Caching and Vectorization Schemes to Accelerate Local Search Algorithms for Assignment Problems

Abstract

Assignment Problems are a class of NP-hard combinatorial optimization problems with a wide range of real-world applications such as Vehicle Routing and FPGA Block Placement. Despite technological advances, solvers that target Assignment Problems still require significant computing resources and time, especially as problem sizes grow. This paper introduces novel cost function formulations to leverage vector processing elements in accelerating local search algorithms for solving Quadratic Assignment and Semi-Assignment problems. We incorporate these vectorization methods within a Parallel Tempering framework to solve some of the most difficult known Quadratic Assignment and Semi-Assignment Problems up to sizes of 729 integer variables and show that this solver system can perform upwards of 300 times faster than other state-of-the-art solvers. We then conduct experiments to quantify the performance and scaling of these vectorization methods and qualify their situational strengths and trade-offs for use in future algorithms and hardware systems.