Search results for "combinatorial optimization"

Greedy Randomized Adaptive Search Procedures

2017

In this chapter, we describe the process of designing heuristic procedures to solve combinatorial optimization problems.

The Multiple Multidimensional Knapsack with Family-Split Penalties

2021

Abstract The Multiple Multidimensional Knapsack Problem with Family-Split Penalties (MMdKFSP) is introduced as a new variant of both the more classical Multi-Knapsack and Multidimensional Knapsack Problems. It reckons with items categorized into families and where if an individual item is selected to maximize the profit, all the items of the same family must be selected as well. Items belonging to the same family can be assigned to different knapsacks; however, in this case, split penalties are incurred. This problem arises in resource management of distributed computing contexts and Service Oriented Architecture environments. An exact algorithm based on the exploitation of a specific combi…

Heuristics for the capacitated dispersion problem

2020

Reactive GRASP for the strip-packing problem

2008

This paper presents a greedy randomized adaptive search procedure (GRASP) for the strip packing problem, which is the problem of placing a set of rectangular pieces into a strip of a given width and infinite height so as to minimize the required height. We investigate several strategies for the constructive and improvement phases and several choices for critical search parameters. We perform extensive computational experiments with well-known instances which have been previously reported, first to select the best alternatives and then to compare the efficiency of our algorithm with other procedures. The results show that the GRASP algorithm outperforms recently reported metaheuristics.

GRASP for the uncapacitated r-allocation p-hub median problem

2014

In this paper we propose a heuristic for the Uncapacitated r-Allocation p-Hub Median Problem. In the classical p-hub location problem, given a set of nodes with pairwise traffic demands, we must select p of them as hub locations and route all traffics through them at a minimum cost. We target here an extension, called the r-allocation p-hub median problem, recently proposed by Yaman [19], in which every node is assigned to r of the p selected hubs (r@?p) and we are restricted to route the traffic of the nodes through their associated r hubs. As it is usual in this type of problems, our method has three phases: location, assignment and routing. Specifically, we propose a heuristic based on t…

Variable neighborhood search for the linear ordering problem

2006

Given a matrix of weights, the linear ordering problem (LOP) consists of finding a permutation of the columns and rows in order to maximize the sum of the weights in the upper triangle. This NP-complete problem can also be formulated in terms of graphs, as finding an acyclic tournament with a maximal sum of arc weights in a complete weighted graph. In this paper, we first review the previous methods for the LOP and then propose a heuristic algorithm based on the variable neighborhood search (VNS) methodology. The method combines different neighborhoods for an efficient exploration of the search space. We explore different search strategies and propose a hybrid method in which the VNS is cou…

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…

A tabu search algorithm for a two-dimensional non-guillotine cutting problem

2007

In this paper we study a two-dimensional non-guillotine cutting problem, the problem of cutting rectangular pieces from a large stock rectangle so as to maximize the total value of the pieces cut. The problem has many industrial applications whenever small pieces have to be cut from or packed into a large stock sheet. We propose a tabu search algorithm. Several moves based on reducing and inserting blocks of pieces have been defined. Intensification and diversification procedures, based on long-term memory, have been included. The computational results on large sets of test instances show that the algorithm is very efficient for a wide range of packing and cutting problems.

A review on discrete diversity and dispersion maximization from an OR perspective

2022

Abstract The problem of maximizing diversity or dispersion deals with selecting a subset of elements from a given set in such a way that the distance among the selected elements is maximized. The definition of distance between elements is customized to specific applications, and the way that the overall diversity of the selected elements is computed results in different mathematical models. Maximizing diversity by means of combinatorial optimization models has gained prominence in Operations Research (OR) over the last two decades, and constitutes nowadays an important area. In this paper, we review the milestones in the development of this area, starting in the late eighties when the first…

Metaheuristics for the linear ordering problem with cumulative costs

2012

The linear ordering problem with cumulative costs (LOPCC) is a variant of the well-known linear ordering problem, in which a cumulative propagation makes the objective function highly non-linear. The LOPCC has been recently introduced in the context of mobile-phone telecommunications. In this paper we propose two metaheuristic methods for this NP-hard problem. The first one is based on the GRASP methodology, while the second one implements an Iterated Greedy-Strategic Oscillation procedure. We also propose a post-processing based on Path Relinking to obtain improved outcomes. We compare our methods with the state-of-the-art procedures on a set of 218 previously reported instances. The compa…