Rescheduling and optimization of logistic processes using GA and ACO

Abstract

This paper presents a comparative study of genetic algorithms (GA) and ant colony optimization (ACO) applied the online re-optimization of a logistic scheduling problem. This study starts with a literature review of the GA and ACO performance for different benchmark problems. Then, the algorithms are compared on two simulation scenarios: a static and a dynamic environment, where orders are canceled during the scheduling process. In a static optimization environment, both methods perform equally well, but the GA are faster. However, in a dynamic optimization environment, the GA cannot cope with the disturbances unless they re-optimize the whole problem again. On the contrary, the ant colonies are able to find new optimization solutions without re-optimizing the problem, through the inspection of the pheromone matrix. Thus, it can be concluded that the extra time required by the ACO during the optimization process provides information that can be useful to deal with disturbances.

Introduction

In the last decade, leading companies all over the world, across all business areas, adopted the supply chain (Barbuceanu and Fox, 1996) organization methodology to face the increasing competitiveness of the markets. One of the most challenging problems in supply chain management is the optimization of the logistic subprocess (Swaminathan et al., 1998). This is a very complex scheduling problem that deals with the planning, handling and control of the storage of goods between the manufacturing point and the consumption point. However, a question that arises throughout the development of every new scheduling application is “What optimization method should be used?”. Is there a method that guarantees a higher chance of finding the global optimum? Which is the easiest method to program and tune?

Over the last decade, meta-heuristics have replaced the analytical methods, exhaustive search methods or local search heuristics in the optimization of scheduling problems (Jain and Meeran, 1999). These type of methods, which includes genetic algorithms (GA) (Holland, 1975), simulated annealing (Kirkpatrick et al., 1983), tabu search (Glover and Laguna, 1997) or ant colony optimization (ACO) (Dorigo et al., 1996), uses an algorithm to guide simple heuristics in the search of global optima. Nowadays, meta-heuristics are considered to be very powerful scheduling techniques (Jain and Meeran, 1999) and therefore suitable to be applied to the optimization of logistic processes (Silva et al., 2005).

GA are the most studied and applied meta-heuristic in the optimization field (Michalewicz, 1999, Michalewicz and Fogel, 2002), because GA are very easy to implement in all sort of problems, and usually guarantee good solutions, whatever the type of solution space. Although is not difficult to find for specific problems methods that outperform GA, it is almost impossible to find any other method that performs as well as GA in so many different types of optimization problems.

ACO is a relatively new optimization technique that has been gaining followers in the past decade, since it is especially suited for problems with dynamic behavior (Dorigo and Stützle, 2004). Furthermore, the intrinsic agent nature makes it also suitable for parallel and multi-agent applications, like supply chain management (Parunak, 1997). However, the application of ACO is restricted to optimization problems that can be described by graphs (Dorigo and Stützle, 2004).

For these reasons, GA and ACO are both very appealing optimization methods to design scheduling applications such as the logistic scheduling problem, because they are simple to implement and efficient in finding optimal solutions. But which of the algorithms should be used? At the end, the optimization method ends up to be the technique that one knows better. Or, if there is the time and the expertise knowledge, it is possible to test more than one method and choose the one that performs better. But the question remains: are there any elements that might tell us before hand which algorithm is better for a specific application?

To answer this question, it would help to have a systematic comparison between the two methods for different problems. Although the literature in optimization is very rich in terms of algorithm implementations, only few authors present comparison results with other algorithms. It is possible, however, to compare algorithms presented in different works when the test instances are the same. Nevertheless, the results often lack accuracy indicators based on statistical analysis; the analyzes do not consider the same measurements or number of trials; different local heuristics are used with each method; finally, the computational effort, when measured, is presented on a pure time basis, which is not easily comparable from one computer to another.

This paper describes a systematic comparison between GA and ACO to assist the decision process about what algorithm should be used to reschedule a logistic system. The comparison includes a literature survey on several benchmark optimization problems, in order to make valid assessments for optimization problems in general, and a study on the performance of each algorithm in a logistic scheduling problem. This paper describes further the importance of the information generated during the optimization process and how this information can be used in dynamic environments. Nowadays, the optimization of real systems is no longer a static problem, where all the parameters remain constant during the optimization process (Sarmiento and Nagi, 1999). In the logistic system case, the changes on the optimization environment may be caused by cancellation of orders from the clients. Therefore, the optimization method of a logistic system has to cope with these issues.

The paper is organized as follows. Section 2 presents a literature survey on optimization results for different benchmark problems with GA and ACO. The logistic scheduling problem is introduced in Section 3, which also describes the GA and ACO implementations. The comparison between the methods for static logistic problem and for dynamic logistic problems is in Section 5. Section 6 concludes the paper and indicates the future research steps.