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Derivative-Free Filter Simulated Annealing Method for Constrained Continuous Global Optimization
- Journal of Global Optimization
, 2004
"... In this paper, a simulated-annealing-based method called Filter Simulated Annealing (FSA) method is proposed to deal with the constrained global optimization problem. The considered problem is reformulated so as to take the form of optimizing two functions; the objective function and the constrai ..."
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Cited by 27 (5 self)
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In this paper, a simulated-annealing-based method called Filter Simulated Annealing (FSA) method is proposed to deal with the constrained global optimization problem. The considered problem is reformulated so as to take the form of optimizing two functions; the objective function and the constraint violation function. Then, the FSA method is applied to solve the reformulated problem. The FSA method invokes a multi-start diversification scheme in order to achieve an e#cient exploration process.
Optimal Anytime Search For Constrained Nonlinear Programming
, 2001
"... In this thesis, we study optimal anytime stochastic search algorithms (SSAs) for solving general constrained nonlinear programming problems (NLPs) in discrete, continuous and mixed-integer space. The algorithms are general in the sense that they do not assume di#erentiability or convexity of functio ..."
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Cited by 6 (2 self)
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In this thesis, we study optimal anytime stochastic search algorithms (SSAs) for solving general constrained nonlinear programming problems (NLPs) in discrete, continuous and mixed-integer space. The algorithms are general in the sense that they do not assume di#erentiability or convexity of functions. Based on the search algorithms, we develop the theory of SSAs and propose optimal SSAs with iterative deepening in order to minimize their expected search time. Based on the optimal SSAs, we then develop optimal anytime SSAs that generate improved solutions as more search time is allowed. Our SSAs
Solving Nonlinear Constrained Optimization Problems Through Constraint Partitioning
, 2005
"... In this dissertation, we propose a general approach that can significantly reduce the com-plexity in solving discrete, continuous, and mixed constrained nonlinear optimization (NLP) problems. A key observation we have made is that most application-based NLPs have struc-tured arrangements of constrai ..."
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Cited by 5 (5 self)
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In this dissertation, we propose a general approach that can significantly reduce the com-plexity in solving discrete, continuous, and mixed constrained nonlinear optimization (NLP) problems. A key observation we have made is that most application-based NLPs have struc-tured arrangements of constraints. For example, constraints in AI planning are often lo-calized into coherent groups based on their corresponding subgoals. In engineering design problems, such as the design of a power plant, most constraints exhibit a spatial structure based on the layout of the physical components. In optimal control applications, constraints are localized by stages or time. We have developed techniques to exploit these constraint structures by partitioning the constraints into subproblems related by global constraints. Constraint partitioning leads to much relaxed subproblems that are significantly easier to solve. However, there exist global constraints relating multiple subproblems that must be resolved. Previous methods cannot exploit such structures using constraint partitioning because they cannot resolve inconsistent global constraints efficiently.
Requirements Controlled Design: A Method for Discovery of Discontinuous System Boundaries in the Requirements Hyperspace
- GEORGIA INSTITUTE OF TECHNOLOGY
, 2004
"... The drive toward robust systems design, especially with respect to system affordablility throughout the system life-cycle, has led to the development of several advanced design methods. While these methods have been extremely successful in satisfying the needs for which they have been developed, the ..."
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Cited by 4 (0 self)
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The drive toward robust systems design, especially with respect to system affordablility throughout the system life-cycle, has led to the development of several advanced design methods. While these methods have been extremely successful in satisfying the needs for which they have been developed, they inherently leave a critical area unaddressed. None of them fully considers the effect of requirements on the selection of solution systems. The goal of all of current modern design methodologies is to bring knowledge forward in the design process to the regions where more design freedom is available and design changes cost less. Therefore, it seems reasonable to consider the point in the design process where the greatest restrictions are placed on the final design, the point in which the system level requirements are set. Historically the requirements have been treated as something handed down from above. However, neither the customer nor the solution provider completely understood all of the options that are available in the broader requirements space. If a method were developed that provided the ability to understand the full scope of the requirements space, it would allow for a better comparison of potential solution systems with respect to both the current and potential future requirements. The key to a requirements conscious method is to treat requirements differently from the traditional approach. The method proposed herein is known as Requirements Controlled Design (RCD). By treating the requirements as a set of variables that control the behavior of the system, instead of variables that only define the response of the system, it is possible to determine a-priori what portions of the requirements space that any given system is capable of satisfying. Additionally, it should be possible to identify which systems can satisfy a given set of requirements and the locations where a small change in one or more requirements poses a significant risk to a design program. This thesis puts forth the theory and methodology to enable RCD, and details and validates a specific method called the Modified Strength Pareto Evolutionary Algorithm (MSPEA).
