Waste collection is an important part of waste management system. Transportation costs and carbon emissions can be greatly reduced by proper vehicle routing. Meanwhile, each vehicle can work again after achieving its capacity limit and unloading the waste. For this, an energy-efficient multi-trip vehicle routing model is established for municipal solid waste collection, which incorporates practical factors like the limited capacity, maximum working hours, and multiple trips of each vehicle. Considering both economy and environment, fixed costs, fuel costs, and carbon emission costs are minimized together. To solve the formulated model effectively, contribution-based adaptive particle swarm optimization is proposed. Four strategies named greedy learning, multi-operator learning, exploring learning, and exploiting learning are specifically designed with their own searching priorities. By assessing the contribution of each learning strategy during the process of evolution, an appropriate one is selected and assigned to each individual adaptively to improve the searching efficiency of the algorithm. Moreover, an improved local search operator is performed on the trips with the largest number of waste sites so that both the exploiting ability and the convergence accuracy of the algorithm are improved. Performance of the proposed algorithm is tested on ten waste collection instances, which include one real-world case derived from the Green Ring Company of Jiangbei New District, Nanjing, China, and nine synthetic instances with increasing scales generated from the commonly-used capacitated vehicle routing problem benchmark datasets. Comparisons with five state-of-the-art algorithms show that the proposed algorithm can obtain a solution with a higher accuracy for the constructed model.

A constrained multi-objective optimization model for the low-carbon vehicle routing problem (VRP) is established. A carbon emission measurement method considering various practical factors is introduced. It minimizes both the total carbon emissions and the longest time consumed by the sub-tours, subject to the limited number of available vehicles. According to the characteristics of the model, a region enhanced discrete multi-objective fireworks algorithm is proposed. A partial mapping explosion operator, a hybrid mutation for adjusting the sub-tours, and an objective-driven extending search are designed, which aim to improve the convergence, diversity, and spread of the non-dominated solutions produced by the algorithm, respectively. Nine low-carbon VRP instances with different scales are used to verify the effectiveness of the new strategies. Furthermore, comparison results with four state-of-the-art algorithms indicate that the proposed algorithm has better performance of convergence and distribution on the low-carbon VRP. It provides a promising scalability to the problem size.