Search results for "combinatorial optimization"
showing 10 items of 59 documents
Branch-and-Bound
2010
We now turn to the discussion of how to solve the linear ordering problem to (proven) optimality. In this chapter we start with the branch-and-bound method which is a general procedure for solving combinatorial optimization problems. In the subsequent chapters this approach will be realized in a special way leading to the so-called branch-and-cut method. There are further possibilities for solving the LOP exactly, e.g. by formulating it as dynamic program or as quadratic assignment problem, but these approaches did not lead to the implementation of practical algorithms and we will not elaborate on them here.
A combinatorial algorithm for the optimization of refraction seismics data inversion
1993
Abstract The problem of data inversion in refraction seismics can be split in two parts: data first must be preprocessed in order to determine the travel-time curve; this essentially is a geometrical problem, complicated, however, by its pattern recognition aspects. Once the geometrical problem is solved, the second part, the inversion proper, is straightforward, as the soil layering model can be calculated according to well-known algorithms. The more difficult part of the problem is the former, which implies a type of pattern recognition; because of this type of difficulty, the geometrical part of the problem usually is committed to the skill of a human operator. This paper describes an al…
Greedy and K-Greedy algoritmhs for multidimensional data association
2011
[EN] The multidimensional assignment (MDA) problem is a combinatorial optimization problem arising in many applications, for instance multitarget tracking (MTT). The objective of an MDA problem of dimension $d\in\Bbb{N}$ is to match groups of $d$ objects in such a way that each measurement is associated with at most one track and each track is associated with at most one measurement from each list, optimizing a certain objective function. It is well known that the MDA problem is NP-hard for $d\geq3$. In this paper five new polynomial time heuristics to solve the MDA problem arising in MTT are presented. They are all based on the semi-greedy approach introduced in earlier research. Experimen…
Scatter Search vs. Genetic Algorithms
2005
The purpose of this work is to compare the performance of a scatter search (SS) implementation and an implementation of a genetic algorithm (GA) in the context of searching for optimal solutions to permutation problems. Scatter search and genetic algorithms are members of the evolutionary computation family. That is, they are both based on maintaining a population of solutions for the purpose of generating new trial solutions. Our computational experiments with four well-known permutation problems reveal that in general a GA with local search outperforms one without it. Using the same problem instances, we observed that our specific scatter search implementation found solutions of a higher …
Domain-wall excitations in the two-dimensional Ising spin glass
2018
The Ising spin glass in two dimensions exhibits rich behavior with subtle differences in the scaling for different coupling distributions. We use recently developed mappings to graph-theoretic problems together with highly efficient implementations of combinatorial optimization algorithms to determine exact ground states for systems on square lattices with up to $10\,000\times 10\,000$ spins. While these mappings only work for planar graphs, for example for systems with periodic boundary conditions in at most one direction, we suggest here an iterative windowing technique that allows one to determine ground states for fully periodic samples up to sizes similar to those for the open-periodic…
Automating the Parameter Selection in VRP: An Off-line Parameter Tuning Tool Comparison
2014
Vehicle route optimization is an important application of combinatorial optimization. Therefore, a variety of methods has been proposed to solve different challenging vehicle routing problems. An important step in adopting these methods to solve real-life problems is to find appropriate parameters for the routing algorithms. In this chapter, we show how this task can be automated using parameter tuning by presenting a set of comparative experiments on seven state-of-the-art tuning methods. We analyze the suitability of these methods in configuring routing algorithms, and give the first critical comparison of automated parameter tuners in vehicle routing. Our experimental results show that t…
Scatter Search and Path-Relinking: Fundamentals, Advances, and Applications
2010
Scatter search is an evolutionary metaheuristic that explores solution spaces by evolving a set of reference points, operating on a small set of solutions while making only limited use of randomization. We give a comprehensive description of the elements and methods that make up its template, including the most recent elements incorporated in successful applications in both global and combinatorial optimization. Path-relinking is an intensification strategy to explore trajectories connecting elite solutions obtained by heuristic methods such as scatter search, tabu search, and GRASP. We describe its mechanics, implementation issues, randomization, the use of pools of high-quality solutions …
Measuring diversity. A review and an empirical analysis
2021
Abstract Maximum diversity problems arise in many practical settings from facility location to social networks, and constitute an important class of NP-hard problems in combinatorial optimization. There has been a growing interest in these problems in recent years, and different mathematical programming models have been proposed to capture the notion of diversity. They basically consist of selecting a subset of elements of a given set in such a way that a measure based on their pairwise distances is maximized to achieve dispersion or representativeness. In this paper, we perform an exhaustive comparison of four mathematical models to achieve diversity over the public domain library MDPLIB, …
Black-Box solvers in combinatorial optimization
2015
Black box optimizers have a long tradition in the field of operations research. These procedures treat the objective function evaluation as a black box and therefore do not take advantage of its specific structure. Black-box optimization refers to the process in which there is a complete separation between the evaluation of the objective function —and perhaps other functions used to enforce constraints— and the solution procedure. The challenge of optimizing black boxes is to develop methods that can produce outcomes of reasonable quality without taking advantage of problem structure and employing a computational effort that is adequate for the context.
Combining finite learning automata with GSAT for the satisfiability problem
2010
A large number of problems that occur in knowledge-representation, learning, very large scale integration technology (VLSI-design), and other areas of artificial intelligence, are essentially satisfiability problems. The satisfiability problem refers to the task of finding a satisfying assignment that makes a Boolean expression evaluate to True. The growing need for more efficient and scalable algorithms has led to the development of a large number of SAT solvers. This paper reports the first approach that combines finite learning automata with the greedy satisfiability algorithm (GSAT). In brief, we introduce a new algorithm that integrates finite learning automata and traditional GSAT use…