约束进化算法及其应用研究综述

约束优化问题广泛存在于科学研究和工程实践中,其对应的约束优化进化算法也成为了进化领域的重要研究方向。约束优化进化算法的本质问题是如何有效地利用不可行解和可行解的信息,平衡目标函数和约束条件,使得算法更加高效。首先对约束优化问题进行定义;然后详细分析了目前主流的约束进化算法,同时,基于不同的约束处理机制,将这些机制分为约束和目标分离法、惩罚函数法、多目标优化法、混合法和其他算法,并对这些方法进行了详细的分析和总结;接着指出约束进化算法亟待解决的问题,并明确指出未来需要进一步研究的方向;最后对约束进化算法在工程优化、电子和通信工程、机械设计、环境资源配置、科研领域和管理分配等方面的应用进行了介绍。     

Introducing robustness in multi-objective optimization

In optimization studies including multi-objective optimization, the main focus is placed on finding the global optimum or global Pareto-optimal solutions, representing the best possible objective values. However, in practice, users may not always be interested in finding the so-called global best solutions, particularly when these solutions are quite sensitive to the variable perturbations which cannot be avoided in practice. In such cases, practitioners are interested in finding the robust solutions which are less sensitive to small perturbations in variables. Although robust optimization is dealt with in detail in single-objective evolutionary optimization studies, in this paper, we present two different robust multi-objective optimization procedures, where the emphasis is to find a robust frontier, instead of the global Pareto-optimal frontier in a problem. The first procedure is a straightforward extension of a technique used for single-objective optimization and the second procedure is a more practical approach enabling a user to set the extent of robustness desired in a problem. To demonstrate the differences between global and robust multi-objective optimization principles and the differences between the two robust optimization procedures suggested here, we develop a number of constrained and unconstrained test problems having two and three objectives and show simulation results using an evolutionary multi-objective optimization (EMO) algorithm. Finally, we also apply both robust optimization methodologies to an engineering design problem.     

An integrated approach to automated innovization for discovering useful design principles: Case studies from engineering

Computational optimization methods are most often used to find a single or multiple optimal or near-optimal solutions to the underlying optimization problem describing the problem at hand. In this paper, we elevate the use of optimization to a higher level in arriving at useful problem knowledge associated with the optimal or near-optimal solutions to a problem. In the proposed innovization process, first a set of trade-off optimal or near-optimal solutions are found using an evolutionary algorithm. Thereafter, the trade-off solutions are analyzed to decipher useful relationships among problem entities automatically so as to provide a better understanding of the problem to a designer or a practitioner. We provide an integrated algorithm for the innovization process and demonstrate the usefulness of the procedure to three real-world engineering design problems. New and innovative design principles obtained in each case should clearly motivate engineers and practitioners for its further application to more complex problems and its further development as a more efficient data analysis procedure.     

基于幂变换的多目标进化算法MOEA?D权重设计方法

在多目标最优化问题中,如何求解一组均匀散布在前沿界面上的有效解具有重要意义.MOEA?D是最近出现的一种杰出的多目标进化算法,当前沿界面的形状是某种已知的类型时,MOEA?D使用高级分解的方法容易求出均匀散布在前沿界面上的有效解.然而,多目标优化问题的前沿界面的形状通常是未知的.为了使MOEA?D能求出一般多目标优化问题的均匀散布的有效解,利用幂函数对目标进行数学变换,使变换后的多目标优化问题的前沿界面在算法的进化过程中逐渐接近希望得到的形状,提出了一种求解一般的多目标优化问题的MOEA?D算法的权重设计方法,并且讨论了经过数学变换后前沿界面的保距性问题.采用建议的权重设计方法,MOEA?D更容易求出一般的多目标优化问题均匀散布的有效解.数值结果验证了算法的有效性.     

