An ant colony optimization for transport scheduling with time windows Rodrigo Henriques Univ. Trás-os-Montes e Alto Douro 5000 Vila Real henriques.rodrigo@live.com.pt Paulo Salgado Engineering Department Univ. Trás-os-Montes e Alto Douro 5000 Vila Real psal@utad.pt António Cunha Engineering Department Univ. Trás-os-Montes e Alto Douro 5000 Vila Real acunha@utad.pt Abstract Many real-world problems, due to the high number of data processing and/or complexity of the problem itself, makes data processing very long and in extreme cases impossible. The combinatorial optimization falls into this category of problems. One way to solve these problems is using Swarm Intelligence. Swarm intelligence describes the collective behavior of decentralized, self-organized systems. Typically made up of a population of simple agents interacting locally with one another and with their environment. The agents follow very simple rules, in which, interactions between such agents lead to the emergence of "intelligent" global behavior, and a feasible solution. Ant colonies, a specific branch of Swarm Intelligence, are used nowadays as multi-agent systems to solve different optimization problems from the NP-hard class. Examples of such problems are the travelling salesman, quadratic assignment, vehicle routing, graph coloring and satisfiability problem. This paper presents an algorithm developed for a specific problem, similar to the travelling salesman problem. Ant colony optimization is used to solve a scheduling problem for school transport. This includes a set of specific restrictions, such as the use of multiple vehicles to pickup/deliver the children and time intervals for each point of pickup/delivery. 1. Introduction In recent years, it is possible to see an always increasing interest among both transportation decision makers and practitioners in exploring the feasibility of applying Artificial Intelligence (AI) paradigms to improve the efficiency, safety and quality of service in transportation systems [1]. A way to improve the efficiency is by optimizing the scheduling. Scheduling is concerned with allocating limited resources to tasks to optimize some performance criterion, such as completion time or production cost [2]. These problems are dynamic and thus require systematic re-optimizations due to system and/or environmental changes. Even though it is possible to handle such dynamic problems as a series of individual processes via restarting the optimization algorithm after each change, this may lead to a significant loss of useful information, especially when the change is not too drastic. Since most of such problems have multimodal nature, which further complicates the dynamic optimization problems, the need for powerful and efficient optimization techniques is imminent [3]. A major thrust in algorithmic development is the design of algorithmic models to solve increasingly complex problems. Enormous successes have been achieved through the modeling of biological and natural intelligence, resulting in so-called “intelligent systems”. These intelligent algorithms include Artificial Neural Networks, Evolutionary Computation, Swarm Intelligence (SI), Artificial Immune Systems, and Fuzzy Systems [4]. Ant Colony Optimization (ACO), a subfield of SI, is successfully used nowadays as multi-agent systems (MAS) to solve difficult optimization problems such as travelling salesman (TSP), quadratic assignment, vehicle routing, graph coloring and satisfiability problem [5]. The problem approached in this paper is very similar to the Multiple Travelling Salesman Problem (mTSP), so ACO presents itself as a good approach for finding a near optimal solution. This paper presents a possible solution for school transport scheduling with timetables. The paper is structured as follows: Section 2 introduces the NP-Hard Problems, TSP and mTSP. SI and some