Multiobjective optimization: When objectives exhibit non-uniform latencies

Building on recent work by the authors, we consider the problem of performing multiobjective optimization when the objective functions of a problem have differing evaluation times (or latencies). This has general relevance to applications since objective functions do vary greatly in their latency, and there is no reason to expect equal latencies for the objectives in a single problem. To deal with this issue, we provide a general problem definition and suitable notation for describing algorithm schemes that can use different evaluation budgets for each objective. We propose three schemes for the bi-objective version of the problem, including methods that interleave the evaluations of different objectives. All of these can be instantiated with existing multiobjective evolutionary algorithms (MOEAs). In an empirical study we use an indicator-based evolutionary algorithm (IBEA) as the MOEA platform to study performance on several benchmark test functions. Our findings generally show that the default approach of going at the rate of the slow objective is not competitive with our more advanced ones (interleaving evaluations) for most scenarios.