一种改进的鲁棒多目标优化方法

针对在解决某些复杂多目标优化问题过程中,所得到的Pareto最优解易受设计参数或环境参数扰动的影响,引入了鲁棒的概念并提出一种改进的鲁棒多目标优化方法,它利用了经典的基于适应度函数期望和方差方法各自的优势,有效地将两种方法结合在一起。为了实现该方法,给出一种基于粒子群优化算法的多目标优化算法。仿真实例结果表明,所给出的方法能够得到更为鲁棒的Pareto最优解。     

Constraint-based modelling and optimization to support the design of complex multi-domain engineering problems

We present a constraint-based methodology which is successfully applied to a variety of engineering problems from a wide range of disciplines. Initially conceived from investigations of the engineering design process, the methodology has helped design engineers to identify and understand the initial limitations placed upon a system. Written as a set of algebraic expressions, the design objectives and design constraints can be formulated and minima found using numerical optimization techniques. These solutions provide initial configurations for the system, corresponding to how “true” all of the constraints are. A bespoke constraint-based modelling environment has been created which embodies the methodology. This is able to resolve large systems, comprising over 100 degrees-of-freedom, using an assortment of optimization routines—direct, gradient and evolutionary algorithms. These algorithms are appropriate for a number of problem types and their inclusion increase the scope of applicability of the methodology which is demonstrated using case studies from a number of engineering domains. Machines and mechanisms; human modelling; force and flow; structural geology and discrete disassembly processes are all studied using constraint-based formulations. The contribution of the paper lies in thus proving that complex (heterogeneous) systems-of-systems can be solved if the connectivity between the systems is expressed using constraint-rules.     

Evolutionary computation approaches for real offshore wind farm layout: A case study in northern Europe

This paper presents the layout optimization of a real offshore wind farm in northern Europe, using evolutionary computation techniques. Different strategies for the wind farm design are tested, such as regular turbines layout or free turbines disposition with fixed number of turbines. Also, different layout quality models have been applied, in order to obtain solutions with different characteristics of high energy production and low interlink cost. In all the cases, evolutionary algorithms are developed and detailed in the paper. The experiments carried out in the real problem show that the free design with fixed number of turbines is more appropriate and obtains better quality layouts than the regular design.     

一个用于多目标优化的进化规划算法

进化计算的群体搜索机制为多目标优化问题的直接求解提供了途径。本文将多目标遗传算法中的一些技术用于进化规划,提出一个多目标进化规划算法,并给出计算实例。     

An adaptive neural network strategy for improving the computational performance of evolutionary structural optimization

This work is focused on improving the computational efficiency of evolutionary algorithms implemented in large-scale structural optimization problems. Locating optimal structural designs using evolutionary algorithms is a task associated with high computational cost, since a complete finite element (FE) analysis needs to be carried out for each parent and offspring design vector of the populations considered. Each of these FE solutions facilitates decision making regarding the feasibility or infeasibility of the corresponding structural design by evaluating the displacement and stress constraints specified for the structural problem at hand. This paper presents a neural network (NN) strategy to reliably predict, in the framework of an evolution strategies (ES) procedure for structural optimization, the feasibility or infeasibility of structural designs avoiding computationally expensive FE analyses. The proposed NN implementation is adaptive in the sense that the utilized NN configuration is appropriately updated as the ES process evolves by performing NN retrainings using information gradually accumulated during the ES execution. The prediction capabilities and the computational advantages offered by this adaptive NN scheme coupled with domain decomposition solution techniques are investigated in the context of design optimization of skeletal structures on both sequential and parallel computing environments.     

A population-based algorithm-generator for real-parameter optimization

In this paper, we propose a population-based, four-step, real-parameter optimization algorithm-generator. The approach divides the task of reaching near the optimum solution into four independent plans of (i) selecting good solutions from a solution base, (ii) generating new solutions using the selected solutions, (iii) choosing inferior or spurious solutions for replacement, and (iv) updating the solution base with good new or old solutions. Interestingly, many classical and evolutionary optimization algorithms are found to be representable by this algorithm-generator. The paper also recommends an efficient optimization algorithm with the possibility of using a number of different recombination plans and parameter values. With a systematic parametric study, the paper finally recommends a real-parameter optimization algorithm which outperforms a number of existing classical and evolutionary algorithms. To extend this study, the proposed algorithm-generator can be utilized to develop new and more efficient population-based optimization algorithms. The treatment of population-based classical and evolutionary optimization algorithms identically through the proposed algorithm-generator is the main hall-mark of this paper and should enable researchers from both classical and evolutionary fields to understand each others methods better and interact in a more coherent manner.     

