Parallel multi-objective optimization for expensive and inexpensive objectives and constraints
Swarm and Evolutionary Computation, vol. 86, pp. 101508
Abstract
Expensive objectives and constraints are key characteristics of real-world multi-objective optimization problems. In practice, they often occur jointly with inexpensive objectives and constraints. This paper presents the Inexpensive Objectives and Constraints Self-Adapting Multi-Objective Constraint Optimization algorithm that uses Radial Basis function Approximations (IOC-SAMO-COBRA) for such problems. This is motivated by the recently proposed Inexpensive Constraint Surrogate-Assisted Non-dominated Sorting Genetic Algorithm II (IC-SA-NSGA-II). These algorithms and their counterparts that do not explicitly differentiate between expensive and inexpensive objectives and constraints are compared on 22 widely used test functions. The IOC-SAMO-COBRA algorithm finds significantly better (identical/worse) Pareto fronts in at least 78% (6%/16%) of all test problems compared to IC-SA-NSGA-II measured with both the hypervolume and Inverted Generational Distance+ performance metric. The empirical cumulative distribution functions confirm this advantage for both algorithm variants that exploit the inexpensive constraints. In addition, the proposed method is compared against state-of-the-art practices on a real-world cargo vessel design problem. On this 17-dimensional two-objective practical problem, the proposed IOC-SAMO-COBRA outperforms SA-NSGA-II as well. From an algorithmic perspective, the comparison identifies specific strengths of both approaches and indicates how they should be hybridized to combine their best components.
Authors 6
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Affiliation as printed
Leiden Institute of Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands
Research and Development, C-Job Naval Architects, Regulusplein 1, Hoofddorp, 2132 JN, Netherlands
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Affiliation as printed
Research and Development, C-Job Naval Architects, Regulusplein 1, Hoofddorp, 2132 JN, Netherlands
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Affiliation as printed
Electrical and Computer Engineering, Michigan State University, 428 S. Shaw Lane, East Lansing, 48824, MI, United States
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Affiliation as printed
Leiden Institute of Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands
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Affiliation as printed
Leiden Institute of Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands
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Affiliation as printed
Electrical and Computer Engineering, Michigan State University, 428 S. Shaw Lane, East Lansing, 48824, MI, United States
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