The constrained-domination principle (CDP) is one of the most popular constraint-handling techniques (CHTs), since it is simple, nonparametric, and easily embedded in unconstrained multiobjective evolutionary algorithms (MOEAs). However, the CDP overly emphasizes the importance of feasibility, which may lead to the search getting stuck in some locally feasible regions or locally optimal, especially when encountering problems with discontinuous and/or narrow feasible regions. This article seeks to capitalize on the strengths of the CDP while overcoming its weaknesses. Accordingly, we propose a novel constrained MOEA (called MOEA/D-LCDP), in which the CDP is applied in a local manner. Unlike most CHTs that emphasize feasibility, which use the feasibility rule in the whole search space, the proposed localized CDP only adopts the CDP within the niche. That is, to maintain the diversity of the population, only solutions within the niche are compared based on the localized CDP. The niche radius is determined a priori by the acute angle between the current subproblem and its nearest subproblem. Additionally, a population-based status detection strategy is developed to allocate computing resources more rationally, and a diversity-enhanced CDP is designed to enhance the exploitation of the search. Comprehensive experiments conducted on four benchmark test suites with a total of 34 problems and three real-world applications demonstrate that MOEA/D-LCDP is very competitive with representative algorithms.

Balancing constraints and objective functions in constrained evolutionary multiobjective optimization is not an easy task. Over-emphasis on constraints satisfaction may easily lead to the search to get stuck in local optimal regions, and over-emphasis on objectives optimization may lead to substantial search resources wasted on infeasible regions. This paper proposes a constrained multiobjective optimization algorithm, called CMOEA-SDE, aiming to achieve a good balance between the above two issues. To do so, CMOEA-SDE presents a strictly constrained dominance relation and a constrained shift-based density estimation strategy. Specifically, the former defines a new dominance relation that considers both constraint satisfaction and the objective functions. It favors good feasible solutions but still leaves room for infeasible solutions to be selected. Unlike most density estimation methods, which only consider the diversity of solutions, our shift-based density estimator covers both the feasibility and the diversity of solutions. That is, our estimator shifts the solutions’ positions based on the extent of the constraints they violate so that solutions violating constraints more severely are shifted to crowded areas, thus being eliminated early. Systematic experiments were conducted on four benchmark test suites and six real-world constrained multiobjective optimization problems. The experimental results suggest that the proposed algorithm can achieve very competitive performance against state-of-the-art constrained multiobjective evolutionary algorithms.

With the increasing global concern over climate change, reducing greenhouse gas emissions has become a universal goal for governments and enterprises. For oversize and heavyweight cargo (OHC) transportation, multimodal transportation has become widely adopted. However, this mode inevitably generates carbon emissions, making research into effective emission reduction strategies essential for achieving low-carbon economic development. This study investigates the optimization of multimodal transportation paths for OHC (OMTP-OHC), considering various direct carbon pricing policies and develops models for these paths under the ordinary scenario—defined as scenarios without any carbon pricing policies—and two carbon pricing policy scenarios, namely the emission trading scheme (ETS) policy and the carbon tax policy, to identify the most cost-effective solutions. An enhanced genetic algorithm incorporating elite strategy and catastrophe theory is employed to solve the models under the three scenarios. Subsequently, we examine the impact of ETS policy price fluctuations, carbon quota factors, and different carbon tax levels on decision-making through a case study, confirming the feasibility of the proposed model and algorithm. The findings indicate that the proposed algorithm effectively addresses this problem. Moreover, the algorithm demonstrates a small impact of ETS policy price fluctuations on outcomes and a slightly low sensitivity to carbon quota factors. This may be attributed to the relatively low ETS policy prices and the characteristics of OHC, where transportation and modification costs are significantly higher than carbon emission costs. Additionally, a comparative analysis of the two carbon pricing policies demonstrates the varying intensities of emission reductions in multimodal transportation, with the ranking of carbon emission reduction intensity as follows: upper-intermediate level of carbon tax > intermediate level of carbon tax > lower-intermediate level of carbon tax = ETS policy > the ordinary scenario. The emission reduction at the lower-intermediate carbon tax level (USD 8.40/t) matches that of the ETS policy at 30%, with a 49.59% greater reduction at the intermediate level (USD 50.48/t) compared to the ordinary scenario, and a 70.07% reduction at the upper-intermediate level (USD 91.14/t). The model and algorithm proposed in this study can provide scientific and technical support to realize the low-carbonization of the multimodal transportation for OHC. The findings of this study also provide scientific evidence for understanding the situation of multimodal transportation for OHC under China’s ETS policy and its performance under different carbon tax levels in China and other regions. This also contributes to achieving the goal of low-carbon economic development.