Generating Instances with Performance Differences for More Than Just Two Algorithms
This work addresses the need for better instance generation to analyze algorithm strengths and weaknesses in optimization, though it is incremental by extending existing two-algorithm methods to multiple algorithms.
The paper tackles the problem of generating optimization instances that highlight performance differences for more than two algorithms simultaneously, proposing new fitness functions and demonstrating their effectiveness on the Traveling Thief Problem with three solvers, showing promising results dependent on algorithm complementarity.
In recent years, Evolutionary Algorithms (EAs) have frequently been adopted to evolve instances for optimization problems that pose difficulties for one algorithm while being rather easy for a competitor and vice versa. Typically, this is achieved by either minimizing or maximizing the performance difference or ratio which serves as the fitness function. Repeating this process is useful to gain insights into strengths/weaknesses of certain algorithms or to build a set of instances with strong performance differences as a foundation for automatic per-instance algorithm selection or configuration. We contribute to this branch of research by proposing fitness-functions to evolve instances that show large performance differences for more than just two algorithms simultaneously. As a proof-of-principle, we evolve instances of the multi-component Traveling Thief Problem~(TTP) for three incomplete TTP-solvers. Our results point out that our strategies are promising, but unsurprisingly their success strongly relies on the algorithms' performance complementarity.