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Peak-A-Boo! Generating Multi-objective Multiple Peaks Benchmark Problems with Precise Pareto Sets

, , , and . Evolutionary Multi-Criterion Optimization, page 291--304. Germany, Springer, (2023)Publisher Copyright: © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 12th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2023, EMO ; Conference date: 20-03-2023 Through 24-03-2023.
DOI: 10.1007/978-3-031-27250-9_21

Abstract

The design and choice of benchmark suites are ongoing topics of discussion in the multi-objective optimization community. Some suites provide a good understanding of their Pareto sets and fronts, such as the well-known DTLZ and ZDT problems. However, they lack diversity in their landscape properties and do not provide a mechanism for creating multiple distinct problem instances. Other suites, like bi-objective BBOB, possess diverse and challenging landscape properties, but their optima are not well understood and can only be approximated empirically without any guarantees. This work proposes a methodology for creating complex continuous problem landscapes by concatenating single-objective functions from version 2 of the multiple peaks model (MPM2) generator. For the resulting problems, we can determine the distribution of optimal points with arbitrary precision w.r.t. a measure such as the dominated hypervolume. We show how the properties of the MPM2 generator influence the multi-objective problem landscapes and present an experimental proof-of-concept study demonstrating how our approach can drive well-founded benchmarking of MO algorithms.

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