2016/04/01 by Dimo Brockhoff, Brockhoff, Dimo, Tea Tušar +5 · 3 citations
Computer Science · Decision Sciences · Engineering · #Advanced Multi-Objective Optimization Algorithms #Probabilistic and Robust Engineering Design #Advanced Control Systems Optimization
paper · pdf · doi:10.48550/arxiv.1604.00359
Several test function suites are being used for numerical benchmarking of\nmultiobjective optimization algorithms. While they have some desirable\nproperties, like well-understood Pareto sets and Pareto fronts of various\nshapes, most of the currently used functions possess characteristics that are\narguably under-represented in real-world problems. They mainly stem from the\neasier construction of such functions and result in improbable properties such\nas separability, optima located exactly at the boundary constraints, and the\nexistence of variables that solely control the distance between a solution and\nthe Pareto front. Here, we propose an alternative way to constructing\nmultiobjective problems-by combining existing single-objective problems from\nthe literature. We describe in particular the bbob-biobj test suite with 55\nbi-objective functions in continuous domain, and its extended version with 92\nbi-objective functions (bbob-biobj-ext). Both test suites have been implemented\nin the COCO platform for black-box optimization benchmarking. Finally, we\nrecommend a general procedure for creating test suites for an arbitrary number\nof objectives. Besides providing the formal function definitions and presenting\ntheir (known) properties, this paper also aims at giving the rationale behind\nour approach in terms of groups of functions with similar properties, objective\nspace normalization, and problem instances. The latter allows us to easily\ncompare the performance of deterministic and stochastic solvers, which is an\noften overlooked issue in benchmarking.\n