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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TL;DR: An algorithm is developed that meets the requirement to obtain solutions where all or some of the design variables take their values from a given set of discrete values, while finding global solutions for the mixed-discrete problem.
85 citations
TL;DR: A framework called Grover adaptive search is set up and a method of Durr and Hoyer and one introduced by the authors fit into this framework and are compared.
Abstract: Grover's quantum computational search procedure can provide the basis for implementing adaptive global optimization algorithms. A brief overview of the procedure is given and a framework called Grover adaptive search is set up. A method of Durr and Hoyer and one introduced by the authors fit into this framework and are compared.
85 citations
TL;DR: It is concluded that solution of the mixed variable non-linear optimization problems usually requires considerable more computational effort compared to the continuous variable optimization problems.
Abstract: Continuous–discrete variable non-linear optimization problems are defined and categorized into six different types. These include a full range of problems from continuous to purely discrete and non-differentiable. Methods for solution of these problems are studied and their characteristics are catalogued. The branch and bound, simulated annealing and genetic algorithms are found to be the most general methods for solving discrete problems. After some enhancements, these and two other methods are implemented into a program for certain applications. Several example problems are solved to study performance of the methods. It is concluded that solution of the mixed variable non-linear optimization problems usually requires considerable more computational effort compared to the continuous variable optimization problems. In addition, there is no guarantee that the best solution has been obtained; however, good practical solutions are usually obtained. © 1997 by John Wiley & Sons, Ltd.
85 citations
TL;DR: An ordinal optimization theory-based algorithm to solve for a good enough solution with high probability for the optimal power flow problem with discrete control variables by comparing with the competing methods and the conventional approach through simulations.
Abstract: The optimal power flow (OPF) problem with discrete control variables is an NP-hard problem in its exact formulation. To cope with the immense computational-difficulty of this problem, we propose an ordinal optimization theory-based algorithm to solve for a good enough solution with high probability. Aiming for hard optimization problems, the ordinal optimization theory, in contrast to heuristic methods, guarantee to provide a top n% solution among all with probability more than 0.95. The approach of our ordinal optimization theory-based algorithm consists of three stages. First, select heuristically a large set of candidate solutions. Then, use a simplified model to select a subset of most promising solutions. Finally, evaluate the candidate promising-solutions of the reduced subset using the exact model. We have demonstrated the computational efficiency of our algorithm and the quality of the obtained solution by comparing with the competing methods and the conventional approach through simulations.
84 citations