Search results for "Modeling and Simulation"
showing 10 items of 1561 documents
The fuzzy p-median problem: A global analysis of the solutions
2001
Abstract We apply fuzzy techniques to incorporate external data into p-median problems. So we can detect certain solutions that would be discarded by usual crisp and fuzzy algorithms but that contrasted with this additional information can be advantageous. This usually reveals a pathology of the model and hence our methods provide some fuzzy validation criteria for p-median models.
Reducing the bandwidth of a sparse matrix with tabu search
2001
The bandwidth of a matrix { } ij a A = is defined as the maximum absolute difference between i and j for which 0 ≠ ij a . The problem of reducing the bandwidth of a matrix consists of finding a permutation of the rows and columns that keeps the nonzero elements in a band that is as close as possible to the main diagonal of the matrix. This NP-complete problem can also be formulated as a labeling of vertices on a graph, where edges are the nonzero elements of the corresponding symmetrical matrix. Many bandwidth reduction algorithms have been developed since the 1960s and applied to structural engineering, fluid dynamics and network analysis. For the most part, these procedures do not incorpo…
A branch and bound algorithm for the maximum diversity problem
2010
This article begins with a review of previously proposed integer formulations for the maximum diversity problem (MDP). This problem consists of selecting a subset of elements from a larger set in such a way that the sum of the distances between the chosen elements is maximized. We propose a branch and bound algorithm and develop several upper bounds on the objective function values of partial solutions to the MDP. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the medium-sized instances (with 50 elements) as well as some large-sized instances (with 100 elements). We compare our method with the best previous line…
A new branch-and-price algorithm for the traveling tournament problem
2010
Abstract The traveling tournament problem ( ttp ) consists of finding a distance-minimal double round-robin tournament where the number of consecutive breaks is bounded. For solving the problem exactly, we propose a new branch-and-price approach. The starting point is a new compact formulation for the ttp . The corresponding extensive formulation resulting from a Dantzig-Wolfe decomposition is identical to one given by Easton, K., Nemhauser, G., Trick, M., 2003. Solving the traveling tournament problem: a combined interger programming and constraint programming approach. In: Burke, E., De Causmaecker, P. (Eds.), Practice and Theory of Automated Timetabling IV, Volume 2740 of Lecture Notes i…
On the Distance-Constrained Close Enough Arc Routing Problem
2021
[EN] Arc routing problems consist basically of finding one or several routes traversing a given set of arcs and/or edges that must be serviced. The Close-Enough Arc Routing Problem, or Generalized Directed Rural Postman Problem, does not assume that customers are located at specific arcs, but can be serviced by traversing any arc of a given subset. Real-life applications include routing for meter reading, in which a vehicle equipped with a receiver travels a street network. If the vehicle gets within a certain distance of a meter, the receiver collects its data. Therefore, only a few streets which are close enough to the meters need to be traversed. In this paper we study the generalization…
Minimizing weighted tardiness of jobs with stochastic interruptions in parallel machines
2000
Abstract In this paper, we address the problem of minimizing expected total weighted tardiness of jobs that have stochastic interruptions and that are processed on a set of parallel machines. Our research generalizes the problem of scheduling parallel machines to minimize total weighted tardiness. The proposed solution method is based on the scatter search methodology and implements an innovative structured combination procedure. Extensive computational testing with more than 400 problem instances shows the merit of the proposed solution method.
Synchronous approach in interactive multiobjective optimization
2006
We introduce a new approach in the methodology development for interactive multiobjective optimization. The presentation is given in the context of the interactive NIMBUS method, where the solution process is based on the classification of objective functions. The idea is to formulate several scalarizing functions, all using the same preference information of the decision maker. Thus, opposed to fixing one scalarizing function (as is done in most methods), we utilize several scalarizing functions in a synchronous way. This means that we as method developers do not make the choice between different scalarizing functions but calculate the results of different scalarizing functions and leave t…
The price of multiobjective robustness : Analyzing solution sets to uncertain multiobjective problems
2021
Defining and finding robust efficient solutions to uncertain multiobjective optimization problems has been an issue of growing interest recently. Different concepts have been published defining what a “robust efficient” solution is. Each of these concepts leads to a different set of solutions, but it is difficult to visualize and understand the differences between these sets. In this paper we develop an approach for comparing such sets of robust efficient solutions, namely we analyze their outcomes under the nominal scenario and in the worst case using the upper set-less order from set-valued optimization. Analyzing the set of nominal efficient solutions, the set of minmax robust efficient …
Solving the discrete multiple criteria problem using linear prospect theory
1994
Abstract Prospect theory developed by Kahneman and Tversky is a popular model of choice in decision problems under uncertainty. Prospect theory has recently been extended to multiple criteria choice problems. In this paper, an interactive method for solving discrete multiple criteria decision problems, based on prospect theory type value functions, has been developed. Piecewise linear marginal value functions are assumed to approximate the S-shaped value functions of prospect theory. Therefore, the proposed procedure is valid only for convex preferences.
A note on the separation of subtour elimination constraints in elementary shortest path problems
2013
Abstract This note proposes an alternative procedure for identifying violated subtour elimination constraints (SECs) in branch-and-cut algorithms for elementary shortest path problems. The procedure is also applicable to other routing problems, such as variants of travelling salesman or shortest Hamiltonian path problems, on directed graphs. The proposed procedure is based on computing the strong components of the support graph. The procedure possesses a better worst-case time complexity than the standard way of separating SECs, which uses maximum flow algorithms, and is easier to implement.