evolutionary algorithms (MOEAs) for multi-objective optimization have appeared in the literature over the past two decades. In this article, a new proposal by means of particle swarm optimization is addressed for solving multi-objective optimization problems. The proposed algorithm is constructed based on the concept of Pareto dominance, taking both the diversified search and empirical movement strategies into account. The proposed particle swarm MOEA with these two strategies is thus dubbed the empirical-movement diversified-search multi-objective particle swarm optimizer (EMDS-MOPSO). Its performance is assessed in terms of a suite of standard benchmark functions taken from the literature and compared to other four state-of-the-art MOEAs. The computational results demonstrate that the proposed algorithm shows great promise in solving multi-objective optimization problems.     

AMGA2: improving the performance of the archive-based micro-genetic algorithm for multi-objective optimization

In this article, an improved Archive-based Micro Genetic Algorithm (referred to as AMGA2) for constrained multi-objective optimization is proposed. AMGA2 is designed to obtain fast and reliable convergence on a wide variety of optimization problems. AMGA2 benefits from the existing literature in that it borrows and improves upon several concepts from existing multi-objective optimization algorithms. Improvements and modifications to the existing diversity assessment techniques and genetic variation operators are also proposed. AMGA2 employs a new kind of selection strategy that attempts to reduce the probability of exploring less desirable search regions. The proposed AMGA2 is a steady-state genetic algorithm that maintains an external archive of best and diverse solutions and a very small working population. AMGA2 has been designed to facilitate the decoupling of the working population, the external archive, and the number of solutions desired as the outcome of the optimization process. Comprehensive benchmarking and comparison of AMGA2 with the current state-of-the-art multi-objective optimization algorithms demonstrate its improved search capability.     

Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems

Two techniques for the numerical treatment of multi-objective optimization problems—a continuation method and a particle swarm optimizer—are combined in order to unite their particular advantages. Continuation methods can be applied very efficiently to perform the search along the Pareto set, even for high-dimensional models, but are of local nature. In contrast, many multi-objective particle swarm optimizers tend to have slow convergence, but instead accomplish the ‘global task’ well. An algorithm which combines these two techniques is proposed, some convergence results for continuous models are provided, possible realizations are discussed, and finally some numerical results are presented indicating the strength of this novel approach.     

Evolutionary methods for multidisciplinary optimization applied to the design of UAV systems†

The implementation and use of a framework in which engineering optimization problems can be analysed are described. In the first part, the foundations of the framework and the hierarchical asynchronous parallel multi-objective evolutionary algorithms (HAPMOEAs) are presented. These are based upon evolution strategies and incorporate the concepts of multi-objective optimization, hierarchical topology, asynchronous evaluation of candidate solutions, and parallel computing. The methodology is presented first and the potential of HAPMOEAs for solving multi-criteria optimization problems is demonstrated on test case problems of increasing difficulty. In the second part of the article several recent applications of multi-objective and multidisciplinary optimization (MO) are described. These illustrate the capabilities of the framework and methodology for the design of UAV and UCAV systems. The application presented deals with a two-objective (drag and weight) UAV wing plan-form optimization. The basic concepts are refined and more sophisticated software and design tools with low- and high-fidelity CFD and FEA models are introduced. Various features described in the text are used to meet the challenge in optimization presented by these test cases.     

一种基于“探测"与“开采"的多目标进化算法

针对实践中多目标优化问题(MOPs)的Pareto解集(PS)未知且比较复杂的特性,提出了一种基于"探测"(Exploration)与"开采"(Exploitation)的多目标进化算法(MOEA)——MOEA/2E。该算法在进化过程中采用"探测"与"开采"相结合的方法,用进化操作不断地探测新的搜索区域,用局部搜索充分开采优秀的解区域,并用隐最优个体保留机制保存每一代的最优个体。与目前最流行且有效的多目标进化算法NSGA-Ⅱ及SPEA-Ⅱ进行的比较实验结果表明,MOEA/2E获得的Pareto最优解集具有更好的收敛性与分布性。     

