2、硬时问窗问题和软时间窗问题根据对车辆到达客户迟到或早到是否允许惩罚

2. Hard time window problem and soft time window problem <br>According to whether penalties are allowed for vehicles arriving late or early to customers, the vehicle routing problem with time window can be divided into hard time window problems and soft time window problems. VRPSTW introduces penalties Function to describe the extra cost incurred in delay or early arrival. Compared with the extensive research on VRPHTW, the research results of VRPSTW are relatively few. Fu has conducted in-depth research on VRPSTW. According to the different characteristics of the penalty function, VRPSTW is further divided into multiple types, and finally designed to adapt to various types of VRPSTW solutions. Search algorithm; for the medium-scale soft time window problem, an accurate algorithm of "enumerate before optimization" is proposed to obtain the optimal solution; the soft time window problem is described as a mixed integer programming model, and a "first" The heuristic solving algorithm of “constructing path after clustering”; using tabu search algorithm to solve the soft time window problem, the soft time window problem with flexible travel time is studied, and the travel time function is convex and time When the window cost function is a non-convex function, a local search algorithm is designed.

2, hard time to ask window questions and soft time window questions<br>Depending on whether penalties are allowed for late or early arrival of the vehicle to the customer, the vehicle path issue with time window can be divided into hard window issues and soft time window issues, and VRPSTW describes the additional costs incurred by introducing a penalty function to describe delays or early arrival. Compared with the extensive research of VRPTW, the research results of VRPSTW are relatively few, Fu has carried out in-depth research on VRPSTW, according to the different characteristics of the punishment function, further divided the VRPSTW into various types, and finally designed a taboo search algorithm to adapt to all kinds of VRPSTW solutions; The heuristic solution algorithm of "clustering and then constructing path" is used to solve the soft time window problem by using taboo search algorithm, the soft time window problem of variable travel time elasticity is studied, and a local search solution algorithm is designed for travel time function as a convex function and time window cost function as a non-convex function.

2. Hard time window problem and soft time window problem<br>VRPSTW can be divided into hard time window problem and soft time window problem according to whether the punishment is allowed for the customers arriving late or early. VRPSTW describes the extra cost of delay or early arrival by introducing a penalty function. Compared with the extensive research of vrphtw, the research results of VRPSTW are relatively less. Fu has carried out in-depth research on VRPSTW. According to the different characteristics of penalty function, VRPSTW is further divided into various types, and finally designed to adapt to all kinds of VRPSTW For the medium-sized soft time window problem, an accurate algorithm of "enumeration before optimization" is proposed to obtain the optimal solution; the soft time window problem is described as a mixed integer programming model, and an heuristic algorithm of "clustering before constructing path" is proposed; the soft time window problem is solved by Tabu Search Algorithm, and the travel time is optimized In this paper, we study the flexible soft time window problem, and design a local search algorithm for the case that the travel time function is convex and the time window cost function is non convex.<br>