Evolutionary robust optimization in production planning – interactions between number of objectives, sample size and choice of robustness measure

Abstract

We aim to find robust solutions in optimization settings where there is uncertainty associated with the operating/environmental conditions, and the fitness of a solution is hence best described by a distribution of outcomes. In such settings, the nature of the fitness distribution (reflecting the performance of a particular solution across a set of operating scenarios) is of potential interest in deciding solution quality, and previous work has suggested the inclusion of robustness as an additional optimization objective. However, there has been limited investigation of different robustness criteria, and the impact this choice may have on the sample size needed to obtain reliable fitness estimates. Here, we investigate different single and multi-objective formulations for robust optimization, in the context of a real-world problem addressed via simulation-based optimization. For the (limited evaluation) setting considered, our results highlight the value of an explicit robustness criterion in steering an optimizer towards solutions that are not only robust (as may be expected), but also associated with a profit that is, on average, higher than that identified by standard single-objective approaches. We also observe significant interactions between the choice of robustness measure and the sample size employed during fitness evaluation, an effect that is more pronounced for our multi-objective models.

A largest empty hypersphere metaheuristic for robust optimisation with implementation uncertainty

“…Given, for example, budgetary restrictions on the number of function evaluations, some trade-off must be achieved between the extent of each inner Γ-radius uncertainty neighbourhood search and globally exploring the search space. But this trade-off between robustness in terms of the extent of the inner searches, and performance in terms of the outer global search, is complex, see [MLM15,DHX17]. For example the determination of an appropriate inner approach -type of search, extent of search and parameter settings -may be both instance (problem and dimension) dependent and dependent on the outer approach.…”

Particle Swarm Metaheuristics for Robust Optimisation with Implementation Uncertainty

“…Under budgetary restrictions we must therefore add the balancing of better estimating a candidate point's robust value versus the extent of the outer minimisation search, into the mix of exploration versus exploitation. This trade-off is complex, see for example [MLM15,DHX17].…”

“…Where there are budgetary restrictions on the number of function evaluations, some tradeoff must be achieved between the extent of each inner maximisation search (robustness) and the overall global search performance. However the trade-off between robustness and performance is not straightforward, see [MLM15,DHX17]. In [BNT10b] the inner maximisation involves a series of two-stage gradient ascent searches within the Γ-uncertainty neighbourhood of a given candidate point, and assumes the availability of gradient information.…”

Scenario-based modeling and solving research on robust weapon project planning problems

“…According to the current articles [24], to some extent, the robust optimization can be done by passing its original goal(s) through its robust equivalents [25] (e.g., robustness measures such as averages rather than individual assessments). In addition, measures of robustness can be integrated into the optimization as a hard constraint [26]. The third method is to consider robustness as part of a composite function that is a weighted sum of different goals [27].…”