Analysis of Ant Colony Optimization for Dynamic Shortest Path Problems

iii Preface This thesis was prepared at the department of Informatics and Mathematical Modelling at the Technical University of Denmark in fulfillment of the requirements for acquiring an M.Sc. in Computer Science and Engineering. It was supervised by associate professor Carsten Witt, and assigned a workload of 30 ECTS credits. The thesis examines how nature-inspired algorithms based on the Ant Colony Optimisation metaheuristic are able to solve dynamic shortest path problems. Source code for the software developed for this thesis has been submitted electronically, and can also be extracted from the PDF version by viewers that support file annotations. Extract source code (ZIP archive) iv Summary Combinatorial optimisation problems have traditionally been solved by specialized algorithms. Such problems also occur abundantly in nature, where they are solved without requiring excessive amounts of computing power or explicit algorithm design. Nature-inspired algorithms are based on behavior observed in nature, and are able to solve a wide variety of combinatorial optimisation problems without requiring much adaptation to a particular problem. Ant Colony Optimisation (ACO) is a metaheuristic encompassing a family of nature-inspired algorithms that are based on the foraging behavior of ants – using simulated pheromone trails to influence construction of random solutions to a problem, and updating the pheromone values to favor constructing good solutions over time. This thesis considers how variants of the Max-Min Ant System algorithm, based on the ACO metaheuristic, are able to solve dynamic shortest path problems. Known results bounding its expected run time on static shortest path problems are presented and applied to rediscovering the shortest paths after a one-time change is made to the graph, showing O(n 3) and Ω(n 3) upper and lower bounds (where n is the number of vertices in the graph) on the expected number of iterations to rediscover the shortest paths after specific one-time changes to the weight function. It is then shown that the λ-MMAS algorithm, which constructs λ solutions in a single iteration in expectation requires fewer iterations to find the shortest paths, and, if parallel computation resources are available, also requires less running time. This approach is shown to reduce the expected number of iterations to O(n) while only requiring a polynomial number of ants (with respect to n) to be started at each vertex. Using additional ants is also shown to allow iteration-best pheromone reinforcement, where the colony reinforces the best paths constructed in the current iteration …