Memetic algorithm using multi-surrogates for computationally expensive optimization problems

In this paper, we present a multi-surrogates assisted memetic algorithm for solving optimization problems with computationally expensive fitness functions. The essential backbone of our framework is an evolutionary algorithm coupled with a local search solver that employs multi-surrogate in the spirit of Lamarckian learning. Inspired by the notion of ‘blessing and curse of uncertainty’ in approximation models, we combine regression and exact interpolating surrogate models in the evolutionary search. Empirical results are presented for a series of commonly used benchmark problems to demonstrate that the proposed framework converges to good solution quality more efficiently than the standard genetic algorithm, memetic algorithm and surrogate-assisted memetic algorithms.     

An orthogonal multi-objective evolutionary algorithm for multi-objective optimization problems with constraints

In this paper, an orthogonal multi-objective evolutionary algorithm (OMOEA) is proposed for multi-objective optimization problems (MOPs) with constraints. Firstly, these constraints are taken into account when determining Pareto dominance. As a result, a strict partial-ordered relation is obtained, and feasibility is not considered later in the selection process. Then, the orthogonal design and the statistical optimal method are generalized to MOPs, and a new type of multi-objective evolutionary algorithm (MOEA) is constructed. In this framework, an original niche evolves first, and splits into a group of sub-niches. Then every sub-niche repeats the above process. Due to the uniformity of the search, the optimality of the statistics, and the exponential increase of the splitting frequency of the niches, OMOEA uses a deterministic search without blindness or stochasticity. It can soon yield a large set of solutions which converges to the Pareto-optimal set with high precision and uniform distribution. We take six test problems designed by Deb, Zitzler et al., and an engineering problem (W) with constraints provided by Ray et al. to test the new technique. The numerical experiments show that our algorithm is superior to other MOGAS and MOEAs, such as FFGA, NSGAII, SPEA2, and so on, in terms of the precision, quantity and distribution of solutions. Notably, for the engineering problem W, it finds the Pareto-optimal set, which was previously unknown.     

A new VPS-based algorithm for multi-objective optimization problems

In this paper, a multi-objective variant of the vibrating particles system (MOVPS) is introduced. The new algorithm uses an external archive to keep the non-dominated solutions. Besides, the...     

Simulated annealing-based immunodominance algorithm for multi-objective optimization problems

Based on the simulated annealing strategy and immunodominance in the artificial immune system, a simulated annealing-based immunodominance algorithm (SAIA) for multi-objective optimization (MOO) is proposed in this paper. In SAIA, all immunodominant antibodies are divided into two classes: the active antibodies and the hibernate antibodies at each temperature. Clonal proliferation and recombination are employed to enhance local search on those active antibodies while the hibernate antibodies have no function, but they could become active during the following temperature. Thus, all antibodies in the search space can be exploited effectively and sufficiently. Simulated annealing-based adaptive hypermutation, population pruning, and simulated annealing selection are proposed in SAIA to evolve and obtain a set of antibodies as the trade-off solutions. Complexity analysis of SAIA is also provided. The performance comparison of SAIA with some state-of-the-art MOO algorithms in solving 14 well-known multi-objective optimization problems (MOPs) including four many objectives test problems and twelve multi-objective 0/1 knapsack problems shows that SAIA is superior in converging to approximate Pareto front with a standout distribution.     

基于混沌的多目标粒子群优化算法

针对多目标优化问题,提出了一种改进的粒子群算法.该算法为了寻找新解,引入了混沌搜索技术,同时采用了一种新的方法--拥挤距离法定义解的适应度.并采取了精英保留策略,在提高非劣解集多样性的同时,使解集更加趋近于Pareto集.最后,把算法应用到4个典型的多目标测试函数.数值结果表明,该算法能够有效的收敛到Pareto非劣最优目标域,并沿着Pareto非劣目标域有很好的分散性.     

求解多目标优化问题的分级变异量子进化算法

分析量子进化算法和免疫算子的特点,提出一种分级变异的量子进化算法,用于求解多目标优化问题,算法主要基于两个策略:首先,利用快速非受控排序和密度距离计算种群抗原-抗体的亲和度;然后,基于亲和度排序将个体进行分级,最优分级中的个体作为算法中的最优个体,大部分实施量子旋转更新和免疫操作,而剩余分级中的个体实施免疫交叉操作以获得新的个体补充种群,求解多目标0/1背包问题的实验结果表明了该算法的有效性.     

