In this paper, we address a hybrid flow-shop scheduling problem with the objective of minimizing the makespan and the cost of delay. The concerned problem considers the diversity of the customers’ requirements, which influences the procedures of the productions and increases the complexity of the problem. The features of the problem are inspired by the real-world situations, and the problem is formulated as a mixed-integer programming model in the paper. In order to tackle the concerned problem, a hybrid metaheuristic algorithm with Differential Evolution (DE) and Local Search (LS) (denoted by DE-LS) has been proposed in the paper. The differential evolution is a state-of-the-art metaheuristic algorithm which can solve complex optimization problem in an efficient way and has been applied in many fields, especially in flow-shop scheduling problem. Moreover, the study not only combines the DE and LS, but also modifies the mutation process and provides the novel initialization process and correction strategy of the approach. The proposed DE-LS has been compared with four variants of algorithms in order to justify the improvements of the proposed algorithm. Experimental results show that the superiority and robustness of the proposed algorithm have been verified.

Financial technology and smart transportation is key cross-field of transportation in the future. The demand for smart transportation investment is constantly released. As typical and efficient financial products, asset-backed securities (ABS) can greatly improve the turnover efficiency of funds between upstream suppliers and downstream buyers in the field of smart transportation and also help participants of the supply chain to maintain healthier financial situations. However, one of the most common problems of ABS is portfolio allocation, which needs portfolio optimization based on massive assets with multiple objectives and constraints. Especially, in the field of smart transportation, sources of underlying assets can always be complex, which may involve a variety of subdivision industries and regions. At the same time, due to the relationships between upstream and downstream entities in the supply chain, correlations among assets can be strong. So, during the optimization of smart transportation ABS portfolio allocation, it is necessary to identify and deal with those problems. Different from forward selection or linear optimization, which could have low efficiency for complicated problems with large sample size and multiple objectives, new methods and algorithms for NP-hard problems would be necessary to be investigated. In this article, a penalty function based on graph density (GD) was introduced to the particle swarm optimization algorithm (PSO), and a GD-PSO algorithm was proposed. Experiments also showed that the GD-PSO algorithm solved the problem of portfolio optimization in smart transportation supply chain ABS effectively.