Walsh-based surrogate-assisted multi-objective combinatorial optimization: A fine-grained analysis for pseudo-boolean functions - Derbel, Bilel; Pruvost, Geoffrey; Liefooghe, Arnaud; Verel, Sébastien; Zhang, Qingfu (Applied soft computing, 2023)
The aim of this paper is to study surrogate-assisted algorithms for expensive multiobjective combinatorial optimization problems. Targeting pseudo-boolean domains, we provide a fine-grained analysis of an optimization framework using the Walsh basis as a core surrogate model. The considered framework uses decomposition in the objective space, and integrates three different components, namely, (i) an inner optimizer for searching promising solutions with respect to the so-constructed surrogate, (ii) a selection strategy to decide which solution is to be evaluated by the expensive objectives, and (iii) the strategy used to setup the Walsh order hyper-parameter. Based on extensive experiments using two benchmark problems, namely bi-objective NK-landscapes and unconstrained binary quadratic programming problems (UBQP), we conduct a comprehensive in-depth analysis of the combined effects of the considered components on search performance, and provide evidence on the effectiveness of the proposed search strategies. As a by-product, our work shed more light on the key challenges for designing a successful surrogate-assisted multi-objective combinatorial search process. •A surrogate-assisted framework for multiobjective pseudo-boolean problems is studied.•Evolutionary techniques are combined with Walsh functions as discrete surrogates.•The impact of design components is analyzed on MNK-landscapes and UBQP.•Strong dependencies exist between the surrogate optimizer and the selection strategy.•The configuration of the Walsh surrogate order is highly impactful.