Abel Garcia-Najera

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

The vehicle routing problem with time windows is a complex combinatorial problem with many real-world applications in transportation and distribution logistics. Its main objective is to find the lowest distance set of routes to deliver goods, using a fleet of identical vehicles with restricted capacity, to customers with service time windows. However, there are other objectives, and having a range of solutions representing the trade-offs between objectives is crucial for many applications. Although previous research has used evolutionary methods for solving this problem, it has rarely concentrated on the optimization of more than one objective, and hardly ever explicitly considered the diversity of solutions. This paper proposes and analyzes a novel multi-objective evolutionary algorithm, which incorporates methods for measuring the similarity of solutions, to solve the multi-objective problem. The algorithm is applied to a standard benchmark problem set, showing that when the similarity measure is used appropriately, the diversity and quality of solutions is higher than when it is not used, and the algorithm achieves highly competitive results compared with previously published studies and those from a popular evolutionary multi-objective optimizer.

Bi-objective Optimization for the Vehicle Routing Problem with Time Windows: Using Route Similarity to Enhance Performance

The Vehicle Routing Problem with Time Windows is a complex combinatorial optimization problem which can be seen as a fusion of two well known sub-problems: the Travelling Salesman Problem and the Bin Packing Problem. Its main objective is to find the lowest-cost set of routes to deliver demand, using identical vehicles with limited capacity, to customers with fixed service time windows. In this paper, we consider the minimization of the number of routes and the total cost simultaneously. Although previous evolutionary studies have considered this problem, none of them has focused on the similarity of solutions in the population. We propose a method to measure route similarity and incorporate it into an evolutionary algorithm to solve the bi-objective VRPTW. We have applied this algorithm to a publicly available set of benchmark instances, resulting in solutions that are competitive or better than others previously published.

An evolutionary approach for multi-objective vehicle routing problems with backhauls

Display Omitted A multiobjective evolutionary algorithm for vehicle routing problems with backhauls.Our approach equals or improves upon some of the best-known single-objective results.Instances have few bi-objective conflicts; SSMOEA, NSGA-II and MOEA/D perform well.Large tri-objective solution sets and significant differences in both algorithms.Triobjective setting finds comparable solutions to those from bi-objective settings. The vehicle routing problem (VRP) is an important aspect of transportation logistics with many variants. This paper studies the VRP with backhauls (VRPB) in which the set of customers is partitioned into two subsets: linehaul customers requiring a quantity of product to be delivered, and backhaul customers with a quantity to be picked up. The basic VRPB involves finding a collection of routes with minimum cost, such that all linehaul and backhaul customers are serviced. A common variant is the VRP with selective backhauls (VRPSB), where the collection from backhaul customers is optional. For most real world applications, the number of vehicles, the total travel cost, and the uncollected backhauls are all important objectives to be minimized, so the VRPB needs to be tackled as a multi-objective problem. In this paper, a similarity-based selection evolutionary algorithm approach is proposed for finding improved multi-objective solutions for VRPB, VRPSB, and two further generalizations of them, with fully multi-objective performance evaluation.

Preserving population diversity for the multi-objective vehicle routing problem with time windows

The Vehicle Routing Problems main objective is to find the lowest-cost set of routes to deliver goods to customers, which have a service time window, using a fleet of identical vehicles with restricted capacity. We consider the simultaneous minimization of the number of routes along with the total travel distance. Although previous research has used evolutionary methods for solving this problem, only a few of them have concentrated on the optimization of more than one objective, and none of them has considered the similarity of solutions. We propose and analyze one simple and straightforward method to measure similarity, which is incorporated into an evolutionary algorithm to solve the multi-objective problem. Results show that when we use the similarity measure to select one of the parents for crossover, solutions are spread over a wider area in the search space than when it is not used. Additionally, our solutions result to be competitive or better than others previously published.

An evolutionary approach to the multi-objective pickup and delivery problem with time windows

The pickup and delivery problem (PDP) has many real-life applications. In this problem there is a customer set which is partitioned into two subsets: the customers requiring an amount of product (delivery) and the customers providing the product (pickup). There is also a set of transportation requests, which specify the quantity of product that has to be picked up from an origin customer and delivered to a destination customer. There exist a number of vehicles available to be used for completing these tasks. PDP consists of finding a collection of routes with minimum cost, such that all transportation request are serviced. Traditionally, the number of routes has been minimized first, and then the travel distance, however, if these objectives are considered to be equally important, the problem can be tackled as a bi-objective problem. Moreover, time is not always directly proportional to distance, thus travel time can also be considered an important criterion to be optimized and, consequently, PDP has to be regarded as a tri-objective problem. In this paper, we solve PDP as a problem with multiple objectives by means of an evolutionary algorithm and evaluate its performance with proper multi-objective performance tools.

