The increasing importance and growth of the transportation of the industrial/nonindustrial hazardous materials and wastes in recent decades have been brought to the attention of the governments. Not paying attention to this issue has the different consequences, including the socially destructive effects leading to transportation incidents, storage and disposal of such materials and the risk of harm to the humans. On the other hand, due to the direct association of these materials with the industry, the supply chain members need to pay attention to this issue which can play a very important role in the economic development of the country. Special attention should be paid to negative environmental impacts from the greenhouse gas emissions due to the widespread transportation of these materials in the supply chain network as well as the disposal of industrial waste in the environment. The importance of the research problem in the social, economic and environmental fields have resulted in developing a mathematical model of a location-inventory-routing problem (LIRP) for hazardous materials and waste management at two levels of the supply chain with considering a heterogeneous vehicle fleet seeking to mitigate the supply chain risk, minimize the supply chain costs and reduce greenhouse gas emissions. Given that the proposed model is NP-hard, a meta-heuristic algorithm to solve the multi-objective optimization problems called multi-objective black widow optimization (MOBWO) algorithm is presented. The performance of the proposed meta-heuristic algorithm has been compared with multi-objective smulated annealing algorithm (MOSA) and non-dominated sorting genetic algorithm II (NSGA II). A new Minkowski-based approach is presented to choose a single solution from a set of non-dominated solutions of the first front as the final optimal solution for the proposed problem. The results of the present study demonstrated that the NSGA II algorithm in small- and medium-scale test problems gives better accuracy, but the MOBWO has better performance in the large-scale test problems in comparison with the other two algorithms.

近几十年来，工业/非工业危险材料和废物运输的重要性和增长已引起各国政府的注意。不注意这个问题会产生不同的后果，包括导致运输事故、储存和处置此类材料的社会破坏性影响以及对人类造成伤害的风险。另一方面，由于这些材料与行业的直接关联，供应链成员需要关注这个对国家经济发展具有非常重要作用的问题。由于这些材料在供应链网络中的广泛运输以及工业废物在环境中的处置，应特别注意温室气体排放对环境的负面影响。研究问题在社会、经济和环境领域的重要性导致开发了一个位置-库存-路由问题 (LIRP) 的数学模型，用于考虑异构车辆的供应链两个级别的危险材料和废物管理车队寻求降低供应链风险，最大限度地降低供应链成本并减少温室气体排放。鉴于所提出的模型是 NP-hard，提出了一种解决多目标优化问题的元启发式算法，称为多目标黑寡妇优化（MOBWO）算法。将所提出的元启发式算法的性能与多目标模拟退火算法（MOSA）和非支配排序遗传算法II（NSGA II）进行了比较。提出了一种新的基于 Minkowski 的方法，从第一条前沿的一组非支配解中选择一个解作为所提出问题的最终最优解。目前的研究结果表明，NSGA II 算法在中小规模测试问题中具有更好的准确性，但与其他两种算法相比，MOBWO 在大规模测试问题中具有更好的性能。将所提出的元启发式算法的性能与多目标模拟退火算法（MOSA）和非支配排序遗传算法II（NSGA II）进行了比较。提出了一种新的基于 Minkowski 的方法，从第一条前沿的一组非支配解中选择一个解作为所提出问题的最终最优解。目前的研究结果表明，NSGA II 算法在中小规模测试问题中具有更好的准确性，但与其他两种算法相比，MOBWO 在大规模测试问题中具有更好的性能。将所提出的元启发式算法的性能与多目标模拟退火算法（MOSA）和非支配排序遗传算法II（NSGA II）进行了比较。提出了一种新的基于 Minkowski 的方法，从第一条前沿的一组非支配解中选择一个解作为所提出问题的最终最优解。目前的研究结果表明，NSGA II 算法在中小规模测试问题中具有更好的准确性，但与其他两种算法相比，MOBWO 在大规模测试问题中具有更好的性能。提出了一种新的基于 Minkowski 的方法，从第一条前沿的一组非支配解中选择一个解作为所提出问题的最终最优解。目前的研究结果表明，NSGA II 算法在中小规模测试问题中具有更好的准确性，但与其他两种算法相比，MOBWO 在大规模测试问题中具有更好的性能。提出了一种新的基于 Minkowski 的方法，从第一条前沿的一组非支配解中选择一个解作为所提出问题的最终最优解。目前的研究结果表明，NSGA II 算法在中小规模测试问题中具有更好的准确性，但与其他两种算法相比，MOBWO 在大规模测试问题中具有更好的性能。