Difficult features of combinatorial optimization problems and the tunable w-model benchmark problem for simulating them

TLDR: The W-Model is put into the context of related model problems targeting ruggedness, neutrality, and epistasis and given an idea about suitable configurations of it that could be included in the BB-DOB benchmark suite.

Abstract: The first event of the Black-Box Discrete Optimization Benchmarking (BB-DOB) workshop series aims to establish a set of example problems for benchmarking black-box optimization algorithms for discrete or combinatorial domains In this paper, we 1) discuss important features that should be embodied by these benchmark functions and 2) present the W-Model problem which exhibits them The W-Model follows a layered approach, where each layer can either be omitted or introduce a different characteristic feature such as neutrality via redundancy, ruggedness and deceptiveness, epistasis, and multi-objectivity, in a tunable way The model problem is defined over bit string representations, which allows for extracting some of its layers and stacking them on top of existing problems that use this representation, such as OneMax, the Maximum Satisfiability or the Set Covering tasks, and the NK landscape The ruggedness and deceptiveness layer can be stacked on top of any problem with integer-valued objectives We put the W-Model into the context of related model problems targeting ruggedness, neutrality, and epistasis We then present the results of a series of experiments to further substantiate the utility of the W-Model and to give an idea about suitable configurations of it that could be included in the BB-DOB benchmark suite