Quadratic Convex Reformulation for Solving Task Assignment Problem with Continuous Hopfield Network

Abstract

This research is an optimal allocation of tasks to processors in order to minimize the total costs of execution and communication. This problem is called the Task Assignment Problem (TAP) with nonuniform communication costs. To solve the latter, the first step concerns the formulation of the problem by an equivalent zero-one quadratic program with a convex objective function using a convexification technique, based on the smallest eigenvalue. The second step concerns the application of the Continuous Hopfield Network (CHN) to solve the obtained problem. The calculation results are presented for the instances from the literature, compared to solutions obtained both the CPLEX solver and by the heuristic genetic algorithm, and show an improvement in the results obtained by applying only the CHN algorithm. We can see that the proposed approach evaluates the efficiency of the theoretical results and achieves the optimal solutions in a short calculation time.