Open AccessPosted Content
An Algorithm For The Three-Index Assignment Problem
Egon Balas,Matthew J. Saltzman +1 more
168
TL;DR: The main features of the algorithm include a Lagrangian relaxation that incorporates a class of facet inequalities and is solved by a modified subgradient procedure to find good lower bounds, a primal heuristic based on the principle of minimizing maximum regret plus a variable depth interchange phase for finding good upper bounds.
read more
Abstract: We describe a branch-and-bound algorithm for solving the axial three-index assignment problem. The main features of the algorithm include a Lagrangian relaxation that incorporates a class of facet inequalities and is solved by a modified subgradient procedure to find good lower bounds, a primal heuristic based on the principle of minimizing maximum regret plus a variable depth interchange phase for finding good upper bounds, and a novel branching strategy that exploits problem structure to fix several variables at each node and reduce the size of the total enumeration tree. Computational experience is reported on problems with up to 78 equations and 17,576 variables. The primal heuristics were tested on problems with up to 210 equations and 343,000 variables. (This abstract was borrowed from another version of this item.)
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
A survey for the quadratic assignment problem
Eliane Maria Loiola,Nair Maria Maia de Abreu,Paulo Oswaldo Boaventura-Netto,Peter M. Hahn,Tania Maia Querido +4 more
TL;DR: This paper presents some of the most important QAP formulations and classify them according to their mathematical sources and gives a detailed discussion of the progress made in both exact and heuristic solution methods, including those formulated according to metaheuristic strategies.
772
A generalized S-D assignment algorithm for multisensor-multitarget state estimation
TL;DR: An efficient and recursive generalized S-D assignment algorithm (S/spl ges/3) employing a successive Lagrangian relaxation technique is presented, with application to the localization of an unknown number of emitters using multiple high frequency direction finder sensors.
411
Linear Assignment Problems and Extensions
Rainer E. Burkard,Eranda Çela +1 more
- 01 Jan 1999
TL;DR: Assignment problems deal with the question how to assign n items to n machines (or workers) in the best possible way and an objective function modeling the ”best way” is modeled.
A survey of dynamic network flows
TL;DR: A state-of-the-art survey of the results, applications, algorithms and implementations for dynamic network flows.
337
A new relaxation algorithm and passive sensor data association
TL;DR: In this paper, the measurement-target association problem is formulated as one of maximizing the joint likelihood function of the measurement partition, which leads to a generalization of the 3D assignment (matching) problem, which is known to be NP hard.
307
References
An Effective Heuristic Algorithm for the Traveling-Salesman Problem
S. Lin,Brian W. Kernighan +1 more
TL;DR: This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem based on a general approach to heuristics that is believed to have wide applicability in combinatorial optimization problems.
4.1K
•Book
Introduction to Operations Research
Frederick S. Hillier,Gerald J. Lieberman +1 more
- 01 Jan 1967
TL;DR: The Simplex Method duality theory and sensitivity analysis for linear programming has been studied extensively in the field of operations research as mentioned in this paper, including the application of queueing theory inventory theory forecasting Markovian decision processes and applications decision analysis simulation.
3.8K
Set Partitioning: A survey
Egon Balas,Manfred Padberg +1 more
TL;DR: A survey of theoretical results and solution methods for the set partitioning problem can be found in this article, and while we have tried not to omit anything important, we have no claim to completeness. Critical comments pointing out possible omissions or misstatements are welcome.
487
A thermodynamically motivated simulation procedure for combinatorial optimization problems
Rainer E. Burkard,Franz Rendl +1 more
TL;DR: Suboptimal solutions differing 1–2% from the best known solutions are obtained by a simple program in short time by starting this program several times with different starting values all known minimal objective function values were reached.
366