Bézier Evolve and Refine Strategy (BERS): a two-stage algorithm for maritime weather routing

Abstract

This paper presents Bézier Evolve and Refine Strategy (BERS), a two-stage optimization framework for maritime weather routing that combines global search using Covariance Matrix Adaptation Evolution Strategy (CMA-ES) with local refinement via a variational method. Unlike traditional approaches that rely on graph discretization or single-objective heuristics, BERS parametrizes routes as Bézier curves, enabling smooth, flexible trajectories unconstrained by grid topology. The method is designed to address seven key criteria for comprehensive weather routing, including continuity, obstacle avoidance, dynamic adaptation, cost function flexibility, constant-speed feasibility, just-in-time arrival, and local optimality. We evaluate BERS on a suite of synthetic benchmarks designed to stress each criterion individually and in combination. These benchmarks feature time-dependent vector fields and complex land geometries, ensuring a conservatively difficult testbed. Results demonstrate that BERS meets all seven criteria under controlled conditions and matches or outperforms existing solutions in published test scenarios. While real-world validation remains future work, the framework establishes a novel foundation for constrained, smooth, and efficient routing in dynamic marine environments.

Authors & Affiliations

• Daniel Precioso
  IE University

• Javier Jiménez de la Jara
  Universidad de Cádiz

• Louis Bu
  Dalhousie University

• Rafael Ballester-Ripoll
  IE University

• David Gómez-Ullate
  IE University