Comparison of evolutionary-based optimization algorithms for structural design optimization

In this paper, a comparison of evolutionary-based optimization techniques for structural design optimization problems is presented. Furthermore, a hybrid optimization technique based on differential evolution algorithm is introduced for structural design optimization problems. In order to evaluate the proposed optimization approach a welded beam design problem taken from the literature is solved. The proposed approach is applied to a welded beam design problem and the optimal design of a vehicle component to illustrate how the present approach can be applied for solving structural design optimization problems. A comparative study of six population-based optimization algorithms for optimal design of the structures is presented. The volume reduction of the vehicle component is 28.4% using the proposed hybrid approach. The results show that the proposed approach gives better solutions compared to genetic algorithm, particle swarm, immune algorithm, artificial bee colony algorithm and differential evolution algorithm that are representative of the state-of-the-art in the evolutionary optimization literature.     

Multiobjective evolutionary optimization of DNA sequences for reliable DNA computing

DNA computing relies on biochemical reactions of DNA molecules and may result in incorrect or undesirable computations. Therefore, much work has focused on designing the DNA sequences to make the molecular computation more reliable. Sequence design involves with a number of heterogeneous and conflicting design criteria and traditional optimization methods may face difficulties. In this paper, we formulate the DNA sequence design as a multiobjective optimization problem and solve it using a constrained multiobjective evolutionary algorithm (EA). The method is implemented into the DNA sequence design system, NACST/Seq, with a suite of sequence-analysis tools to help choose the best solutions among many alternatives. The performance of NACST/Seq is compared with other sequence design methods, and analyzed on a traveling salesman problem solved by bio-lab experiments. Our experimental results show that the evolutionary sequence design by NACST/Seq outperforms in its reliability the existing sequence design techniques such as conventional EAs, simulated annealing, and specialized heuristic methods.     

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.     

Interactive Evolutionary Multiobjective Search and Optimization of Set-Based Concepts

This paper deals with interactive concept-based multiobjective problems (IC-MOPs) and their solution by an evolutionary computation approach. The presented methodology is motivated by the need to support engineers during the conceptual design stage. IC-MOPs are based on a nontraditional concept-based approach to search and optimization. It involves conceptual solutions, which are represented by sets of particular solutions, with each concept having a one-to-many relation with the objective space. Such a set-based concept representation is most suitable for human–computer interaction. Here, a fundamental type of IC-MOPs, namely, the Pareto-directed one, is formally defined, and its solution is presented. Next, a new interactive concept-based multiobjective evolutionary algorithm is introduced, and measures to assess its resulting fronts are devised. Finally, the proposed approach and the suggested search algorithm are studied using both academic test functions and an engineering problem.      

基于多点加点准则的代理模型辅助社会学习微粒群算法

代理模型辅助的进化算法目前已广泛用于解决计算代价高的复杂优化问题.然而,大多数现有的代理辅助进化算法只适用于低维问题且仍然需要数千次昂贵的真实适应值评价来获得较优解.为此,提出一种基于多点加点准则的代理模型辅助的社会学习微粒群算法,用于解决高维问题并使用更少的评价次数.该算法选用高斯过程构造代理模型,以社会学习微粒群算法(SLPSO)作为优化器,提出一种基于相似度的多点加点规则(SMIC),用于选取需要使用原函数进行实际计算的候选解.在仿真实验中将该方法与现有研究成果进行比较,通过对50维sim100维的基准函数的测试,验证了所提出算法在有限的适应值计算次数下拥有更好的寻优性能,尤其是在高维优化问题上拥有更显著的优势.     

