Algorithms for Variants of Routing Problems

In this thesis, we propose mathematical optimization models and algorithms for variants of routing problems. The first contribution consists of models and algorithms for the Traveling Salesman Problem with Time-dependent Service times (TSP-TS). We propose a new Mixed Integer Programming model and develop a multi-operator genetic algorithm and two Branch-and-Cut methods, based on the proposed model. The algorithms are tested on benchmark symmetric and asymmetric instances from the literature, and compared with an existing approach, showing the effectiveness of the proposed algorithms. The second work concerns the Pollution Traveling Salesman Problem (PTSP). We present a Mixed Integer Programming model for the PTSP and two mataheuristic algorithms: an Iterated Local Search algorithm and a Multi-operator Genetic algorithm. We performed extensive computational experiments on benchmark instances. The last contribution considers a rich version of the Waste Collection Problem (WCP) with multiple depots and stochastic demands using Horizontal Cooperation strategies. We developed a hybrid algorithm combining metaheuristics with simulation. We tested the proposed algorithm on a set of large-sized WCP instances in non-cooperative scenarios and cooperative scenarios

A Hybrid Lehmer Code Genetic Algorithm and Its Application on Traveling Salesman Problems

Traveling Salesman Problems (TSP) is a widely studied combinatorial optimization problem. The goal of the TSP is to find a tour which begins in a specific city, visits each of the remaining cities once and returns to the initial cities such that the objective functions are optimized, typically involving minimizing functions like total distance traveled, total time used or total cost. Genetic algorithms were first proposed by John Holland (1975). It uses an iterative procedure to find the optimal solutions to optimization problems. This research proposed a hybrid Lehmer code Genetic Algorithm. To compensate for the weaknesses of traditional genetic algorithms in exploitation while not hampering its ability in exploration, this new genetic algorithm will combine genetic algorithm with 2-opt and non-sequential 3-opt heuristics. By using Lehmer code representation, the solutions created by crossover parent solutions are always feasible. The new algorithm was used to solve single objective and multi-objectives Traveling Salesman Problems. A non Pareto-based technique will be used to solve multi-objective TSPs. Specifically we will use the Target Vector Approach. In this research, we used the weighted Tchebycheff function with the ideal points as the reference points as the objective function to evaluate solutions, while the local search heuristics, the 2-opt and non-sequential 3-opt heuristics, were guided by a weighted sum function

Coarse-grained parallel genetic algorithms: Three implementations and their analysis

Although solutions to many problems can be found using direct analytical methods such as those calculus provides, many problems simply are too large or too difficult to solve using traditional techniques. Genetic algorithms provide an indirect approach to solving those problems. A genetic algorithm applies biological genetic procedures and principles to a randomly generated collection of potential solutions. The result is the evolution of new and better solutions. Coarse-Grained Parallel Genetic Algorithms extend the basic genetic algorithm by introducing genetic isolation and distribution of the problem domain. This thesis compares the capabilities of a serial genetic algorithm and three coarse-grained parallel genetic algorithms (a standard parallel algorithm, a non-uniform parallel algorithm and an adaptive parallel algorithm). The evaluation is done using an instance of the traveling salesman problem. It is shown that while the standard course-grained parallel algorithm provides more consistent results than the serial genetic algorithm, the adaptive distributed algorithm out-performs them both. To facilitate this analysis, an extensible object-oriented library for genetic algorithms, encompassing both serial and coarse-grained parallel genetic algorithms, was developed. The Java programming language was used throughout