A benchmark generator for scenario-based discrete optimization

Abstract

Multi-objective evolutionary algorithms (MOEAs) are a practical tool to solve non-linear problems with multiple objective functions. However, when applied to expensive black-box scenario-based optimization problems, MOEA’s performance becomes constrained due to computational or time limitations. Scenario-based optimization refers to problems that are subject to uncertainty, where each solution is evaluated over an ensemble of scenarios to reduce risks. A primary reason for MOEA’s failure is that algorithm development is challenging in these cases as many of these problems are black-box, high-dimensional, discrete, and computationally expensive. For this reason, this paper proposes a benchmark generator to create fast-to-compute scenario-based discrete test problems with different degrees of complexity. Our framework uses the structure of the Multi-Objective Knapsack Problem to create test problems that simulate characteristics of expensive scenario-based discrete problems. To validate our proposition, we tested four state-of-the-art MOEAs in 30 test instances generated with our framework, and the empirical results demonstrate that the suggested benchmark generator can analyze the ability of MOEAs in tackling expensive scenario-based discrete optimization problems.