A largest empty hypersphere metaheuristic for robust optimisation with implementation uncertainty

Abstract

We consider box-constrained robust optimisation problems with implementation uncertainty. In this setting, the solution that a decision maker wants to implement may become perturbed. The aim is to find a solution that optimises the worst possible performance over all possible perturbances.Previously, only few generic search methods have been developed for this setting. We introduce a new approach for a global search, based on placing a largest empty hypersphere. We do not assume any knowledge on the structure of the original objective function, making this approach also viable for simulation-optimisation settings. In computational experiments we demonstrate a strong performance of our approach in comparison with state-of-the-art methods, which makes it possible to solve even high-dimensional problems.

Particle Swarm Metaheuristics for Robust Optimisation with Implementation Uncertainty

“…We undertake a series of computational experiments comparing these new methods with a baseline robust PSO (rPSO), a global version of d.d. and LEH, see [BNT10b,HGW19]. We find that our new metaheuristics considerably outperform these approaches on a large number of problem instances.…”

“…Specifically we employ a PSO frame, augmenting it with adapted elements of the robust local search descent directions (d.d.) approach due to [BNT07,BNT10b,BNT10a], and the robust global largest empty hypersphere (LEH) approach due to [HGW19], and introducing original features in order to generate novel techniques. We undertake a series of computational experiments comparing these new methods with a baseline robust PSO (rPSO), a global version of d.d.…”

“…Of particular interest here are the single-solution descent directions [BNT07, BNT10a, BNT10b] and largest empty hypersphere [HGW19] robust (min max) metaheuristics, and standard (i.e. not robust) population based metaheuristic, particle swarm optimisation [KE95, KES01,Tal09].…”

“…In terms of a robust PSO approach, [SK02, MKA11] consider two-swarm co-evolutionary PSO techniques while [HGW19] employs a baseline rPSO approach as a comparator test heuristic. [Dip10] develops several PSO formulations, and includes material on topologies, memory (archive) and test functions, however the approaches considered are essentially stochastic and only very low dimensional problems are used in the testing.…”

Grand Tour Algorithm: Novel Swarm-Based Optimization for High-Dimensional Problems

“…However, the GTA was the closest, with a low standard deviation, which indicates the determination of a local minimum. These two functions are well-known examples of very challenging benchmark optimization functions, which have presented many difficulties for all metaheuristics; see, for example [45][46][47], which use different algorithms and report the same difficulty in reaching the global minimum for these functions despite using less than 100 variables. Finally, for the Salomon function, the GTA presents the worst success rate, while GA presents the best one.…”