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: In this article, a review of alternative formulations for optimization and simulation of structural and mechanical systems and other related fields is presented, and the basic ideas of the formulations presented in diverse fields can be integrated to conduct further research and develop alternative formulations and solution procedures for practical engineering applications.
Abstract: Alternative formulations for optimization and simulation of structural and mechanical systems and other related fields are reviewed. The material is divided roughly into two parts. Part 1 focuses on the developments in structural and mechanical systems, including configuration and topology optimization. Here the formulations are classified into three broad categories: (i) the conventional formulation where only the structural design variables are treated as optimization variables, (ii) simultaneous analysis and design (SAND) formulations where design and some of the state variables are treated as optimization variables, and (iii) a displacement-based two-phase approach where the displacements are treated as unknowns in the outer loop and the design variables as the unknowns in the inner loop. Part 2 covers more general formulations that are applicable to diverse fields, such as economics, optimal control, multidisciplinary problems and other engineering disciplines. In these fields, SAND-type formulations have been called mathematical programs with equilibrium constraints (MPEC), and partial differential equations (PDE)-constrained optimization problems. These formulations are viewed as generalizations of the SAND formulations developed in the structural optimization field. Based on the review, it is concluded that the basic ideas of the formulations presented in diverse fields can be integrated to conduct further research and develop alternative formulations and solution procedures for practical engineering applications. The paper lists 187 references on the subject.
164 citations
Book•
01 Jan 1997
TL;DR: This paper presents a meta-anatomy of the optimization of nonstationary functions in the context of discrete-time decision-making using a reinforcement learning approach.
Abstract: Stochastic optimization.- On learning automata.- Unconstrained optimization problems.- Constrained optimization problems.- Optimization of nonstationary functions.
163 citations
TL;DR: Optimization results indicate that the modified TLBO algorithm can generate improved designs when compared to other population-based techniques and in some cases improve the overall computational efficiency.
163 citations
TL;DR: A new discrete method for particle swarm optimization which can be widely applied in transmission network expansion planning (TNEP) has been discussed and the author analyses the parameter selection, convergence judgment, optimization fitness function construction, and their characters.
162 citations
TL;DR: In this paper, three approaches are presented for generating scenario trees for 3nancial portfolio problems based on simulation, optimization and hybrid simulation/optimization.
160 citations