Petrică C. Pop

An improved hybrid algorithm for solving the generalized vehicle routing problem

The generalized vehicle routing problem (GVRP) is a natural extension of the classical vehicle routing problem (VRP). In GVRP, we are given a partition of the customers into groups (clusters) and a depot and we want to design a minimum length collection of routes for the fleet of vehicles, originating and terminating at the depot and visiting exactly one customer from each group, subject to capacity restrictions. The aim of this paper is to present an efficient hybrid heuristic algorithm obtained by combining a genetic algorithm (GA) with a local-global approach to the GVRP and a powerful local search procedure. The computational experiments on several benchmark instances show that our hybrid algorithm is competitive to all of the known heuristics published to date.

An efficient Reverse Distribution System for solving sustainable supply chain network design problem

This paper deals with a sustainable supply chain network design problem (SSCNDP) arising in the public sector. In the considered SSCNDP, given a manufacturer, a set of m potential distribution centers (DCs) having a given distinct capacity, and a set of n customers, each one with a particular demand, we have to select the number and the location of the DCs necessary to supply demands to all the customers and the allocation of the customers to these DCs such that the installation and transportation costs integrated with greenhouse gas (GHG) emissions are minimized. Due to the complexity of the problem, an efficient Reverse Distribution System (RDS) consisting of several improved classical heuristic algorithms is proposed. The developed approaches were tested and promising results were obtained on benchmark instances based on the literature, involving between 10 and 50 distribution centers and between 10 and 100 customers.

An efficient genetic algorithm for solving the generalized traveling salesman problem

The generalized traveling salesman problem (GTSP) is a generalization of the classical traveling salesman problem. The GTSP is known to be an NP-hard problem and has many interesting applications. In this paper we present a local-global approach for the generalized traveling salesman problem and as well an efficient algorithm for solving the problem based on genetic algorithms. Computational results are reported for Euclidean TSPlib instances and compared with the existing ones. The obtained results point out that our 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.

An improved immigration memetic algorithm for solving the heterogeneous fixed fleet vehicle routing problem

This paper deals with the heterogeneous fixed fleet vehicle routing problem (HFFVRP) which is a generalization of the classical vehicle routing problem (VRP) in the sense that the fixed fleet of vehicles is assumed to be heterogeneous. The objective of HFFVRP is to find the best fleet composition and the collection of routes such that the total costs are minimized. To address this combinatorial optimization problem, we design and implement a hybrid heuristic model integrating a genetic algorithm, a local search mechanism and an immigration strategy. Several strategies for generating the initial population of the genetic algorithm in relation with six local search heuristics are considered. An important feature of the proposed approach refers to the immigration strategy used to ensure diversification by which the level of evolution for the new immigrant individuals increases along with the evolution of the population. The proposed algorithm is tested on a set of HFFVRP benchmark instances and the preliminary results point out that our approach is an attractive and appropriate method to explore the solution space of this complex problem leading to good solutions within reasonable computational times.

A two-level solution approach for solving the generalized minimum spanning tree problem

Abstract In this paper, we are addressing the generalized minimum spanning tree problem, denoted by GMSTP, which is a variant of the classical minimum spanning tree (MST) problem. The main characteristic of this problem is the fact that the vertices of the graph are partitioned into a given number of clusters and we are looking for a minimum-cost tree spanning a subset of vertices which includes exactly one vertex from each cluster. We describe a two-level solution approach for solving the GMSTP obtained by decomposing the problem into two logical and natural smaller subproblems: an upper-level (global) subproblem and a lower-level (local) subproblem and solving them separately. The goal of the first subproblem is to determine (global) trees spanning the clusters using a genetic algorithm with a diploid representation of the individuals, while the goal of the second subproblem is to determine the best tree (w.r.t. cost minimization), for the above mentioned global trees, spanning exactly one vertex from each cluster. The second subproblem is solved optimally using dynamic programming. Extensive computational results are reported and discussed for an often used set of benchmark instances. The obtained results show an improvement in the quality of the achieved solutions, and demonstrate the efficiency of our approach compared to the existing methods from the literature.

Reducing the bandwidth of a sparse matrix with a genetic algorithm

Abstract The matrix bandwidth minimization problem (MBMP) consists in finding a permutation of the lines and columns of a given sparse matrix in order to keep the non-zero elements in a band that is as close as possible to the main diagonal. Equivalently in terms of graph theory, MBMP is defined as the problem of finding a labelling of the vertices of a given graph G such that its bandwidth is minimized. In this paper, we propose an improved genetic algorithm (GA)-based heuristic for solving the matrix bandwidth minimization problem, motivated by its robustness and efficiency in a wide area of optimization problems. Extensively computational results are reported for an often used set of benchmark instances. The obtained results on the different instances investigated show improvement of the quality of the solutions and demonstrate the efficiency of our GA compared to the existing methods in the literature.

A Novel Hybrid Algorithm for Solving the Clustered Vehicle Routing Problem

This paper presents a new hybrid optimization approach based on genetic algorithm and simulated annealing for solving the clustered vehicle routing problem (CluVRP). The problem investigated in this paper is a NP-hard combinatorial optimization problem that generalizes the classical vehicle routing problem (VRP) and it is closely related to the generalized vehicle routing problem (GVRP). Preliminary computational results on two sets of benchmark instances are reported and discussed.

A Memetic Algorithm for Solving the Generalized Minimum Spanning Tree Problem

The generalized minimum spanning tree problem is a natural extension of the classical minimum spanning tree problem, looking for a tree with minimum cost, spanning exactly one node from each of a given number of predefined, mutually exclusive and exhaustive node sets. In this paper we present a memetic algorithms for solving the generalized minimum spanning tree problem that combines the population concept of genetic algorithms with a fast local improvement method. The proposed algorithm is competitive with other heuristics published to date in both solution quality and computation time. The computational results for several benchmarks problems are reported and the results point out that the memetic algorithm is an appropriate method to explore the search space of this complex problem and leads to good solutions in a reasonable amount of time.

A Variable Neighborhood Search Approach for Solving the Generalized Vehicle Routing Problem

Variable Neighborhood Search (VNS) is quite a recent metaheuristic used for solving optimization problems based on a systematic change of the neighborhoods structures within the search in order to avoid local optima. In this paper, we propose a VNS based heuristic for solving the generalized vehicle routing problem (GVRP) that uses different neighborhood structures which are adapted for the problem. Computational results for an often used collection of benchmark instances show that our proposed heuristic delivered competitive results compared to the existing state-of-the-art algorithms for solving the GVRP.

An Innovative Approach to Manage Heterogeneous Information Using Relational Database Systems

In this paper, we propose a novel database design structure that can deal with all the aspects of the complexity of data that has to be managed, using the concepts of defining objects in object oriented programming (OOP). As well, we create a set of procedures in database system that allows us to manage all type of data, without knowing the structure of the database. The creation of the database structure, also the mechanism of inserting and retrieval the information is made by using a metadata set of information.