Search results for "Branch"
showing 10 items of 1278 documents
Structure and dynamics in amorphous tellurium and Te-n clusters: A density functional study
2012
Density functional/molecular dynamics simulations have been performed on amorphous tellurium (a melt-quenched sample of 343 atoms at 300 K) and on Te clusters with up to 16 atoms. The former extend our calculations on liquid Te at 560, 625, 722, and 970 K [Phys. Rev. B 81, 094202 (2010)]. We discuss trends in structures (including those of other group-16 elements), electronic densities of states, and vibration frequencies. Chain structures are common in S and Se, but the chains in amorphous Te are short, and branching sites with threefold-coordinated atoms are common. The energy difference between two- and threefold local coordination depends sensitively on the exchange-correlation function…
A branch-and-cut algorithm for the Orienteering Arc Routing Problem
2016
[EN] In arc routing problems, customers are located on arcs, and routes of minimum cost have to be identified. In the Orienteering Arc Routing Problem (OARP),in addition to a set of regular customers that have to be serviced, a set of potential customers is available. From this latter set, customers have to be chosen on the basis of an associated profit. The objective is to find a route servicing the customers which maximize the total profit collected while satisfying a given time limit on the route.In this paper, we describe large families of facet-inducing inequalities for the OARP and present a branch-and-cut algorithm for its solution. The exact algorithm embeds a procedure which builds…
Advanced Greedy Randomized Adaptive Search Procedure for the Obnoxious p-Median problem
2016
Abstract The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP -hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been recently proposed. In this paper, we propose a heuristic method – based on the Greedy Randomized Adaptive Search Procedure, GRASP, methodology – for finding approximate solutions to this optimization problem. In particular, we consider an advanced GRASP design in which a filtering mechanism avo…
The stacker crane problem and the directed general routing problem
2015
[EN] This article deals with the polyhedral description and the resolution of the directed general routing problem (DGRP) and the stacker crane problem (SCP). The DGRP contains a large number of important arc and node routing problems as special cases, including the SCP. Large families of facet-defining inequalities for the DGRP are described and a branch-and-cut algorithm for these problems is presented. Extensive computational experiments over different sets of DGRP and SCP instances are included.
A branch-and-cut algorithm for the pallet loading problem
2005
We propose a branch-and-cut algorithm for the pallet loading problem. The 0-1 formulation proposed by Beasley for cutting problems is adapted to the problem, adding new constraints and new procedures for variable reduction. We then take advantage of the relationship between this problem and the maximum independent set problem to use the partial linear description of its associated polyhedron. Finally, we exploit the specific structure of our problem to define the solution graph and to develop efficient separation procedures. We present computational results for the complete sets Cover I (up to 50 boxes) and Cover II (up to 100 boxes).
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…
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.
Separating capacity constraints in the CVRP using tabu search
1998
Abstract Branch and Cut methods have shown to be very successful in the resolution of some hard combinatorial optimization problems. The success has been remarkable for the Symmetric Traveling Salesman Problem (TSP). The crucial part in the method is the cutting plane algorithm: the algorithm that looks for valid inequalities that cut off the current nonfeasible linear program (LP) solution. In turn this part relies on a good knowledge of the corresponding polyhedron and our ability to design algorithms that can identify violated valid inequalities. This paper deals with the separation of the capacity constraints for the Capacitated Vehicle Routing Problem (CVRP). Three algorithms are prese…