A polar-based guided multi-objective evolutionary algorithm to search for optimal solutions interested by decision-makers in a logistics network design problem

In practical multi-objective optimization problems, respective decision-makers might be interested in some optimal solutions that have objective values closer to their specified values. Guided multi-objective evolutionary algorithms (guided MOEAs) have been significantly used to guide their evolutionary search direction toward these optimal solutions using by decision makers. However, most guided MOEAs need to be iteratively and interactively evaluated and then guided by decision-makers through re-formulating or re-weighting objectives, and it might negatively affect the algorithms performance. In this paper, a novel guided MOEA that uses a dynamic polar-based region around a particular point in objective space is proposed. Based on the region, new selection operations are designed such that the algorithm can guide the evolutionary search toward optimal solutions that are close to the particular point in objective space without the iterative and interactive efforts. The proposed guided MOEA is tested on the multi-criteria decision-making problem of flexible logistics network design with different desired points. Experimental results show that the proposed guided MOEA outperforms two most effective guided and non-guided MOEAs, R-NSGA-II and NSGA-II.     

Exterior lighting computer-automated design based on multi-criteria parallel evolutionary algorithm: optimized designs for illumination quality and energy efficiency

A proper professional lighting design implies in a continuous search for the best compromise between both low power consumption and better lighting quality. This search converts this design into a hard to solve multi-objective optimization problem. Evolutionary algorithms are widely used to attack that type of hard optimization problems. However, professionals could not benefit from that kind of assistance since evolutionary algorithms have been unexplored by several commercial lighting design computer-aided softwares. This work proposes a system based on evolutionary algorithms which implement a computer-automated exterior lighting design both adequate to irregular shaped areas and able to respect lighting pole positioning constraints. The desired lighting design is constructed using a cluster of computers supported by a web client, turning this application into an efficient and easy tool to reduce project cycles, increase quality of results and decrease calculation times. This ELCAutoD-EA system consists in a proposal for a parallel multi-objective evolutionary algorithm to be executed in a cluster of computers with a Java remote client. User must choose lighting pole heights, allowed lamps and fixtures, as well as the simplified blue print of the area to be illuminated, marking the sub-areas with restrictions to pole positioning. The desired average illuminance must also be informed as well as the accepted tolerance. Based on user informed data, the developed application uses a dynamic representation of variable size as a chromosome and the cluster executes the evolutionary algorithm using the Island model paradigm. Achieved solutions comply with the illumination standards requirements and have a strong commitment to lighting quality and power consumption. In the present case study, the evolved design used 37.5% less power than the reference lighting design provided by a professional and at the same time ensured a 227.3% better global lighting uniformity. A better lighting quality is achieved because the proposed system solves multi-objective optimization problems by avoiding power wastes which are often unclear to a professional lighting engineer in charge of a given project.     

An evolutionary strategy for global minimization and its Markovchain analysis

The mutation-or-selection evolutionary strategy (MOSES) is presented. The goal of this strategy is to solve complex discrete optimization problems. MOSES evolves a constant sized population of labeled solutions. The dynamics employ mechanisms of mutation and selection. At each generation, the best solution is selected from the current population. A random binomial variable N which represents the number of offspring by mutation is sampled. Therefore the N first solutions are replaced by the offspring, and the other solutions are replaced by replicas of the best solution. The relationships between convergence, the parameters of the strategy, and the geometry of the optimization problem are theoretically studied. As a result, explicit parametrizations of MOSES are proposed     

Evolutionary natural frequency optimization of thin plate bending vibration problems

This paper extends the evolutionary structural optimization method to the solution for maximizing the natural frequencies of bending vibration thin plates. Two kinds of constraint conditions are considered in the evolutionary structural optimization method. If the weight of a target structure is set as a constraint condition during the natural frequency optimization, the optimal structural topology can be found by removing the most ineffectively used material gradually from the initial design domain of a structure until the weight requirement is met for the target structure. However, if the specific value of a particular natural frequency is set as a constraint condition for a target structure, the optimal structural topology can be found by using a design chart. This design chart describes the evolutionary process of the structure and can be generated by the information associated with removing the most inefficiently used material gradually from the initial design domain of a structure until the minimum weight is met for maintaining the integrity of a structure. The main advantage in using the evolutionary structural optimization method lies in the fact that it is simple in concept and easy to be included into existing finite element codes. Through applying the extended evolutionary structural optimization method to the solution for the natural frequency optimization of a thin plate bending vibration problem, it has been demonstrated that the extended evolutionary structural optimization method is very useful in dealing with structural topology optimization problems.