Discrepancy-based evolutionary diversity optimization

Abstract

Diversity plays a crucial role in evolutionary computation. While diversity has been mainly used to prevent the population of an evolutionary algorithm from premature convergence, the use of evolutionary algorithms to obtain a diverse set of solutions has gained increasing attention in recent years. Diversity optimization in terms of features on the underlying problem allows to obtain a better understanding of possible solutions to the problem at hand and can be used for algorithm selection when dealing with combinatorial optimization problems such as the Traveling Salesperson Problem. We explore the use of the star-discrepancy measure to guide the diversity optimization process of an evolutionary algorithm.In our experimental investigations, we consider our discrepancy-based diversity optimization approaches for evolving diverse sets of images as well as instances of the Traveling Salesperson problem where a local search is not able to find near optimal solutions. Our experimental investigations comparing three diversity optimization approaches show that a discrepancy-based diversity optimization approach using a tie-breaking rule based on weighted differences to surrounding feature points provides the best results in terms of the star discrepancy measure.

Automated Algorithm Selection: Survey and Perspectives

“…Recent studies build upon these concepts by explicitly focusing on the diversity of evolved instances (Gao et al, 2015;Neumann et al, 2018), paving the way for a systematic approach to construct most informative and relevant benchmarks specifically tailored to a given set of solvers. The next promising step in this direction will be the complementation of state-of-the-art benchmarks with those specifically designed instances in order to provide most informative benchmark sets tailored to given sets of solvers.…”

Evolutionary diversity optimization using multi-objective indicators

“…Recently, [17] have used the mathematical concept of "discrepancy" to measure the irregularities of distributions and used this measure for evolutionary diversity optimization. The used star-discrepancy uses axis-parallel boxes: ideally, the number of points inside the box is proportional to the size of the box.…”

“…In addition, we use EA DIS with discrepancy minimization, as used in [17]. As IGD and EPS require a reference set (e.g.…”

“…Instead of applying the star discrepancy [23] to measure diversity we use the multi-objective indicators as previously introduced. Otherwise, the configuration of Algorithm 1 is the same as in [17]. In order to produce a new solution the algorithm uses a self-adaptive offset random walk mutation introduced in [17].…”

“…The weighted contribution approach used in [10,1] has the disadvantage that it heavily depends on the chosen weightening of the features and does not distribute that well for two or three dimensions. In [17], an evolutionary diversity optimization approach has been introduced that aims to minimize the discrepancy of the solution set in the feature space. It has been shown that using the star discrepancy as a diversity measure achieves sets of higher diversity than the previous approaches using weighted contributions.…”