Open Competency Optimization with Combinatorial Operators for the Dynamic Green Traveling Salesman Problem

Abstract

This paper proposes the Open Competency Optimization (OCO) approach, based on adaptive combinatorial operators, to solve the Dynamic Green Traveling Salesman Problem (DG-TSP), which extends the classical TSP by incorporating dynamic travel conditions, realistic road gradients, and energy consumption considerations. The objective is to minimize fuel consumption and emissions by reducing the total tour length under varying conditions. Unlike conventional metaheuristics based on real-coded representations, our method directly operates on combinatorial structures, ensuring efficient adaptation without costly transformations. Embedded within a dynamic metaheuristic framework, our operators continuously refine the routing decisions in response to environmental and demand changes. Experimental assessments conducted in practical contexts reveal that our algorithm attains a tour length of 21,059, which is indicative of a 36.16% reduction in fuel consumption relative to Ant Colony Optimization (ACO) (32,994), a 4.06% decrease when compared to Grey Wolf Optimizer (GWO) (21,949), a 2.95% reduction in relation to Particle Swarm Optimization (PSO) (21,701), and a 0.90% decline when juxtaposed with Genetic Algorithm (GA) (21,251). In terms of overall offline performance, our approach achieves the best score (21,290.9), significantly outperforming ACO (36,957.6), GWO (122,881.04), GA (59,296.5), and PSO (36,744.29), confirming both solution quality and stability over time. These findings underscore the resilience and scalability of the proposed approach for sustainable logistics, presenting a pragmatic resolution to enhance transportation operations within dynamic and ecologically sensitive environments.