Petrica C. Pop

A new relaxation method for the generalized minimum spanning tree problem

We consider a generalization of the minimum spanning tree problem, called the generalized minimum spanning tree problem, denoted by GMST. It is known that the GMST problem is -hard. We present several mixed integer programming formulations of the problem. Based on a new formulation of the problem we give a new solution procedure that finds the optimal solution of the GMST problem for graphs with nodes up to 240. We discuss the advantages of our approach in comparison with earlier methods.

A genetic algorithm for solving the generalized vehicle routing problem

The generalized vehicle routing problem is a variant of the well-known vehicle routing problem in which the nodes of a graph are partitioned into a given number of node sets (clusters) and the objective is to find the minimum-cost delivery or collection of routes, subject to capacity restrictions, from a given depot to the number of predefined clusters passing through one node from each clusters We present an effective metaheuristic algorithm for the problem based on genetic algorithms The proposed metaheuristic is competitive with other heuristics published to date in both solution quality and computation time Computational results for benchmarks problems are reported and the results point out that GA is an appropriate method to explore the search space of this complex problem and leads to good solutions in a short amount of time.

New Models of the Generalized Minimum Spanning Tree Problem

We consider a generalization of the Minimum Spanning Tree Problem, called the Generalized Minimum Spanning Tree Problem, denoted by GMST. It is known that the GMST problem is NP-hard. We present a stronger result regarding its complexity, namely, the GMST problem is NP-hard even on trees as well an exact exponential time algorithm for the problem based on dynamic programming. We describe new mixed integer programming models of the GMST problem, mainly containing a polynomial number of constraints. We establish relationships between the polytopes corresponding to their linear relaxations. Based on a new model of the GMST we present a solution procedure that solves the problem to optimality for graphs with nodes up to 240. We discuss the advantages of our method in comparison with earlier methods.

The generalized traveling salesman problem solved with ant algorithms

A well known

Generalized network design problems : modeling and optimization

\mathcal{NP}

Solving the Generalized Vehicle Routing Problem with an ACS‐based Algorithm

NP-hard problem called the generalized traveling salesman problem (GTSP) is considered. In GTSP the nodes of a complete undirected graph are partitioned into clusters. The objective is to find a minimum cost tour passing through exactly one node from each cluster. An exact exponential time algorithm and an effective meta-heuristic algorithm for the problem are presented. The meta-heuristic proposed is a modified Ant Colony System (ACS) algorithm called reinforcing Ant Colony System which introduces new correction rules in the ACS algorithm. Computational results are reported for many standard test problems. The proposed algorithm is competitive with the other already proposed heuristics for the GTSP in both solution quality and computational time.

On the complexity of the selective graph coloring problem in some special classes of graphs

The idea of sensitivity in ant colony systems has been exploited in hybrid ant-based models with promising results for many combinatorial optimization problems. Heterogeneity is induced in the ant population by endowing individual ants with a certain level of sensitivity to the pheromone trail. The variable pheromone sensitivity within the same population of ants can potentially intensify the search while in the same time inducing diversity for the exploration of the environment. The performance of sensitive ant models is investigated for solving the generalized vehicle routing problem. Numerical results and comparisons are discussed and analysed with a focus on emphasizing any particular aspects and potential benefits related to hybrid ant-based models.

A hybrid heuristic approach for solving the generalized traveling salesman problem

Chapter 1: Introduction Chapter 2: The generalized minimum spanning tree problem Chapter 3: The generalized traveling salesman problem Chapter 4: The railway traveling salesman problem Chapter 5: The generalized vehicle routing problem Chapter 6: The generalized fixed-charge network design problem.