The Theory And Applications Of Discrete Constrained Optimization Using Lagrange Multipliers
, 2000
"... In this thesis, we present a new theory of discrete constrained optimization using Lagrange multipliers and an associated first-order search procedure (DLM) to solve general constrained optimization problems in discrete, continuous and mixed-integer space. The constrained problems are general in the ..."
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Cited by 4 (0 self)
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In this thesis, we present a new theory of discrete constrained optimization using Lagrange multipliers and an associated first-order search procedure (DLM) to solve general constrained optimization problems in discrete, continuous and mixed-integer space. The constrained problems are general in the sense that they do not assume the differentiability or convexity of functions. Our proposed theory and methods are targeted at discrete problems and can be extended to continuous and mixed-integer problems by coding continuous variables using a floating-point representation (discretization). We have characterized the errors incurred due to such discretization and have proved that there exists upper bounds on the errors. Hence, continuous and mixed-integer constrained problems, as well as discrete ones, can be handled by DLM in a unified way with bounded errors.
A COMPARATIVE STUDY ON OPTIMIZATION METHODS FOR THE CONSTRAINED NONLINEAR PROGRAMMING PROBLEMS
, 2004
"... Constrained nonlinear programming problems often arise in many engineering appli-cations. The most well-known optimization methods for solving these problems are se-quential quadratic programming methods and generalized reduced gradient methods. This study compares the performance of thesemethods wi ..."
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Cited by 3 (0 self)
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Constrained nonlinear programming problems often arise in many engineering appli-cations. The most well-known optimization methods for solving these problems are se-quential quadratic programming methods and generalized reduced gradient methods. This study compares the performance of thesemethods with the genetic algorithms which gained popularity in recent years due to advantages in speed and robustness. We present a comparative study that is performed on fifteen test problems selected from the literature.
Three Applications of Optimization in Computer Graphics
, 2003
"... This thesis addresses the application of nonlinear optimization to three different problems in computer graphics: the generation of gait cycles for legged creatures, the generation of models of truss structures, and the generation of models of constant mean curvature structures. ..."
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Cited by 1 (0 self)
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This thesis addresses the application of nonlinear optimization to three different problems in computer graphics: the generation of gait cycles for legged creatures, the generation of models of truss structures, and the generation of models of constant mean curvature structures.
Extended Duality in Fuzzy Optimization Problems
"... Duality theorem is an attractive approach for solving fuzzy optimization problems. However, the duality gap is generally nonzero for nonconvex problems. So far, most of the studies focus on continuous variables in fuzzy optimization problems. And, in real problems and models, fuzzy optimization pro ..."
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Duality theorem is an attractive approach for solving fuzzy optimization problems. However, the duality gap is generally nonzero for nonconvex problems. So far, most of the studies focus on continuous variables in fuzzy optimization problems. And, in real problems and models, fuzzy optimization problems also involve discrete and mixed variables. To address the above problems, we improve the extended duality theory by adding fuzzy objective functions. In this paper, we first define continuous fuzzy nonlinear programming problems, discrete fuzzy nonlinear programming problems, and mixed fuzzy nonlinear programming problems and then provide the extended dual problems, respectively. Finally we prove the weak and strong extended duality theorems, and the results show no duality gap between the original problem and extended dual problem.
Constrained Global Optimization by Constraint Partitioning and Simulated Annealing*
"... Abstract In this paper, we present constraint-partitioned sim-ulated annealing (CPSA), an algorithm that extends our previous constrained simulated annealing (CSA)for constrained optimization. The algorithm is based on the theory of extended saddle points (ESPs). Bydecomposing the ESP condition into ..."
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Abstract In this paper, we present constraint-partitioned sim-ulated annealing (CPSA), an algorithm that extends our previous constrained simulated annealing (CSA)for constrained optimization. The algorithm is based on the theory of extended saddle points (ESPs). Bydecomposing the ESP condition into multiple necessary conditions, CPSA partitions a problem by itsconstraints into subproblems, solves each independently using CSA, and resolves those violated globalconstraints across the subproblems. Because each subproblem is exponentially simpler and the numberof global constraints is very small, the complexity of solving the original problem is significantly reduced.We state without proof the asymptotic convergence of CPSA with probability one to a constrained globalminimum in discrete space. Last, we evaluate CPSA on some continuous constrained benchmarks. 1 Problem Definition A general mixed-integer nonlinear programming prob-lem (MINLP) is formulated as follows: (Pm) : minz f (z) (1) subject to h(z) = 0 and g(z) < = 0, where z = (x, y) 2 Z; x 2 Rv and y 2 Dw are,respectively, bounded continuous and discrete variables; f (z) is a lower-bounded objective function; g(z) = (g1(z),..., gr(z))T is a vector of r inequalityconstraint functions, and h(z) = (h1(z),..., hm(z))T
