Multi-objective optimization for multimodal transport path under the cap-and-trade policy to minimize cost, duration and carbon emission

Abstract Aiming at the issues of insufficient systematic multi-objective coordination mechanisms and inadequate integration of the dynamic impacts of carbon trading policies in current research on multimodal transport path optimization, this paper introduces a carbon trading mechanism and constructs a multi-objective optimization model that minimizes total cost, total duration, and total carbon emissions. The model systematically integrates transportation costs, transfer costs, duration costs, and carbon trading costs. To enhance solution quality and decision-making objectivity, an improved ant colony algorithm incorporating a simulated annealing mechanism and projection pursuit evaluation is proposed. The simulated annealing mechanism enhances global search capability, while projection pursuit evaluation enables objective assessment and selection of Pareto solution sets, effectively overcoming the premature convergence and subjective weight assignment issues of traditional algorithms. A case study based on a typical transport network demonstrates that: (1) Under the baseline scenario, the optimal solution achieves reductions of 21.28%, 57.97%, and 51.64% in cost, duration, and carbon emissions, respectively, compared to rail, water, and road transport modes; (2) The improved algorithm exhibits excellent convergence and distribution performance, stably approaching a high-quality Pareto front with strong practical applicability; (3) Carbon trading prices play a significant regulatory role in multimodal transport path optimization, effectively promoting the transition toward low-carbon transport modes. This study provides a theoretical foundation and decision-making support for the low-carbon, economical, and efficient operation of multimodal transport systems under the ‘Dual Carbon’ goals.