Tuning optimization algorithms under multiple objective function evaluation budgets

Abstract

The performance of optimization algorithms is sensitive to both the optimization problem's numerical characteristics and the termination criteria of the algorithm. Given these considerations two tuning algorithms named tMOPSO and MOTA are proposed to assist optimization practitioners to nd algorithm settings which are approximate for the problem at hand. For a speci ed problem tMOPSO aims to determine multiple groups of control parameter values, each of which results in optimal performance at a di erent objective function evaluation budget. To achieve this, the control parameter tuning problem is formulated as a multi-objective optimization problem. Furthermore, tMOPSO uses a noise-handling strategy and control parameter value assessment procedure, which are specialized for tuning stochastic optimization algorithms. The principles upon which tMOPSO were designed are expanded into the context of many objective optimization, to create the MOTA tuning algorithm. MOTA tunes an optimization algorithm to multiple problems over a range of objective function evaluation budgets. To optimize the resulting many objective tuning problem, MOTA makes use of bi-objective decomposition. The last section of work entails an application of the tMOPSO and MOTA algorithms to benchmark optimization algorithms according to their tunability. Benchmarking via tunability is shown to be an effective approach for comparing optimization algorithms, where the various control parameter choices available to an optimization practitioner are included into the benchmarking process.