Scalability of surrogate-assisted multi-objective optimization of antenna structures exploiting variable-fidelity electromagnetic simulation models

Multi-objective optimization of antenna structures is a challenging task owing to the high computational cost of evaluating the design objectives as well as the large number of adjustable parameters. Design speed-up can be achieved by means of surrogate-based optimization techniques. In particular, a combination of variable-fidelity electromagnetic (EM) simulations, design space reduction techniques, response surface approximation models and design refinement methods permits identification of the Pareto-optimal set of designs within a reasonable timeframe. Here, a study concerning the scalability of surrogate-assisted multi-objective antenna design is carried out based on a set of benchmark problems, with the dimensionality of the design space ranging from six to 24 and a CPU cost of the EM antenna model from 10 to 20 min per simulation. Numerical results indicate that the computational overhead of the design process increases more or less quadratically with the number of adjustable geometric parameters of the antenna structure at hand, which is a promising result from the point of view of handling even more complex problems.     

Constrained multi-objective optimization algorithm with an ensemble of constraint handling methods

Different constraint handling techniques have been used with multi-objective evolutionary algorithms (MOEA) to solve constrained multi-objective optimization problems. It is impossible for a single constraint handling technique to outperform all other constraint handling techniques always on every problem irrespective of the exhaustiveness of the parameter tuning. To overcome this selection problem, an ensemble of constraint handling methods (ECHM) is used to tackle constrained multi-objective optimization problems. The ECHM is integrated with a multi-objective differential evolution (MODE) algorithm. The performance is compared between the ECHM and the same single constraint handling methods using the same MODE (using codes available from http://www3.ntu.edu.sg/home/EPNSugan/index.htm). The results show that ECHM overall outperforms the single constraint handling methods.     

Optimisation of a multi-objective two-dimensional strip packing problem based on evolutionary algorithms

This paper considers a real-world two-dimensional strip packing problem involving specific machinery constraints and actual cutting production industry requirements. To adapt the problem to a wider range of machinery characteristics, the design objective considers the minimisation of material length and the total number of cuts for guillotinable-type patterns. The number of cuts required for the cutting process is crucial for the life of the industrial machines and is an important aspect in determining the cost and efficiency of the cutting operation. In this paper we propose the application of evolutionary algorithms to address the multi-objective problem, for which numerous approaches to its single-objective formulation exist, but for which multi-objective approaches are almost non-existent. The multi-objective evolutionary algorithms applied provide a set of solutions offering a range of trade-offs between the two objectives from which clients can choose according to their needs. By considering both the length and number of cuts, they derive solutions with wastage levels similar to most previous approximations which just seek to optimise the overall length.     

Sequential interactive evolution for finding high-quality topologies

Finding a diverse set of high-quality (HQ) topologies for a single-objective optimization problem using an evolutionary computation algorithm can be difficult without a reliable measure that adequately describes the dissimilarity between competing topologies. In this article, a new approach for enhancing diversity among HQ topologies for engineering design applications is proposed. The technique initially selects one HQ solution and then searches for alternative HQ solutions by performing an optimization of the original objective and its dissimilarity with respect to the previously found solution. The proposed multi-objective optimization approach interactively amalgamates user articulated preferences with an evolutionary search so as sequentially to produce a set of diverse HQ solutions to a single-objective problem. For enhancing diversity, a new measure is suggested and an approach to reducing its computational time is studied and implemented. To illustrate the technique, a series of studies involving different topologies represented as bitmaps is presented.     

