Concave minimum cost network flow problems solved with a colony of ants (original) (raw)
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Heuristic solutions for general concave minimum cost network flow problems
Networks, 2007
We address the single-source uncapacitated minimum cost network flow problem with general concave cost functions. Exact methods to solve this class of problems in their full generality are only able to address small to medium size instances, since this class of problems is known to be NP-Hard. Therefore, approximate methods are more suitable. In this work, we present a hybrid approach combining a genetic algorithm with a local search. Randomly generated test problems have been used to test the computational performance of the algorithm. The results obtained for these test problems are compared to optimal solutions obtained by a dynamic programming method for the smaller problem instances and to upper bounds obtained by a local search method for the larger problem instances. From the results reported it can be shown that the hybrid methodology improves upon previous approaches in terms of efficiency and also on the pure genetic algorithm, i.e., without using the local search procedure.
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.
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.
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...
Algorithms for the single-source uncapacitated minimum concave-cost network flow problem
Journal of Global Optimization, 1991
We investigate algorithms, applications, and complexity issues for the single-source uncapacitated (SSU) version of the minimum concave-cost network flow problem (MCNFP). We present applications arising from production planning, and prove complexity results for both global and local search. We formally state the local search algorithm of Gallo and Sodini [5], and present alternative local search algorithms. Computational results are provided to compare the various local search algorithms proposed and the effects of initial solution techniques.
A Lagrangean heuristic for the capacitated concave minimum cost network flow problem
European Journal of Operational Research, 1994
We propose a heuristic solution technique for the capacitated concave minimum cost network flow problem based on a Lagrangean dualization of the problem. Despite its dual character the algorithm guarantees the generation of primal feasible solutions which are local optima and therefore candidates of being the global optimum. The Lagrangean dual is solved by a subgradient search procedure and provides a lower bound to the optimal value. The lower bound is, in general, stronger than the one obtained by a linear approximation of the original problem. It can be used as a judgement of the quality of the solution or in a branch and bound procedure. Computational results from randomly generated problems are presented.
European Journal of Operational Research, 2006
In this paper, we describe a dynamic programming approach to solve optimally the single-source uncapacitated minimum cost network flow problem with general concave costs. This class of problems is known to be NP-Hard and there is a scarcity of methods to solve them in their full generality. The algorithms previously developed critically depend on the type of cost functions considered and on the number of nonlinear arc costs. Here, a new dynamic programming approach that does not depend on any of these factors is proposed. Computational experiments were performed using randomly generated problems. The computational results reported for small and medium size problems indicate the effectiveness of the proposed approach.
A new ant colony routing approach with a trade-off between system and user optimum
2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC), 2011
Dynamic traffic routing (DTR) refers to the process of (re)directing traffic at junctions in a traffic network corresponding to the evolving traffic conditions as time progresses. This paper considers the DTR problem for a traffic network defined as a directed graph, and deals with the mathematical aspects of the resulting optimization problem from the viewpoint of network flow theory. Traffic networks may have thousands of links and nodes, resulting in a sizable and computationally complex nonlinear, non-convex DTR optimization problem. To solve this problem Ant Colony Optimization (ACO) is chosen as the optimization method in this paper because of its powerful optimization heuristic for combinatorial optimization problems. However, the standard ACO algorithm is not capable of solving the routing optimization problem aimed at the system optimum, and therefore a new ACO algorithm is developed to achieve the goal of finding the optimal distribution of traffic flows in the network.
Ant colony optimization: Introduction and recent trends
Physics of Life Reviews, 2005
Ant colony optimization is a technique for optimization that was introduced in the early 1990's. The inspiring source of ant colony optimization is the foraging behavior of real ant colonies. This behavior is exploited in artificial ant colonies for the search of approximate solutions to discrete optimization problems, to continuous optimization problems, and to important problems in telecommunications, such as routing and load balancing. First, we deal with the biological inspiration of ant colony optimization algorithms. We show how this biological inspiration can be transfered into an algorithm for discrete optimization. Then, we outline ant colony optimization in more general terms in the context of discrete optimization, and present some of the nowadays bestperforming ant colony optimization variants. After summarizing some important theoretical results, we demonstrate how ant colony optimization can be applied to continuous optimization problems. Finally, we provide examples of an interesting recent research direction: The hybridization with more classical techniques from artificial intelligence and operations research.
Ant Colony Optimization Applied on Combinatorial Problem for Optimal Power Flow Solution
This paper presents an efficient and reliable evolutionary-based approach to solve the optimal power flow (OPF) combinatorial problem. The proposed approach employs Ant Colony Optimization (ACO) algorithm for optimal settings of OPF combinatorial problem control variables. Incorporation of ACO as a derivative-free optimization technique in solving OPF problem significantly relieves the assumptions imposed on the optimized objective functions. The proposed approach has been examined and tested on the standard IEEE 57-bus test System with different objectives that reflect fuel cost minimization, voltage profile improvement, and voltage stability enhancement. The proposed approach results have been compared to those that reported in the literature recently. The results are promising and show the effectiveness and robustness of the proposed approach.