Scalability constitutes a key property in Peer-to-Peer environments. One way to foster this property is the introduction of super-peers, a concept which has gained widespread acceptance in recent years. However, the problem of finding the set of super-peers that minimizes the total communication cost is NP-hard. We present a new heuristic based on Evolutionary Techniques and Local Search to solve this problem. Using actual Internet distance measurements, we demonstrate the savings in total communication cost attainable by such a super-peer topology. Our heuristic can also be applied to the more general Uncapacitated Single Assignment p-Hub Median Problem. The Local Search is then further enhanced by generalized don’t look bits. We show that our heuristic is competitive with other heuristics even in this general problem, and present new best solutions for the largest instances in the well known Australia Post data set.
This paper studies the Split Delivery Vehicle Routing problem (SDVRP), a variant of the VRP in which multiple visits to customers are allowed. This NP-hard problem is solved by a recent metaheuristic called Memetic Algorithm with Population Management or MA|PM (Sörensen, 2003). It consists in a genetic algorithm, combined with a local search procedure for intensification and a distance measure to control population diversity. Special moves dedicated to split deliveries are introduced in the local search. This solution approach is evaluated and compared with the tabu search algorithm of Archetti et al. (2006) and with lower bounds designed by Belenguer et al. (2000). Our method outperforms the tabu search both in solution quality and running time. On a set of 49 instances, it improves the best-known solution 32 times. The savings obtained confirm the interest and the power of the MA|PM.
We present two hybrid Metaheuristics, a hybrid Iterated Local Search and a hybrid Simulated Annealing, for solving real-world extensions of the Vehicle Routing Problem with Time Windows. Both hybrid Metaheuristics are based on the same neighborhood generating operators and local search procedures. The initial solutions are obtained by the Coefficient Weighted Distance Time Heuristics with automated parameter tuning. The strategies are compared in an empirical study on four real-world problems. A performance measure is used that also considers multiple restarts of the algorithms.
In this paper the influence of structural information obtained from a problem relaxation on the performance of an ACO algorithm for the symmetric TSP is studied. More precisely, a very simple ACO algorithm is guided by including Minimal Spanning Tree information into the visibility. Empirical results on a large number of benchmark instances from TSPLIB are presented. The paper concludes with remarks on some more elaborate ideas for using problem relaxation within ACO.
This paper proposes a local search algorithm that makes use of a complex neighborhood relation based on a hybridization with a constructive heuristics for the classical resource-constrained project scheduling problem (RCPSP).
We perform an experimental analysis to tune the parameters of our algorithm and to compare it with a tabu search based on a combination of neighborhood relations borrowed from the literature. Finally, we show that our algorithm is also competitive with the ones reported in the literature.
This paper deals with the Permutation Flow Shop scheduling problem with the objective of minimizing total flow time, and therefore reducing in-process inventory. A new hybrid metaheuristic Genetic Algorithm - Cluster Search is proposed for the scheduling problem solution. The performance of the proposed method is evaluated and results are compared with the best reported in the literature. Experimental tests show the new method superiority for the test problems set, regarding the solution quality.
Optimization in sports is a field of increasing interest. A novel problem in sports management is the Referee Assignment Problem, in which a limited number of referees with different qualifications and availabilities should be assigned to a set of games already scheduled. We extend and improve a previous three-phase approach for this problem, based on a constructive heuristic, a repair heuristic to make the initial solutions feasible, and an ILS improvement heuristic. We propose a new constructive algorithm based on a greedy criterion to build initial solutions. Furthermore, we develop a hybridization strategy in which a mixed integer programming exact algorithm replaces the original neighborhood-based local search within the ILS heuristic. Computational experiments are performed for large realistic instances. The use of time-to-target-solution-value plots is emphasized in the evaluation of the numerical results, illustrating the efficiency and the robustness of the new approach. The proposed hybridization of MIP with local search can be extended to other metaheuristics and applications, opening a new research avenue to more robust algorithms.
Sudoku is a notorious logic-based puzzle that is popular with puzzle enthusiasts the world over. From a computational perspective, Sudoku is also a problem that belongs to the set of NP-complete problems, implying that we cannot hope to find a polynomially bounded algorithm for solving the problem in general. Considering this feature, in this paper we demonstrate how a metaheuristic-based method for solving Sudoku puzzles (which was reported by the same author in an earlier paper), can actually be significantly improved if it is coupled with Constraint Programming techniques. Our results, which have been gained through a large amount of empirical work, suggest that this combination of techniques results in a hybrid algorithm that is significantly more powerful than either of its constituent parts.
