Tuning the Parameters of a Memetic Algorithm to Solve Vehicle Routing Problem with Backhauls Using Design of Experiments

Vehicle Routing Problem with Backhauls (VRPB) is an extension of the general Vehicle Routing Problem (VRP). In contrast with general VRP, VRPB considers two types of linehaul and backhaul customers. VRPB tries to find optimal routes with minimum cost in which backhaul customers are visited after linehaul customers for a fleet of heterogeneous vehicles. In this paper, a Memetic Algorithm (MA) is developed to solve the VRPB. Similar to other metaheuristic algorithms, an important issue that affects the performance of MA is the selection of components employed in the algorithm along with their parameters' values. This work examines the effect of employing different combinations of MA components and parameter values on both the algorithm's efficiency and the quality of solutions. Design of Experiments (DOE) is introduced as a systematic approach to find the best combination of these parameters' values. Analysis of variance (ANOVA) is used to analyze the main effect and interaction effects of the considered parameters. Results verified the efficacy of the proposed MA method and the systematic tuning approach for MA to solve VRPB. Combinatorial optimization problems have attracted many researchers in recent decades due to their practical relevance and their considerable difficulties. Usually three different categories of approaches are used to solve these problems, namely, exact, heuristics, and metaheuristic methods. Exact methods apply analytical and mathematical approaches to solve the problems. Due to the considerable complexity of the problems, the efficacy of exact methods is limited to small scale problems. However exact methods yield analytically optimal solutions. Heuristic methods are employed to solve problems that are difficult to solve by using exact methods. They use simple intuitive techniques to make the search limited to potentially better solutions. Although heuristic methods can find a solution in a short time compared to exact methods, the analytically optimal solution is not guaranteed. To cope with the long computational time and limitation on quality of the obtained solutions, metaheuristic approaches are employed to solve combinatorial problems. Metaheuristic methods improve a solution 's quality by exploring the search space while using heuristics to make the search more intelligent. Metaheuristic methods try to obtain quality solutions in a reasonable time, employing heuristic algorithms as a part of their search algorithm. Metaheuristic methods have been applied to many research areas. In this paper, a new Memetic Algorithm (MA) will be developed to solve the Vehicle Routing Problem (VRP), a well-known combinatorial optimization problem. VRP is considered as the determination of optimal routes for fleet vehicles which are based on one depot to serve a number of customers. The optimality can be considered in terms of minimizing the total cost of transportation, minimizing the total distance of travel routes, and/or minimizing the total number of vehicles employed for serving customers. Several requirements and operational constraints confine VRP. For example, serving nodes can include deliveries along with pickups from customers, capacity of vehicles for carrying loads is limited, the length of each route should not exceed a pre-defined value, each customer should have a definite time of being served, the fleet can be composed of one or different types of vehicles, and some precedence relation can exist between customers. If the precedence is considered in VRP, then the problem becomes a Vehicle Routing Problem with Backhauls (VRPB). The complexity of metaheuristic algorithms originates from the need of setting the values of several components and parameters within them. These parameters' values can drastically affect the performance of metaheuristic algorithms. Therefore, it is very important to develop a systematic method of tuning up these parameters for the best performance of the developed metaheuristic algorithms.