An enhanced preference-inspired co-evolutionary algorithm using orthogonal design and an ε-dominance archiving strategy

The concept of co-evolution of preferences and candidate solutions has proven effective for many-objective optimization. One realization of this concept, namely preference-inspired co-evolutionary algorithms using goal vectors (PICEA-g), is found to outperform many state-of-the-art multi-objective evolutionary algorithms for many-objective problems. However, PICEA-g is susceptible to unevenness in the solution distribution. This study seeks to tackle this issue and to improve the performance of PICEA-g further. Two established strategies are incorporated into PICEA-g: (i) an adaptive ε-dominance archiving strategy which is applied to obtain a set of well spread solutions online; and (ii) the orthogonal design method which is used to initialize candidate solutions. The improved algorithm, denoted as aε-ODPICEA-g, shows a better performance than PICEA-g on both 2- and 7-objective benchmark problems as well as a real-world problem.     

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.     

Optimal reservoir flood operation using a decomposition-based multi-objective evolutionary algorithm

Reservoir flood control operation (RFCO) is a challenging optimization problem with interdependent decision variables and multiple conflicting criteria. By considering safety both upstream and downstream of the dam, a multi-objective optimization model is built for RFCO. To solve this problem, a multi-objective optimizer, the multi-objective evolutionary algorithm based on decomposition–differential evolution (MOEA/D-DE), is developed by introducing a differential evolution-inspired recombination into the algorithmic framework of the decomposition-based multi-objective optimization algorithm, which has been proven to be effective for solving complex multi-objective optimization problems. Experimental results on four typical floods at the Ankang reservoir illustrated that the suggested algorithm outperforms or performs as well as the comparison algorithms. It can significantly reduce the flood peak and also guarantee the dam’s safety.     

Multi-objective analysis of a component-based representation within an interactive evolutionary design system

This article describes research relating to a user-centered evolutionary design system that evaluates both engineering and aesthetic aspects of design solutions during early-stage conceptual design. The experimental system comprises several components relating to user interaction, problem representation, evolutionary search and exploration and online learning. The main focus of the article is the evolutionary aspect of the system when using a single quantitative objective function plus subjective judgment of the user. Additionally, the manner in which the user-interaction aspect affects system output is assessed by comparing Pareto frontiers generated with and without user interaction via a multi-objective evolutionary algorithm (MOEA). A solution clustering component is also introduced and it is shown how this can improve the level of support to the designer when dealing with a complex design problem involving multiple objectives. Supporting results are from the application of the system to the design of urban furniture which, in this case, largely relates to seating design.     

一种快速构造非支配集的方法--擂台法则

多目标进化算法是用来解决多目标优化问题的,为了提高多目标算法的效率,提出了一种快速构造非支配集的方法——擂台法则。它的时间耗费要低于Deb和Jensen提出的构造非支配集的方法。在实验中将擂台法则同Deb和Jensen的方法进行了比较,最后实验结果证明前者在运行时间上要优于后两者。     

Multi-objective optimization of engineering systems using game theory and particle swarm optimization

This study proposes particle swarm optimization (PSO) based algorithms to solve multi-objective engineering optimization problems involving continuous, discrete and/or mixed design variables. The original PSO algorithm is modified to include dynamic maximum velocity function and bounce method to enhance the computational efficiency and solution accuracy. The algorithm uses a closest discrete approach (CDA) to solve optimization problems with discrete design variables. A modified game theory (MGT) approach, coupled with the modified PSO, is used to solve multi-objective optimization problems. A dynamic penalty function is used to handle constraints in the optimization problem. The methodologies proposed are illustrated by several engineering applications and the results obtained are compared with those reported in the literature.     

Optimum plate-fin heat sinks by using a multi-objective evolutionary algorithm

This article demonstrates the practical applications of a multi-objective evolutionary algorithm (MOEA) namely population-based incremental learning (PBIL) for an automated shape optimization of plate-fin heat sinks. The computational procedure of multi-objective PBIL is detailed. The design problem is posed to find heat sink shapes which minimize the junction temperature and fan pumping power while meeting predefined constraints. Three sets of shape design variables used in this study are defined as: vertical straight fins with fin height variation, oblique straight fins with steady fin heights, and oblique straight fins with fin height variation. The optimum results obtained from using the various sets of design variables are illustrated and compared. It can be said that, with this sophisticated design system, efficient and effective design of plate-fin heat sinks is achievable and the best design variables set is the oblique straight fins with fin height variation.     

