Particle Swarm Algorithm for Improved Handling of the Mirrored Traveling Tournament Problem

Abstract

In this study, we used a particle swarm optimization (PSO) algorithm to address a variation of the non-deterministic polynomial-time NP-hard traveling tournament problem, which determines the optimal schedule for a double round-robin tournament, for an even number of teams, to minimize the number of trips taken. Our proposed algorithm iteratively explored the search space with a swarm of particles to find near-optimal solutions. We also developed three techniques for updating the particle velocity to move towards optimal points, which randomly select and replace row and column parameters to find candidate positions close to an optimal solution. To further optimize the solution, we calculated the particle cost function, an important consideration within the problem conditions, for team revenues, fans, and media. We compared our computation results with two well-known meta-Heuristics: a genetics algorithm utilizing a swapping method and a Greedy Randomized Adaptive Search Procedure Iterated Local Search algorithm heuristic on a set of 20 teams. Ultimately, the PSO algorithm generated solutions that were comparable, and often superior, to the existing wellknown solutions. Our results indicate that our proposed algorithm could aid in reducing the overall budget expenditures of international sports league organizations, which could enable significant monetary savings and increase profit margins.