An interactive method using genetic algorithm for multi-objective optimization problems modeled in fuzzy environment

In this paper, an interactive approach based method is proposed for solving multi-objective optimization problems. The proposed method can be used to obtain those Pareto-optimal solutions of the mathematical models of linear as well as nonlinear multi-objective optimization problems modeled in fuzzy or crisp environment which reasonably meet users aspirations. In the proposed method the objectives are treated as fuzzy goals and the satisfaction of constraints is considered at different α-level sets of the fuzzy parameter used. Product operator is used to aggregate the membership functions of the objectives. To initiate the algorithm, the decision maker has to specify his(er) preferences for the desired values of the objectives in the form of reference levels in the membership space. In each iterative phase, a single objective nonlinear (usually nonconvex) optimization problem has to be solved. It is solved using real coded genetic algorithm, MI-LXPM. Based on its outcomes, the decision maker has the option to modify, if felt necessary, some or all of the reference levels in the membership function space before initiating the next iterative phase. The algorithm is stopped where user’s aspirations are reasonably met.     

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.     

Memetic quantum evolution algorithm for global optimization

Neural Computing and Applications - Quantum-inspired heuristic search algorithms have attracted considerable research interest in recent years. However, existing quantum simulation methods are...     

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.     

An interval algorithm for multi-objective optimization

This paper presents an interval algorithm for solving multi-objective optimization problems. Similar to other interval optimization techniques, [see Hansen and Walster (2004)], the interval algorithm presented here is guaranteed to capture all solutions, namely all points on the Pareto front. This algorithm is a hybrid method consisting of local gradient-based and global direct comparison components. A series of example problems covering convex, nonconvex, and multimodal Pareto fronts is used to demonstrate the method.     

A novel evolutionary root system growth algorithm for solving multi-objective optimization problems

This paper proposes a novel multi-objective root system growth optimizer (MORSGO) for the copper strip burdening optimization. The MORSGO aims to handle multi-objective problems with satisfactory convergence and diversity via implementing adaptive root growth operators with a pool of multi-objective search rules and strategies. Specifically, the single-objective root growth operators including branching, regrowing and auxin-based tropisms are deliberately designed. They have merits of appropriately balancing exploring & exploiting and self-adaptively varying population size to reduce redundant computation. The effective multi-objective strategies including the fast non-dominated sorting and the farthest-candidate selection are developed for saving and retrieving the Pareto optimal solutions with remarkable approximation as well as uniform spread of Pareto-optimal solutions. With comprehensive evaluation against a suit of benchmark functions, the MORSGO is verified experimentally to be superior or at least comparable to its competitors in terms of the IGD and HV metrics. The MORSGO is then validated to solve the real-world copper strip burdening optimization with different elements. Computation results verifies the potential and effectiveness of the MORSGO to resolve complex industrial process optimization.     

A memetic algorithm with adaptive hill climbing strategy for dynamic optimization problems

Dynamic optimization problems challenge traditional evolutionary algorithms seriously since they, once converged, cannot adapt quickly to environmental changes. This paper investigates the application of memetic algorithms, a class of hybrid evolutionary algorithms, for dynamic optimization problems. An adaptive hill climbing method is proposed as the local search technique in the framework of memetic algorithms, which combines the features of greedy crossover-based hill climbing and steepest mutation-based hill climbing. In order to address the convergence problem, two diversity maintaining methods, called adaptive dual mapping and triggered random immigrants, respectively, are also introduced into the proposed memetic algorithm for dynamic optimization problems. Based on a series of dynamic problems generated from several stationary benchmark problems, experiments are carried out to investigate the performance of the proposed memetic algorithm in comparison with some peer evolutionary algorithms. The experimental results show the efficiency of the proposed memetic algorithm in dynamic environments.     

