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.

Single and multiobjective structural optimization in discrete-continuous variables using simulated annealing

Abstract: A multivariable optimization technique based on the Monte-Carlo method used in statistical mechanics studies of condensed systems is adapted for solving single and multiobjective structural optimization problems. This procedure, known as simulated annealing, draws an analogy between energy minimization in physical systems and objective function minimization in structural systems. The search for a minimum is simulated by a relaxation of the statistical mechanical system where a probabilistic acceptance criterion is used to accept or reject candidate designs. To model the multiple objective functions in the problem formulation, a cooperative game theoretic approach is used. Numerical results obtained using three different annealing strategies for the single and multiobjective design of structures with discrete-continuous variables are presented. The influence of cooling schedule parameters on the optimum solutions obtained is discussed. Simulation results indicate that, in several instances, the optimum solutions obtained using simulated annealing outperform the optimum solutions obtained using some gradient-based and discrete optimization techniques. The results also indicate that simulated annealing has substantial potential for additional applications in optimization, especially for problems with mixed discrete-continuous variables.

Decision Diagrams for Optimization

Abstract: This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming."Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world." [Pascal Van Hentenryck]

Constructing large-scale genetic maps using an evolutionary strategy algorithm

Abstract: This article is devoted to the problem of ordering in linkage groups with many dozens or even hundreds of markers. The ordering problem belongs to the field of discrete optimization on a set of all possible orders, amounting to n!/2 for n loci; hence it is considered an NP-hard problem. Several authors attempted to employ the methods developed in the well-known traveling salesman problem (TSP) for multilocus ordering, using the assumption that for a set of linked loci the true order will be the one that minimizes the total length of the linkage group. A novel, fast, and reliable algorithm developed for the TSP and based on evolution-strategy discrete optimization was applied in this study for multilocus ordering on the basis of pairwise recombination frequencies. The quality of derived maps under various complications (dominant vs. codominant markers, marker misclassification, negative and positive interference, and missing data) was analyzed using simulated data with approximately 50-400 markers. High performance of the employed algorithm allows systematic treatment of the problem of verification of the obtained multilocus orders on the basis of computing-intensive bootstrap and/or jackknife approaches for detecting and removing questionable marker scores, thereby stabilizing the resulting maps. Parallel calculation technology can easily be adopted for further acceleration of the proposed algorithm. Real data analysis (on maize chromosome 1 with 230 markers) is provided to illustrate the proposed methodology.

Global methods for dynamic optimization and mixed-integer dynamic optimization

Abstract: An overview of global methods for dynamic optimization and mixed-integer dynamic optimization (MIDO) is presented, with emphasis placed on the control parametrization approach. These methods consist of extending existing continuous and mixed-integer global optimization algorithms to encompass solution of problems with ODEs embedded. A prerequisite for so doing is a convexity theory for dynamic optimization as well as the ability to build valid convex relaxations for Bolza-type functionals. For solving dynamic optimization problems globally, our focus is on the use of branch-and-bound algorithms; on the other hand, MIDO problems are handled by adapting the outer-approximation algorithm originally developed for mixed-integer nonlinear problems (MINLPs) to optimization problems embedding ODEs. Each of these algorithms is thoroughly discussed and illustrated. Future directions for research are also discussed, including the recent developments of general, convex, and concave relaxations for the solutions of nonlinear ODEs.