Solving Hop-constrained MST problems with ACO (original) (raw)
Related papers
2013
In this work we address the Hop-Constrained Minimum cost Flow Spanning Tree (HMFST) problem with nonlinear costs. The HMFST problem is an extension of the Hop-Constrained Minimum Spanning Tree problem since it considers flow requirements other than unit flows. We propose a hybrid heuristic, based on Ant Colony Optimization (ACO) and on Local Search (LS), to solve this class of problems given its combinatorial nature and also that the total costs are nonlinearly flow dependent with a fixed-charge component. In order to test the performance of our algorithm we have solved a set of benchmark problems available online and compared the results obtained with the ones reported in the literature for a Multi-Population hybrid biased random key Genetic Algorithm (MPGA). Our algorithm proved to be able to find an optimum solution in more than 75% of the runs, for each problem instance solved, and was also able to improve on many results reported for the MPGA. Furthermore, for every single prob...
In this work we address the Hop-Constrained Minimum cost Flow Spanning Tree (HMFST) problem with nonlinear costs. The HMFST problem is an extension of the Hop-Constrained Minimum Spanning Tree problem since it considers flow requirements other than unit flows. We propose a hybrid heuristic, based on Ant Colony Optimization (ACO) and on Local Search (LS), to solve this class of problems given its combinatorial nature and also that the total costs are nonlinearly flow dependent with a fixed-charge component. In order to test the performance of our algorithm we have solved a set of benchmark problems available online and compared the results obtained with the ones reported in the literature for a Multi-Population hybrid biased random key Genetic Algorithm (MPGA). Our algorithm proved to be able to find an optimum solution in more than 75% of the runs, for each problem instance solved, and was also able to improve on many results reported for the MPGA. Furthermore, for every single problem instance we were able to find a feasible solution, which was not the case for the MPGA. Regarding running times, our algorithm improves upon the computational time used by CPLEX and was always lower than that of the MPGA.
Optimization Letters, 2014
Performance appraisal increasingly assumes a more important role in any organizational environment. In the trucking industry, drivers are the company's image and for this reason it is important to develop and increase their performance and commitment to the company's goals. This paper aims to create a performance appraisal model for trucking drivers, based on a multi-criteria decision aid methodology. The PROMETHEE and MMASSI methodologies were adapted using the criteria used for performance appraisal by the trucking company studied. The appraisal involved all the truck drivers, their supervisors and the company's Managing Director. The final output is a ranking of the drivers, based on their performance, for each one of the scenarios used. The results are to be used as a decisionmaking tool to allocate drivers to the domestic haul service.
An ant colony optimization metaheuristic for single-path multicommodity network flow problems
2010
This paper studies the single-path multicommodity network flow problem (SMNF), in which the flow of each commodity can only use one path linking its origin and destination in the network. We study two versions of this problem based on two different objectives. The first version is to minimize network congestion, an issue of concern in traffic grooming over wavelength division multiplexing (WDM), and in which there generally exists a commodity flow between every pair of nodes. The second problem is a constrained version of the general linear multicommodity flow problem, in which, for each commodity, a single path is allowed to send the required flow, and the objective is to determine a flow pattern that obeys the arc capacities and minimizes the total shipping cost. Based on the node-arc and the arc-chain representations, we first present two formulations. Owing to computational impracticality of exact algorithms for practical networks, we propose an ant colony optimization-(ACO) based metaheuristic to deal with SMNF. Considering different problem properties, we devise two versions of ACO metaheuristics to solve these two problems, respectively. The proposed algorithms' efficiencies are experimentally investigated on some generated instances of SMNF. The test results demonstrate that the proposed ACO metaheuristics are computationally efficient and robust approaches for solving SMNF.
An Improved Ant-Based Algorithm for the Degree-Constrained Minimum Spanning Tree Problem
IEEE Transactions on Evolutionary Computation, 2012
The degree-constrained minimum spanning tree (DCMST) problem is the problem of finding the minimum cost spanning tree in an edge weighted complete graph such that each vertex in the spanning tree has degree ≤ d for some d ≥ 2. The DCMST problem is known to be NP-hard. This paper presents an ant-based algorithm to find low cost degree-constrained spanning trees (DCST). The algorithm employs a set of ants which traverse the graph and identify a set of candidate edges, from which a DCST is constructed. Local optimization algorithms are then used to further improve the DCST. Extensive experiments using 612 problem instances show many improvements over existing algorithms.
2020
The minimum spanning tree problem consists of finding a minimum cost spanning tree in an undirected graph in various types of networks. Minimum weight spanning tree visits all vertices that are in the similar associated part as the beginning node. In this investigation, we examine the various techniques for solving a Generalized Minimum Weight Spanning Tree Problem. Also, we present <em>the An Approach for Solving Minimum Spanning Tree Problem and Transportation Problem Using Modified Ant Colony Algorithm</em>. Different methodologies have been made in the composition for dealing with transportation on finding an initial basic feasible solution and the rest to find the optimal solution to the TP. Northwest, Least Cost, and Vogel's Approximation techniques are created to find an initial basic feasible solution whereas the Modified Distribution (MODI) Method and Stepping Stone Method is designed to find an optimal solution to the TP. In this examination, we propose a h...
Concave minimum cost network flow problems solved with a colony of ants
Journal of Heuristics, 2012
In this work we address the Single-Source Uncapacitated Minimum Cost Network Flow Problem with concave cost functions. This problem is NP-hard, therefore we propose a hybrid heuristic to solve it. Our goal is not only to apply an Ant Colony Optimization (ACO) algorithm to such a problem, but also to provide an insight on the behaviour of the parameters in the performance of the algorithm. The performance of the ACO algorithm is improved with the hybridization of a local search procedure. The core ACO procedure is used to mainly deal with the exploration of the search space, while the Local Search is incorporated to further cope with the exploitation of the best solutions found. The method we have developed has proven to be very efficient while solving both small and large size problem instances. The problems we have used to test the algorithm were previously solved by other authors using other population based heuristics. Our algorithm was able to improve upon some of their results in terms of solution quality, proving that the HACO algorithm is a very good alternative approach to solve these problems. In addition, our algorithm is substantially faster at achieving these improved solutions. Furthermore, the magnitude of the reduction of the computational requirements grows with problem size.
2006
We consider the Bounded Diameter Minimum Spanning Tree problem and describe four neighbourhood searches for it. They are used as local improvement strategies within a variable neighbourhood search (VNS), an evolutionary algorithm (EA) utilising a new encoding of solutions, and an ant colony optimisation (ACO). We compare the performance in terms of effectiveness between these three hybrid methods on a suite of popular benchmark instances, which contains instances too large to solve by current exact methods. Our results show that the EA and the ACO outperform the VNS on almost all used benchmark instances. Furthermore, the ACO yields most of the time better solutions than the EA in long-term runs, whereas the EA dominates when the computation time is strongly restricted.
A review on the ant colony optimization metaheuristic: basis, models and new trends
2002
Resumen: Ant Colony Optimization (ACO) is a recent metaheuristic method that is inspired by the behavior of real ant colonies. In this paper, we review the underlying ideas of this approach that lead from the biological inspiration to the ACO metaheuristic, which gives a set of rules of how to apply ACO algorithms to challenging combinatorial problems.