Finding appropriate values for the parameters of an algorithm is a challenging, important, and time consuming task. While typically parameters are tuned by hand, recent studies have shown that automatic tuning procedures can effectively handle this task and often find better parameter settings. F-Race has been proposed specifically for this purpose and it has proven to be very effective in a number of cases. F-Race is a racing algorithm that starts by considering a number of candidate parameter settings and eliminates inferior ones as soon as enough statistical evidence arises against them. In this paper, we propose two modifications to the usual way of applying F-Race that on the one hand, make it suitable for tuning tasks with a very large number of initial candidate parameter settings and, on the other hand, allow a significant reduction of the number of function evaluations without any major loss in solution quality. We evaluate the proposed modifications on a number of stochastic local search algorithms and we show their effectiveness.
In recent years it has been shown by means of practical applications that the incorporation of branch & bound concepts within construction-based metaheuristics can be very useful. In this paper, we attempt to give an explanation of why this type of hybridization works. First, we introduce the concepts of primal and dual problem knowledge, and we show that metaheuristics only exploit the primal problem knowledge. In contrast, hybrid metaheuristic that include branch & bound concepts exploit both the primal and the dual problem knowledge. After giving a survey of these techniques, we conclude the paper with an application example that concerns the longest common subsequence problem.
The problem of computing a good approximation set of the Pareto front of a multiobjective optimization problem can be recasted as the maximization of its S-metric value, which measures the dominated hypervolume. In this way, the S-metric has recently been applied in a variety of metaheuristics. In this work, a novel high-precision method for computing approximation sets of a Pareto front with maximal S-Metric is proposed as a high-level relay hybrid of an evolutionary algorithm and a gradient method, both guided by the S-metric. First, an evolutionary multiobjective optimizer moves the initial population close to the Pareto front. The gradient-based method takes this population as its starting point for computing a local maximal approximation set with respect to the S-metric. Thereby, the population is moved according to the gradient of the S-metric.
This paper introduces expressions for computing the gradient of a set of points with respect to its S-metric on basis of the gradients of the objective functions. It discusses singularities where the gradient is vanishing or differentiability is one sided. To circumvent the problem of vanishing gradient components of the S-metric for dominated points in the population a penalty approach is introduced.
In order to test the new hybrid algorithm, we compute the precise maximizer of the S-metric for a generalized Schaffer problem and show, empirically, that the relay hybrid strategy linearly converges to the precise optimum. In addition we provide first case studies of the hybrid method on complicated benchmark problems.
The connected facility location (ConFL) problem generalizes the facility location problem and the Steiner tree problem in graphs. Given a graph G = (V,E), a set of customers \({\cal D} \subseteq V\), a set of potential facility locations \({\cal F} \subseteq V\) (including a root r), and a set of Steiner nodes in the graph G = (V,E), a solution (F,T) of ConFL represents a set of open facilities \(F\subseteq \cal F\), such that each customer is assigned to an open facility and the open facilities are connected to the root via a Steiner Tree T. The total cost of the solution (F,T) is the sum of the cost for opening the facilities, the cost of assigning customers to the open facilities and the cost of the Steiner tree that interconnects the facilities.
We show how to combine a variable neighborhood search method with a reactive tabu-search, in order to find sub-optimal solutions for large scale instances. We also propose a branch-and-cut approach for solving the ConFL to provable optimality. In our computational study, we test the quality of the proposed hybrid strategy by comparing its values to lower and upper bounds obtained within a branch-and-cut framework.
For the NP-hard Optimum Communication Spanning Tree (OCST) problem a cost minimizing spanning tree has to be found, where the cost depends on the communication volume between each pair of nodes routed over the tree. We present a memetic algorithm (MA) for this problem and focus our discussion on the evaluation of recombination operators for the OCST. The proposed algorithm outperforms evolutionary algorithms (EA) for known benchmark instances and outperforms state-of-the-art solvers for non-Euclidean instances.
We discuss a general approach to hybridize traditional construction heuristics for combinatorial optimization problems with numerical based evolutionary algorithms. Therefore, we show how to augment a construction heuristic with real-valued parameters, called control values. An evolutionary algorithm for numerical optimization uses this enhanced heuristic to find assignments for these control values, which in turn enable the latter to find high quality solutions for the original combinatorial problem. Additionally to the actual optimization task, we thereby experimentally analyze the heuristic’s substeps.
Furthermore, after finding a good assignment for a specific instance set, we can use it for similar yet different problem instances, without the need of an additional time-consuming run of the evolutionary algorithm. This concept is of particular interest in the context of computing efficient bounds within Branch-and-Cut algorithms. We apply our approach to a real-world problem in network optimization, and present a study on its effectiveness.
