A Cost–Carbon Synergy Adaptive Genetic Algorithm for Unbalanced Transportation Problem

Traditional vehicle routing problems focus primarily on cost minimization. This paper addresses the unbalanced transportation problem, aiming to minimize both costs and carbon emissions. We propose a Cost–Carbon Emissions Adaptive Genetic Algorithm (CSC-AGA) based on the Cost–Carbon Synergy (CSC) mechanism, which quantifies the marginal cost of carbon emission reduction by comparing intergenerational changes in cost and emissions. This mechanism enables dynamic adjustment of penalty coefficients during the evolutionary process. The algorithm adapts penalty coefficients and search parameters to optimize both objectives within a single framework. Experimental results demonstrate that the proposed algorithm outperforms traditional approaches in both cost control and emission reduction, while also approximating or surpassing the approximate Pareto front of existing multi-objective methods with better computational efficiency. The Generalized Unbalanced Transportation Problem (G-UTP) is an NP-hard optimization problem, inheriting the complexity of classical transportation problems while also balancing economic and environmental objectives.