Abstract not found

Adaptive tools in virtual environments Independent component analysis for multimedia

Ph.D. degree in engineering. The thesis deals with different aspects of mathematical modelling of systems

We present a column generation approach for obtaining strong lower bounds to the periodic vehicle routing problem with time windows (PVRPTW) where customers must be served several times during a planning period. For this a set-covering model is introduced whose linear programming relaxation is solved. The pricing subproblem, responsible for generating new columns, is an elementary shortest path problem with resource constraints. The latter is solved by a label correcting dynamic programming algorithm for which we introduce appropriate label resources, extension functions, and dominance rules. Different settings for this algorithm are suggested and applied in combination to tune its behavior. We further propose a greedy randomized adaptive search procedure (GRASP) to solve the pricing subproblem. Experimental results on test instances differing in size, time windows and period length indicate strong lower bounds for many instances and the advantage of applying the metaheuristic in combination with the dynamic programming algorithm to save computation time on larger instances.

This thesis is submitted in partial fulfilment of the requirements for the Ph.D. degree at the Technical University of Denmark (DTU). The project took place as an industrial research Ph.D. project administered by the Danish Academy of Technical Sciences (ATV) and financially supported by the Danish Agency for Trade and Industry in the period August 1st 1997 – August 31st 2001 during which there was a total of 10.5 months leave. It was carried out with the following partners: Math-Tech Aps, Informatics and Mathematical Modelling (IMM) at DTU, and

(VRPTW) is an example of scheduling in constrained environment. It is a well known NP hard combinatorial scheduling optimization problem in which minimum number of routes have to be determined to serve all the customers within their specified time windows. So far different analytic and heuristic approaches have been tried to solve such problems. In this paper we proposed an algorithm which incorporates a new local search technique with genetic algorithm approach to solve time constrained vehicle routing and scheduling problems in various scenarios. Keywords- Vehicle routing problem, genetic algorithm, heuristics based search techniques I.