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.
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01 Jan 1996TL;DR: The surprising variety of continuous approaches reveal interesting theoretical properties which can be explored to develop new algorithms for computing (sub)optimal solutions to discrete optimization problems.
Abstract: This paper contains expository notes about continuous approaches to several discrete optimization problems. There are many ways to formulate discrete problems as equivalent continuous problems or to embed the discrete feasible domain in a larger continuous space (relaxation). The surprising variety of continuous approaches reveal interesting theoretical properties which can be explored to develop new algorithms for computing (sub)optimal solutions to discrete optimization problems.
51 citations
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TL;DR: An active set algorithm is proposed to solve a discrete network design problem as a mathematical program with complementarity constraints and assigns one of the nonnegative variables in each pair a value of zero to reduce the design problem to a regular nonlinear program.
Abstract: In this paper, we formulate a discrete network design problem as a mathematical program with complementarity constraints and propose an active set algorithm to solve the problem. Each complementarity constraint requires the product of a pair of nonnegative variables to be zero. Instead of dealing with this type of constraints directly, the proposed algorithm assigns one of the nonnegative variables in each pair a value of zero. Doing so reduces the design problem to a regular nonlinear program. Using the multipliers associated with the constraints forcing nonnegative variables to be zero, the algorithm then constructs and solves binary knapsack problems to make changes to the zero-value assignments in order to improve the system delay. Numerical experiments with data from networks in the literature indicate that the algorithm is effective and has the potential for solving larger network design problems.
51 citations
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01 Mar 1993
TL;DR: An alternative approach to obtaining a discrete-time counterpart to the two-axis continuous model of an induction machine is presented and a discrete time-variant reduced-order flux observer based on the discrete model is proposed.
Abstract: An alternative approach to obtaining a discrete-time counterpart to the two-axis continuous model of an induction machine is presented. The discrete time-variant equations are derived from a partial discretization of the continuous state equation. The discrete model can be used with advantage in simulation and real-time control applications. A discrete time-variant reduced-order flux observer based on the discrete model is proposed. Computer simulation results are shown to compare the proposed discrete model with that obtained from the Euler method and the exact continuous model. >
51 citations
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TL;DR: This work considers an implementation of a recursive model-based active-set trust-region method for solving bound-constrained nonlinear non-convex optimization problems without derivatives using the technique of self- correcting geometry, which allows US to maintain much smaller interpolation sets while proceeding optimization in lower-dimensional subspaces.
Abstract: We consider an implementation of a recursive model-based active-set trust-region method for solving bound-constrained nonlinear non-convex optimization problems without derivatives using the technique of self-correcting geometry proposed in K. Scheinberg and Ph.L. Toint [Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization. SIAM Journal on Optimization, (to appear), 2010]. Considering an active-set method in bound-constrained model-based optimization creates the opportunity of saving a substantial amount of function evaluations. It allows US to maintain much smaller interpolation sets while proceeding optimization in lower-dimensional subspaces. The resulting algorithm is shown to be numerically competitive.
51 citations
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TL;DR: This work compiles and assess a selection of 23 discrete optimization problems that subscribe to different types of fitness landscapes, and provides a new module for IOHprofiler which extents the fixed-target and fixed-budget results for the individual problems by ECDF results, which allows one to derive aggregated performance statistics for groups of problems.
51 citations