Surrogate-assisted multiobjective optimization based on decomposition

International audienceA number of surrogate-assisted evolutionary algorithms are being developed for tackling expensive multiobjective optimization problems. On the one hand, a relatively broad range of techniques from both machine learning and multiobjective optimization can be combined for this purpose. Diferent taxonomies exist in order to better delimit the design choices, advantages and drawbacks of existing approaches. On the other hand, assessing the relative performance of a given approach is a diicult task, since it depends on the characteristics of the problem at hand. In this paper, we focus on surrogate-assisted approaches using objective space decomposition as a core component. We propose a reined and ine-grained classiication, ranging from EGO-like approaches to iltering or pre-screening. More importantly, we provide a comprehensive comparative study of a representative selection of state-of-the-art methods , together with simple baseline algorithms. We rely on selected benchmark functions taken from the bbob-biobj benchmarking test suite, that provides a variable range of objective function diiculties. Our empirical analysis highlights the efect of the available budget on the relative performance of each approach, and the impact of the training set and of the machine learning model construction on both solution quality and runtime eiciency

Surrogate-assisted Multi-objective Combinatorial Optimization based on Decomposition and Walsh Basis

International audienceWe consider the design and analysis of surrogate-assisted algorithms for expensive multi-objective combinatorial optimization. Focusing on pseudo-boolean functions, we leverage existing techniques based on Walsh basis to operate under the decomposition framework of MOEA/D. We investigate two design components for the cheap generation of a promising pool of offspring and the actual selection of one solution for expensive evaluation. We propose different variants, ranging from a filtering approach that selects the most promising solution at each iteration by using the constructed Walsh surrogates to discriminate between a pool of offspring generated by variation, to a substitution approach that selects a solution to evaluate by optimizing the Walsh surrogates in a multi-objective manner. Considering bi-objective NK landscapes as benchmark problems offering different degree of non-linearity, we conduct a comprehensive empirical analysis including the properties of the achievable approximation sets, the anytime performance, and the impact of the order used to train the Walsh surrogates. Our empirical findings show that, although our surrogate-assisted design is effective, the optimal integration of Walsh models within a multi-objective evolutionary search process gives rise to particular questions for which different trade-off answers can be obtained

A survey on handling computationally expensive multiobjective optimization problems with evolutionary algorithms

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record.Evolutionary algorithms are widely used for solving multiobjective optimization problems but are often criticized because of a large number of function evaluations needed. Approximations, especially function approximations, also referred to as surrogates or metamodels are commonly used in the literature to reduce the computation time. This paper presents a survey of 45 different recent algorithms proposed in the literature between 2008 and 2016 to handle computationally expensive multiobjective optimization problems. Several algorithms are discussed based on what kind of an approximation such as problem, function or fitness approximation they use. Most emphasis is given to function approximation-based algorithms. We also compare these algorithms based on different criteria such as metamodeling technique and evolutionary algorithm used, type and dimensions of the problem solved, handling constraints, training time and the type of evolution control. Furthermore, we identify and discuss some promising elements and major issues among algorithms in the literature related to using an approximation and numerical settings used. In addition, we discuss selecting an algorithm to solve a given computationally expensive multiobjective optimization problem based on the dimensions in both objective and decision spaces and the computation budget available.The research of Tinkle Chugh was funded by the COMAS Doctoral Program (at the University of Jyväskylä) and FiDiPro Project DeCoMo (funded by Tekes, the Finnish Funding Agency for Innovation), and the research of Dr. Karthik Sindhya was funded by SIMPRO project funded by Tekes as well as DeCoMo