Effective multi-objective optimization with the coral reefs optimization algorithm

In this article a new algorithm for multi-objective optimization is presented, the Multi-Objective Coral Reefs Optimization (MO-CRO) algorithm. The algorithm is based on the simulation of processes in coral reefs, such as corals' reproduction and fight for space in the reef. The adaptation to multi-objective problems is a process based on domination or non-domination during the process of fight for space in the reef. The final MO-CRO is an easily-implemented and fast algorithm, simple and robust, since it is able to keep diversity in the population of corals (solutions) in a natural way. The experimental evaluation of this new approach for multi-objective optimization problems is carried out on different multi-objective benchmark problems, where the MO-CRO has shown excellent performance in cases with limited computational resources, and in a real-world problem of wind speed prediction, where the MO-CRO algorithm is used to find the best set of features to predict the wind speed, taking into account two objective functions related to the performance of the prediction and the computation time of the regressor.     

多学科集成下的老年智能产品设计研究

目的 基于多学科集成理论,分析老年智能产品设计现状,在了解老年用户群体对产品需求的基础上,进行设计实践创新方法研究。方法 通过阐明多学科集成方法中系统化、框架化、协同化、优化算法等理论,针对使用者、设计者双方进行分析,寻找出产品设计过程中存在的问题,在服务设计原则和多学科集成的理论支持下,进而推导出设计思路和方法。 结论 提出老年智能产品设计的基础是用户的操作体验和特定需求,设计过程涉及多学科、多目标;以“多目标实现”“多学科综合系统模型”“新技术融合”等应用实例,解释了如何解决产品设计过程中,由于用户需求复杂所产生的计算复杂性和选择复杂性等问题,优化了设计框架,归纳了设计信息,提升了设计过程的合理性、高效性和准确性。     

基于满意度函数的新型逃生管道多目标稳健性设计

新型逃生管道参数具有不确定性且单目标优化存在局限性，为了实现新型逃生管道多目标稳健性设计，结合田口稳健性设计方法与满意度函数，提出了一种基于满意度函数的多目标稳健性设计方法。该方法将产品质量特性的信噪比转换为具有田口稳健性设计的望大特性的满意度，然后通过加权几何均值实现结构的多目标稳健性设计。通过使用Hypermesh和LS-DYNA建立新型逃生管道的有限元模型，并对该有限元模型进行验证，然后运用所提出的方法对新型逃生管道进行多目标稳健性设计。结果表明，稳健性设计后新型逃生管道的信噪比提升了5.3%，说明管道抵抗噪声因子的干扰能力增强，结构更稳健；新型逃生管道质量降低了9.6%，实现了管道轻量化的目的。研究结果对提高新型逃生管道的稳健性具有一定的理论和工程意义。     

Aerodynamic optimization using a parallel asynchronous evolutionary algorithm controlled by strongly interacting demes

A parallel asynchronous evolutionary algorithm controlled by strongly interacting demes for single- and multi-objective optimization problems is proposed. It is suitable even for non-homogeneous, multiprocessor systems, ensuring maximum exploitation of the available processors. The search algorithm utilizes a structured topology of evaluation agents organized in a number of inter-communicating demes arranged on a 2D supporting mesh. Once an evaluation terminates and a processor becomes idle, a series of intra- and inter-deme processes determines the next agent to undergo evaluation on this specific processor. Real coding and differential evolution operators are used. Mathematical and aerodynamic-turbomachinery optimization problems are presented to assess the proposed method in terms of CPU cost, parallel efficiency and quality of solutions obtained within a predefined number of evaluations. Comparisons with conventional evolutionary algorithms, parallelized based on the master–slave model on the same computational platform, are presented.