A two-stage adaptive multi-fidelity surrogate model-assisted multi-objective genetic algorithm for computationally expensive problems

Surrogate model-assisted multi-objective genetic algorithms (MOGA) show great potential in solving engineering design problems since they can save computational cost by reducing the calls of expensive simulations. In this paper, a two-stage adaptive multi-fidelity surrogate (MFS) model-assisted MOGA (AMFS-MOGA) is developed to further relieve their computational burden. In the warm-up stage, a preliminary Pareto frontier is obtained relying only on the data from the low-fidelity (LF) model. In the second stage, an initial MFS model is constructed based on the data from both LF and high-fidelity (HF) models at the samples, which are selected from the preliminary Pareto set according to the crowding distance in the objective space. Then the fitness values of individuals are evaluated using the MFS model, which is adaptively updated according to two developed strategies, an individual-based updating strategy and a generation-based updating strategy. The former considers the prediction uncertainty from the MFS model, while the latter takes the discrete degree of the population into consideration. The effectiveness and merits of the proposed AMFS-MOGA approach are illustrated using three benchmark tests and the design optimization of a stiffened cylindrical shell. The comparisons between the proposed AMFS-MOGA approach and some existing approaches considering the quality of the obtained Pareto frontiers and computational efficiency are made. The results show that the proposed AMFS-MOGA method can obtain Pareto frontiers comparable to that obtained by the MOGA with HF model, while significantly reducing the number of evaluations of the expensive HF model.

     

DEMORS: A hybrid multi-objective optimization algorithm using differential evolution and rough set theory for constrained problems

The aim of this paper is to show how the hybridization of a multi-objective evolutionary algorithm (MOEA) and a local search method based on the use of rough set theory is a viable alternative to obtain a robust algorithm able to solve difficult constrained multi-objective optimization problems at a moderate computational cost. This paper extends a previously published MOEA [Hernández-Díaz AG, Santana-Quintero LV, Coello Coello C, Caballero R, Molina J. A new proposal for multi-objective optimization using differential evolution and rough set theory. In: 2006 genetic and evolutionary computation conference (GECCO’2006). Seattle, Washington, USA: ACM Press; July 2006], which was limited to unconstrained multi-objective optimization problems. Here, the main idea is to use this sort of hybrid approach to approximate the Pareto front of a constrained multi-objective optimization problem while performing a relatively low number of fitness function evaluations. Since in real-world problems the cost of evaluating the objective functions is the most significant, our underlying assumption is that, by aiming to minimize the number of such evaluations, our MOEA can be considered efficient. As in its previous version, our hybrid approach operates in two stages: in the first one, a multi-objective version of differential evolution is used to generate an initial approximation of the Pareto front. Then, in the second stage, rough set theory is used to improve the spread and quality of this initial approximation. To assess the performance of our proposed approach, we adopt, on the one hand, a set of standard bi-objective constrained test problems and, on the other hand, a large real-world problem with eight objective functions and 160 decision variables. The first set of problems are solved performing 10,000 fitness function evaluations, which is a competitive value compared to the number of evaluations previously reported in the specialized literature for such problems. The real-world problem is solved performing 250,000 fitness function evaluations, mainly because of its high dimensionality. Our results are compared with respect to those generated by NSGA-II, which is a MOEA representative of the state-of-the-art in the area.     

Improving collaborative optimization for MDO problems with multi-objective subsystems

Structural and Multidisciplinary Optimization - This paper investigates collaborative optimization (CO) for multidisciplinary design optimization problems with multi-objective subsystems. A...     

Vehicle power train optimization using multi-objective bird swarm algorithm

In this paper, a multi-objective bird swarm algorithm (MOBSA) is proposed to cope with multi-objective optimization problems. The algorithm is explored based on BSA which is an evolutionary algorithm suitable for single objective optimization. In this paper, non-dominated sorting approach is used to distinguish optimal solutions and parallel coordinates is applied to evaluate the distribution density of non-dominated solution and further update the external archive when it is full to overflowing, which ensure faster convergence and more widespread of Pareto front. Then, the MOBSA is adopted to optimize benchmark problems. The results demonstrate that MOBSA gets better performance compared with NSGA-II and MOPSO. Since a vehicle power train problem could be treated as a typical multi-objective optimization problem with constraints, with integration of constrained non-dominated solution, MOBSA is adopted to acquire optimal gear ratios and optimize vehicle power train. The results compared with other popular algorithm prove the proposed algorithm is more suitable for constrained multi-objective optimization problem in engineering field.