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

1. Roy de Winter corresponding Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   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

2. Bas Milatz
   Affiliation as printed

   Research and Development, C-Job Naval Architects, Regulusplein 1, Hoofddorp, 2132 JN, Netherlands

3. Julian Blank

   Michigan State University

   Affiliation as printed

   Electrical and Computer Engineering, Michigan State University, 428 S. Shaw Lane, East Lansing, 48824, MI, United States

4. Bas van Stein Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands

5. Thomas Bäck Aachen Leiden Institute of Advanced Computer Science

   Leiden University

   Affiliation as printed

   Leiden Institute of Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands

6. Kalyanmoy Deb

   Michigan State University

   Affiliation as printed

   Electrical and Computer Engineering, Michigan State University, 428 S. Shaw Lane, East Lansing, 48824, MI, United States