Metaheuristics Approach for Mathematical Programs with Switching Constraints and Application to Robotic Task Planning

Abstract

We propose a fast optimization algorithm to find feasible solutions for a special class of switching structured problems. A type of continuous optimization problem that has switching structured constraints is called mathematical programs with switching constraints (MPSC). Relaxation methods are well known gradient descent-based approaches for solving MPSC. However, with the use of these conventional algorithms, we reveal that the sequence of solutions easily converges to an infeasible stationary point due to a special class of switching constraint whose feasible set is geometrically separated into mutually exclusive sets in variable space. We define this kind of switching constraint as the disjunctive allowable set constraint (DAS-constraint). To force the sequence of solutions to escape from such infeasible stationary points, we construct a new algorithm that introduces random sampling if convergence to an infeasible point is detected. Furthermore, to reduce the computation cost due to random sampling, we randomize only specific variables that are relevant to DAS-constraints. Numerical experiments show that feasible solutions can be found by using our proposed algorithm, even for large-scale optimization problems where no solutions are found within a practical time limit when using a conventional algorithm.