Topic
Discrete optimization
About: Discrete optimization is a research topic. Over the lifetime, 4598 publications have been published within this topic receiving 158297 citations. The topic is also known as: discrete optimisation.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this article, a general formulation for hypergraph correlation clustering is proposed and a comparison of LP and ILP cutting plane methods and rounding procedures for the multicut problem is provided.
56 citations
TL;DR: In this paper, it was shown that a discrete maximum principle similar to the Pontryagin maximum principle is valid for a subclass of these problems, specifically systems with linear dynamics, convex inequality constraints and convex performance criteria.
Abstract: A certain class of discrete optimization problems is investigated using the framework of nonlinear programming. It is shown that a discrete maximum principle similar to the Pontryagin maximum principle is valid for a subclass of these problems, specifically systems with linear dynamics, convex inequality constraints and convex performance criteria. This result extends the applicability of the discrete maximum principle to a class of problems not covered by the Rozonoer-Halkin formulation.
55 citations
TL;DR: By using an innovative combination of simulation and discrete optimization models, this work addressed the problem of analyzing a large number of alternatives efficiently and indicated opportunities for significant savings in estimated annual transportation costs.
Abstract: In 1995, Volkswagen of America began a review of its vehicle-distribution system looking for opportunities to improve customer responsiveness and simultaneously reduce system costs. An analytical tool was required to evaluate alternative designs in terms of cost and customer service level, both of which are functions of probabilistic and dynamic elements. These elements include inventory policies, demand seasonality and volume, customer-choice patterns, and transportation delays. By using an innovative combination of simulation and discrete optimization models, we addressed the problem of analyzing a large number of alternatives efficiently. Our analysis indicated opportunities for significant savings in estimated annual transportation costs, and it provided insights on how to implement the proposed system.
55 citations
TL;DR: A modified SA algorithm is presented and it is shown that under suitable conditions on the random error, the modifiedSA algorithm converges in probability to a global optimizer.
55 citations
18 Jun 2018
TL;DR: This paper presents a discrepancy minimizing model to address the discrete optimization problem in hashing learning and transforms the original binary optimization into differentiable optimization problem over hash functions through series expansion.
Abstract: This paper presents a discrepancy minimizing model to address the discrete optimization problem in hashing learning. The discrete optimization introduced by binary constraint is an NP-hard mixed integer programming problem. It is usually addressed by relaxing the binary variables into continuous variables to adapt to the gradient based learning of hashing functions, especially the training of deep neural networks. To deal with the objective discrepancy caused by relaxation, we transform the original binary optimization into differentiable optimization problem over hash functions through series expansion. This transformation decouples the binary constraint and the similarity preserving hashing function optimization. The transformed objective is optimized in a tractable alternating optimization framework with gradual discrepancy minimization. Extensive experimental results on three benchmark datasets validate the efficacy of the proposed discrepancy minimizing hashing.
55 citations