Comparison of similarity measures for the multi-objective vehicle routing problem with time windows

The Vehicle Routing Problem can be seen as a fusion of two well known combinatorial problems, the Travelling Salesman Problem and Bin Packing Problem. It has several variants, the one with Time Windows being the case of study in this paper. Its main objective is to find the lowest-distance set of routes to deliver goods to customers, which have service time windows, using a fleet of identical vehicles with restricted capacity. We consider the simultaneous minimisation of the number of routes along with the total travel distance. Although previous research has considered evolutionary methods for solving this problem, none of them has concentrated on the similarity of solutions. We analyse here two methods to measure similarity, which are incorporated into an evolutionary algorithm to solve the multi-objective problem. We have applied this algorithm to a publicly available set of benchmark instances, and when these similarity measures are considered, our solutions are seen to be competitive or better than others previously published.

A Multi-objective Genetic Algorithm for the Software Project Scheduling Problem

The software project scheduling problem considers the assignment of employees to project tasks with the aim of minimizing the project cost and delivering the project on time. Recent research takes into account that each employee is proficient in some development tasks only, which requiere specific skills. However, this cannot be totally applied in the Mexican context due to software companies do not categorize their employees by software skills, but by their skill level instead. In this study we propose a model that is closer to how software companies operate in Mexico. Moreover, we propose a multi-objective genetic algorithm for solving benchmark instances of this model. Results show that our proposed genetic algorithm performs similarly to two recent approaches and that it finds better multi-objective solutions when they are compared to those found by a well-known multi-objective optimizer.

Optimizing delivery time in multi-objective vehicle routing problems with time windows

The Vehicle Routing Problem with Time Windows involves finding the lowest-cost set of routes to deliver goods to customers, which have service time windows, using a homogeneous fleet of vehicles with limited capacity. In this paper, we propose and analyze the performance of an improved multi-objective evolutionary algorithm, that simultaneously minimizes the number of routes, the total travel distance, and the delivery time. Empirical results indicate that the simultaneous minimization of all three objectives leads the algorithm to find similar or better results than any combination of only two objectives. These results, although not the best in all respects, are better in some aspects than all previously published approaches, and fully multi-objective comparisons show clear improvement over the popular NSGA-II algorithm.

A Comparison of Bio-Inspired Approaches for the Cluster-Head Selection Problem in WSN

A Wireless Sensor Network (WSN) is composed of a set of energy and processing-constrained devices that gather data about a set of phenomena. An efficient way to enlarge the lifetime of a wireless sensor network is clustering organization, which structures hierarchically the sensors in groups and assigns one of them as a cluster head. Such cluster head is responsible of specific tasks like gathering data from other cluster sensors and resending it to the base station through the network. Using a cluster-head organization, data gathering process is improved and by extension, the network lifetime is enlarged. However, due to the additional tasks that every cluster head has to perform, their own energy is spent faster than that of the other sensors in the cluster. Each time that a cluster head is out of battery, it is necessary to select a new cluster head from the survival sensors to continue with head duties. In this chapter, we present a performance comparison of three state-of-the-art MOEAs, namely NSGA-II, SMS-EMOA, and MOEA/D for the cluster-head selection problem in Wireless Sensor Networks.

Discrete many-objective optimization problems: The case of the pickup and delivery problem

The pickup and delivery problem (PDP) deals with a set of transportation requests, which specify the quantity of product that has to be picked up from an origin and delivered to a destination. PDP consists of finding a set of routes with minimum cost, such that all transportation requests are serviced by a fleet of vehicles. Usually, only two objectives have been considered to evaluate the cost of a solution. However, in many applications, some other objectives emerge, for example, the minimization of the workload imbalance, and the minimization of the uncollected profit. If we consider all these objectives equally important, PDP can be tackled as a many-objective problem. Although some studies have analyzed the scalability of continuous optimization problems, there are just a few studies using discrete optimization problems. Thus, in this paper we study the following elements: (i) the properties of the many-objective PDP regarding scalability, i.e., conflict between each pair of objectives and the proportion of non-dominated solutions as we vary the number of objectives, and finally (ii) the change of PDPs difficulty when the number of objectives is increased. Results show that most of the objectives pairs are actually in conflict, and that the problem is more difficult to solve as more objectives are considered, thus making it complicated to differentiate between equally good solutions.