A New Parallel Cooperative Landscape Smoothing Algorithm and Its Applications on TSP and UBQP

Combinatorial optimization problem (COP) is difficult to solve because of the massive local optimal solutions in his solution space. Various methods have been put forward to smooth the solution space of COPs, including homotopic convex (HC) transformation for the traveling salesman problem (TSP). This paper first extends the HC transformation approach to the unconstrained binary quadratic programming (UBQP). We theoretically prove the effectiveness of the proposed HC transformation method on smoothing the landscape of the UBQP. Subsequently, we introduce an iterative algorithmic framework incorporating HC transformation, referred as landscape smoothing iterated local search (LSILS). Our experimental analyses, conducted on various UBQP instances show the effectiveness of LSILS. Furthermore, this paper proposes a parallel cooperative variant of LSILS, denoted as PC-LSILS and apply it to both the UBQP and the TSP. Our experimental findings highlight that PC-LSILS improves the smoothing performance of the HC transformation, and further improves the overall performance of the algorithm.