Extending water wave optimization algorithm for mirrored traveling tournament problems

Abstract

The Mirrored Traveling Tournament Problem (mTTP), an NP-hard sports scheduling challenge, re- quires minimizing team travel distance under strict constraints, notably a mirrored two-half tourna- ment structure. This thesis introduces a novel adaptation of the Water Wave Optimization (WWO) algorithm, a nature-inspired metaheuristic, to effectively solve the mTTP. The WWO framework, originally for continuous optimization, is systematically redesigned for the discrete and constrained mTTP landscape. Our WWO-mTTP methodology employs a matrix-based encoding manipulating only the first tournament half, with the second deterministically mirrored. The fitness function prioritizes total travel distance, managing constraints via feasibility-preserving operators. Core WWO operators (propagation, breaking, refraction/replacement) are customized for discrete schedules: propagation uses wavelength-influenced neighborhood moves (Home-Away Swap, Round Swap, Team Swap on the first half) to balance exploration/exploitation; a Solis-inspired breaking operator intensifies search around quality solutions; and wave re-initialization diversifies stagnant solutions. Implemented in Python with Numba JIT acceleration, the algorithm was empirically validated on standard benchmarks. Results demonstrate its capability to consistently find feasible, good-quality solutions and effectively escape local optima. This work offers a detailed framework for applying WWO to mTTP, laying groundwork for future research in operator refinement and hybridization for complex sports scheduling.