Worst‐case regret algorithms for selected optimization problems with interval uncertainty

The purpose of this paper is to consider selected optimization problems with parameter uncertainty. A case is studied when uncertain parameters in functions undergoing the optimization belong to intervals of known bounds as well as the absolute regret based approach for coping with such an uncertainty is applied. The paper presents three different cases depending on properties of optimization problems and proposes which method can be used to solve corresponding problems.

The worst‐case absolute regret method is employed to manage interval uncertainty in functions to be optimized. To solve resulting uncertain optimization problems, optimal, approximate as well as heuristic solution algorithms have been elaborated for particular problems presented and described in the paper. The latter one is based on Scatter Search metaheuristics.

Solution algorithms for worst‐case absolute regret versions of the following optimization problems have been determined: resource allocation in a complex of independent operations and two task scheduling problems Q‖∑C_i and P‖C_max.

It is very difficult to generalize the results obtained and to use them for solving other optimization problems which correspond to real‐world applications. Such new cases require separate investigations.

The considered allocations as well as task scheduling problems have plenty of applications, for example in computer and manufacturing systems. Their versions with not precisely known parameters can be met commonly.

The investigations presented correspond to previous works on so‐called minimax regret problems and extend them for new optimization problems.