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• Study the full cover charging segment location problem with routing. • Formulate a location model with routing in space-time-electricity network. • Propose a column-based model and a column generation method. The driving range limitations and insufficient charging facilities impede the widespread application of electric vehicles. Generally, electric vehicles charge on static charging facilities (such as charging stations) for a long period and lose mobility during this period. With the development of charging-while-driving techniques, electric vehicles can recharge on the wireless charging segments without stopping. Given a set of origin-destination (OD) trips, the problem is to determine how many wireless charging segments we need and the exact distribution of these segments. Based on the space-time-electricity modeling framework, we formulate a novel full cover location model with routing to determine the number and distribution of charging segments. The battery capacity and travel time budget limitations can be naturally embedded and satisfied in the space-time-electricity network. We transform this model into an equivalent column-based model and develop a column-generation based decomposition approach. A set of independent pricing subproblems is solved by a time-dependent forward dynamic-programming algorithm. Numerical experiments are conducted on three transportation networks, showing that the proposed method can achieve good integrality gaps. Several parameters are analyzed including the number of OD trips, battery capacity, travel time budget, and charging speed of wireless charging segments. [ABSTRACT FROM AUTHOR]

In real-world routing applications such as waste collection or fuel distribution, multiple products that cannot be mixed should be jointly collected or delivered. Multi-compartment vehicles are applied with great flexibility in routing and assignment decisions for these real-world applications. This study concentrates on the multi-compartment vehicle routing problem with fixed compartment size and fixed assignment products to compartments. For this problem, we develop two new formulations in the space–time network and state-space–time network. For the state-space–time network formulation, we dualize the task allocation constraints to the objective function and decompose the Lagrangian relaxed problem (LR) into a series of identical routing subproblems. To produce high-quality feasible solutions, the augmented Lagrangian relaxed problem (ALR) with superior convergence and feasibility is further applied to this problem. The ALR is decomposed into many solvable routing subproblems by alternating direction method of multipliers. A time-dependent dynamic programming algorithm is developed to settle the obtained subproblems of the LR and ALR. The subgradient optimization method solves the Lagrangian dual problems. The solution quality can be evaluated by the relative gap between the global lower and upper bounds at each iteration. In numerical experiments, the proposed method produces solutions with good integrality gaps. Based on Lagrangian relaxation and decomposition techniques, this research provides a novel solving scheme for the multi-compartment vehicle routing problem. [ABSTRACT FROM AUTHOR]

The driving range of electric vehicles limits the accessibility of their users. Charging infrastructures such as charging stations are essential to improve the accessibility of electric vehicles. Existing charging station location studies neglected accessibility-based indicators in their optimization models. For the charging station location problem, this paper proposes a novel objective function that maximizes the space–time-electricity accessibility of electric vehicles. Then we formulate an integer-programming model in the space–time-electricity network. A Lagrangian relaxation-based decomposition scheme is developed to solve this problem. The constraints that couple flow with location variables are dualized to the objective function, resulting in a set of independent routing subproblems and a knapsack subproblem. At each iteration, a primal heuristic utilizes the result of the intermediate knapsack subproblem to generate a feasible solution and Lagrangian multipliers are updated by the subgradient optimization method. The numerical experiments are conducted on three networks, showing that the proposed method achieves good integrality gaps. [ABSTRACT FROM AUTHOR]

• Study the accessibility-oriented charging station location problem. • Formulate a model in space-time-electricity network. • Develop a benders decomposition scheme with stabilizing techniques. Electric vehicles are a promising selection to deal with climate change and energy crises. However, the development of electric vehicles is impeded by various barriers including shortened driving range, lack of charging facilities, and long recharging periods. Setting additional charging facilities is essential to construct an efficient charging network. Previous studies neglected accessibility-oriented indicators to locate charging stations. This study locates charging stations by maximizing the space-time-electricity accessibility of electric vehicle travelers. For the accessibility-oriented charging station location problem, we formulate a multi-commodity network flow model in the space-time-electricity network. Then, we reformulate this model into a two-stage integer program and develop a Benders decomposition method with stabilizing techniques. At each iteration, a relaxed Benders master problem (RMP) and a set of dual routing subproblems (DSPs) are solved. The RMP provides an ascending lower bound and a feasible charging station location scheme. These DSPs generate a set of Benders optimality cuts for RMP and a feasible solution to update the upper bound. All instances in three transportation networks are solved optimally, showing that the stabilizing techniques can significantly improve the performance of the standard Benders decomposition method. [ABSTRACT FROM AUTHOR]

• Propose a new variant of the GAP and formulate a mean-standard deviation model. • Develop a Lagrangian relaxation based decomposition method. • Propose a decomposition method based on alternating direction method of multipliers. The well-known generalized assignment problem has many real-world applications. The assignment costs between agents and tasks affected by several factors could be unstable and uncertain. In this paper, we assume that the means and variances of assignment costs are known in advance. The idea is that the decision-maker aims to minimize the total assignment costs not only on average, but also to keep their variability as small as possible. Then, a reliability-oriented model with a nonlinear and concave objective function is formulated, and two decomposition-based methods are systematically developed for this challenging problem. The task allocation constraints are dualized and the Lagrangian relaxed problem is broken into many reliability-oriented knapsack subproblems. By the Lagrangian substitution technique, each subproblem is further decomposed into a standard knapsack problem and a simple univariate concave minimization problem. A lower bound is constructed and multipliers are optimized in dual problems by the subgradient method. Feasible solutions can be generated from the results of these reliability-oriented subproblems by Lagrangian heuristic. To further improve the convergence and solution quality, an Alternating Direction Method of Multipliers (ADMM) based decomposition approach is proposed. The augmented Lagrangian relaxed problem is split into a sequence of subproblems by the block coordinate descent method. To cope with the quadratic terms and the concave terms in these subproblems, linearization and Lagrangian substitution techniques are applied. Feasible solutions are produced from these subproblems, and solution quality can be evaluated by the lower bound provided by the Lagrangian relaxed problem. Numerical experiments are conducted on the test cases transformed from the standard benchmark instances, and the ADMM-based method has superior convergence and solution quality. [ABSTRACT FROM AUTHOR]