Book ChapterDOI
Lagrangian Relaxation for Integer Programming
Arthur M. Geoffrion
- pp 243-281
Reads0
Chats0
TLDR
It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8].Abstract:
It is a pleasure to write this commentary because it offers an opportunity to express my gratitude to several people who helped me in ways that turned out to be essential to the birth of [8]. They also had a good deal to do with shaping my early career and, consequently, much of what followed.read more
Citations
More filters
Journal ArticleDOI
A Lagrangian Relaxation Approach for Binary Multiple Instance Classification
TL;DR: The main result is to prove that a Lagrangian relaxation approach, equipped with a dual ascent scheme, allows us to obtain an optimal solution of the original problem.
Journal ArticleDOI
Mean Value Cross Decomposition for Nonlinear Convex Problems
Kaj Holmberg,Krzysztof C. Kiwiel +1 more
TL;DR: Convergence is proved for a somewhat generalized version of Mean value cross decomposition, allowing more general weights and to indicate that this decomposition approach is more efficient than direct solution with a well established general code.
Proceedings ArticleDOI
A Particle Swarm Optimization with Feasibility-Based Rules for Mixed-Variable Optimization Problems
TL;DR: A Particle Swarm Optimization algorithm with feasibility-based rules (FRPSO) is proposed in this paper to solve mixed-variable optimization problems and it is found to be highly competitive compared to other existing stochastic algorithms.
Journal ArticleDOI
The Weighted Total Tardiness Problem with Fixed Shipping Times and Overtime Utilization
TL;DR: This paper presents an approximate algorithm based on a capacitated transshipment formulation that provides a feasible solution along with its error bound and is implementable in terms of both speed and accuracy.
Journal ArticleDOI
Graph theoretic relaxations of set covering and set partitioning problems
Elia El-Darzi,Gautam Mitra +1 more
TL;DR: Three graph theoretic relaxations of the set covering problem (SCP) and the set partitioning problem (SSP) are reviewed: a network relaxation which can be solved by the greedy method, a matching relaxation and a graph covering relaxation.
References
More filters
Journal ArticleDOI
The Traveling-Salesman Problem and Minimum Spanning Trees
Michael Held,Richard M. Karp +1 more
TL;DR: It is shown that maxπwπ = C* precisely when a certain well-known linear program has an optimal solution in integers.
Journal ArticleDOI
Validation of subgradient optimization
TL;DR: It is concluded that the “relaxation” procedure for approximately solving a large linear programming problem related to the traveling-salesman problem shows promise for large-scale linear programming.
Journal ArticleDOI
Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources
TL;DR: The use of Lagrange multipliers for optimization in the presence of constraints is not limited to differentiable functions but can be applied to problems of maximizing an arbitrary real valued objective function over any set whatever, subject to bounds on the values of any other finite collection of real valued functions denned on the same set as mentioned in this paper.
Book ChapterDOI
Multicommodity Distribution System Design by Benders Decomposition
Arthur M. Geoffrion,G. W. Graves +1 more
TL;DR: In this paper, a multicommodity capacitated single-period version of the problem is formulated as a mixed integer linear program, and a solution technique based on Benders Decomposition is developed, implemented, and successfully applied to a real problem for a major food firm with 17 commodity classes, 14 plants, 45 possible distribution center sites, and 121 customer zones.
Journal ArticleDOI
The traveling-salesman problem and minimum spanning trees: Part II
Michael Held,Richard M. Karp +1 more
TL;DR: An efficient iterative method for approximating this bound closely from below is presented, and a branch-and-bound procedure based upon these considerations has easily produced proven optimum solutions to all traveling-salesman problems presented to it.