A Multioperator Search Strategy Based on Cheap Surrogate Models for Evolutionary Optimization

Self Cite

Abstract-Due to the fact that a nonlinear equation system may contain multiple optimal solutions, solving nonlinear equation systems is one of the most important challenges in numerical computation. When applying evolutionary algorithms to solve nonlinear equation systems, two issues should be considered: i) how to transform a nonlinear equation system into a kind of optimization problem, and ii) how to develop an optimization algorithm to solve the transformed optimization problem. In this paper, we tackle the first issue by transforming a nonlinear equation system into a weighted biobjective optimization problem. By the above transformation, not only do all the optimal solutions of an original nonlinear equation system become the Pareto optimal solutions of the transformed biobjective optimization problem, but also their images are different points on a linear Pareto front in the objective space. In addition, we suggest an adaptive multiobjective differential evolution, the goal of which is to effectively locate the Pareto optimal solutions of the transformed biobjective optimization problem. Once these solutions are found, the optimal solutions of the original nonlinear equation system can also be obtained correspondingly. By combining the weighted biobjective transformation technique with the adaptive multiobjective differential evolution, we propose a generic framework for the simultaneous locating of multiple optimal solutions of nonlinear equation systems. Comprehensive experiments on 38 nonlinear equation systems with various features have demonstrated that our framework provides very competitive overall performance compared with several state-ofthe-art methods.

Section: Discussionmentioning

confidence: 99%

A Weighted Biobjective Transformation Technique for Locating Multiple Optimal Solutions of Nonlinear Equation Systems

Gong

Wang

Cai

et al. 2017

Self Cite

“…A Gaussian Process surrogate model was proposed by Liu et al [39] to assist differential evolution to solve computationally expensive optimization problems, in which dimension reduction techniques were utilized to reduce the dimension of the Gaussian Process surrogate model. Different to the surrogate model building, Gong et al [40] proposed a cheap surrogate model based on density estimation for pre-screening the candidate individuals in evolutionary optimization.…”

Section: ) Global-surrogate Assisted Metaheuristic Algorithmsmentioning

confidence: 99%

Surrogate-Assisted Cooperative Swarm Optimization of High-Dimensional Expensive Problems

Sun

Jin

Cheng

et al. 2017

339

131

Abstract-Surrogate models have shown to be effective in assisting metaheuristic algorithms for solving computationally expensive complex optimization problems. The effectiveness of existing surrogate-assisted metaheuristic algorithms, however, has only been verified on low-dimensional optimization problems. In this paper, a surrogate-assisted cooperative swarm optimization algorithm is proposed, in which a surrogate-assisted particle swarm optimization algorithm and a surrogate-assisted social learning based particle swarm optimization algorithm cooperatively search for the global optimum. The cooperation between the particle swarm optimization and the social learning based particle swarm optimization consists of two aspects. First, they share promising solutions evaluated by the real fitness function. Second, the social learning based particle swarm optimization focuses on exploration while the particle swarm optimization concentrates on local search. Empirical studies on six 50-dimensional and six 100-dimensional benchmark problems demonstrate that the proposed algorithm is able to find high-quality solutions for high-dimensional problems on a limited computational budget.

“…Several ideas have been proposed for choosing individuals to be re-evaluated using the original objective functions, which is one key issue in surrogate management. These include selecting potentially good solutions [48], [47], [49], selecting representative solutions [25], [50], or selecting solutions with a large amount of uncertainty [51], [52]. As an approximation of the original objective function, surrogate models are subject to errors.…”

Section: B Surrogate Models and Surrogate Managementmentioning

confidence: 99%

Data-Driven Surrogate-Assisted Multiobjective Evolutionary Optimization of a Trauma System

Wang

Jin

Jansen

2016

214

102

Abstract-Most existing work on evolutionary optimization assumes that there are analytic functions for evaluating the objectives and constraints. In the real-world, however, the objective or constraint values of many optimization problems can be evaluated solely based on data and solving such optimization problems is often known as data-driven optimization. In this paper, we divide data-driven optimization problems into two categories, i.e., off-line and on-line data-driven optimization, and discuss the main challenges involved therein. An evolutionary algorithm is then presented to optimize the design of a trauma system, which is a typical off-line data-driven multi-objective optimization problem, where the objectives and constraints can be evaluated using incidents only. As each single function evaluation involves large amount of patient data, we develop a multi-fidelity surrogate management strategy to reduce the computation time of the evolutionary optimization. The main idea is to adaptively tune the approximation fidelity by clustering the original data into different numbers of clusters and a regression model is constructed to estimate the required minimum fidelity. Experimental results show that the proposed algorithm is able to save up to 90% of computation time without much sacrifice of the solution quality.