Particle swarm optimization (PSO) is an optimization technique based on population, which has similarities to other evolutionary algorithms. It is initialized with a population of random solutions and searches for opt...
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Particle swarm optimization (PSO) is an optimization technique based on population, which has similarities to other evolutionary algorithms. It is initialized with a population of random solutions and searches for optima by updating generations. Particle swarm optimization has become the hotspot of evolutionary computation because of its excellent performance and simple implementation. After introducing the basic principle of the PSO, a particle swarm optimization algorithm embedded with constraint fitness priority-based ranking method is proposed in this paper to solve nonlinear programming problem. By designing the fitness function and constraints-handling method, the proposed PSO can evolve with a dynamic neighborhood and varied inertia weighted value to find the global optimum. The results from this preliminary investigation are quite promising and show that this algorithm is reliable and applicable to almost all of the problems in multiple-dimensional, nonlinear and complex constrained programming. It is proved to be efficient and robust by testing some example and benchmarks of the constrained nonlinear programming problems. (c) 2005 Elsevier Ltd. All rights reserved.
This paper presents it combined genetic algorithm-fuzzy logic controller (GA-FLC) technique for constrained nonlinear programming problems. In the standard Genetic algorithms, the upper and lower limits of the search ...
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This paper presents it combined genetic algorithm-fuzzy logic controller (GA-FLC) technique for constrained nonlinear programming problems. In the standard Genetic algorithms, the upper and lower limits of the search regions Should be given by the decision maker in advance to the optimization process. In general it needlessly large search region is used in fear of missing the global Optimum Outside the search region. Therefore, if the search region is able to adapt toward a promising area during the optimization process, the performance of GA will be enhanced greatly. Thus in this work we tried to investigate the influence of the bounding intervals on the final result. The proposed algorithm is made of classical GA Coupled with FLC. This controller monitors the variation of the decision variables during process of the algorithm and modifies the boundary intervals to restart the next round of the algorithm. These characteristics make this approach well suited for finding optimal solutions to the highly NLP problems. Compared to previous works on NLP, our method proved to be more efficient in Computation time and accuracy of the final solution. (c) 2005 Elsevier Inc. All rights reserved.
This article considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The i...
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This article considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible set makes the dynamics anytime, when viewed as an algorithm, meaning it returns a feasible solution regardless of when it is terminated. Our approach augments the gradient flow of the objective function with inputs defined by the constraint functions, treats the feasible set as a safe set, and synthesizes a safe feedback controller using techniques from the theory of control barrier functions. The resulting closed-loop system, termed safe gradient flow, can be viewed as a primal-dual flow, where the state corresponds to the primal variables and the inputs correspond to the dual ones. We provide a detailed suite of conditions based on constraint qualification under which (both isolated and nonisolated) local minimizers are asymptotically stable with respect to the feasible set and the whole state space. Comparisons with other continuous-time methods for optimization in a simple example illustrate the advantages of the safe gradient flow.
Convexity and concavity properties of the optimal value functionf* are considered for the general parametric optimization problemP(ɛ) of the form min x f(x, ɛ), s.t.x εR(ɛ). Such prope...
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Convexity and concavity properties of the optimal value functionf* are considered for the general parametric optimization problemP(ɛ) of the form min
x
f(x, ɛ), s.t.x εR(ɛ). Such properties off* and the solution set mapS* form an important part of the theoretical basis for sensitivity, stability, and parametric analysis in mathematical optimization. Sufficient conditions are given for several standard types of convexity and concavity off*, in terms of respective convexity and concavity assumptions onf and the feasible region point-to-set mapR. Specializations of these results to the general parametric inequality-equality constrained nonlinear programming problem and its right-hand-side version are provided. To the authors' knowledge, this is the most comprehensive compendium of such results to date. Many new results are given.
This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properti...
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This paper proposes a Cumulant Method-based solution to solve a maximum loading problem incorporating a constraint on the maximum variance of the loading parameter. The proposed method takes advantage of some properties regarding saddle node bifurcations to create a linear mapping relationship between random bus loading variables and all other system variables. The proposed methodology is tested using a sample system based on the IEEE 30-bus system using random active and reactive bus loading. Monte Carlo simulations consisting of 10000 samples are used as a reference solution for evaluation of the accuracy of the proposed method.
The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust, efficient, and feasible at intermediate iterations. Based on the strengths of the generalized reduced gra...
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The optimization of many engineering design problems requires a nonlinear programming algorithm that is robust, efficient, and feasible at intermediate iterations. Based on the strengths of the generalized reduced gradient (GRG) and sequential quadratic programming (SQP) algorithms, a hybrid SQP-GRG algorithm is developed. The hybrid algorithm uses the SQP search direction and a modified GRG line search. The resulting SQP-GRG algorithm is shown to be robust, feasible at intermediate iterations, and comparable in efficiency to Powell’s SQP algorithm on 26 test problems.
Techniques that identify the active constraints at a solution of a nonlinear programming problem from a point near the solution can be a useful adjunct to nonlinear programming algorithms. They have the potential to i...
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Techniques that identify the active constraints at a solution of a nonlinear programming problem from a point near the solution can be a useful adjunct to nonlinear programming algorithms. They have the potential to improve the local convergence behavior of these algorithms and in the best case can reduce an inequality constrained problem to an equality constrained problem with the same solution. This paper describes several techniques that do not require good Lagrange multiplier estimates for the constraints to be available a priori, but depend only on function and first derivative information. Computational tests comparing the effectiveness of these techniques on a variety of test problems are described. Many tests involve degenerate cases, in which the constraint gradients are not linearly independent and/or strict complementarity does not hold.
Quite often, engineers obtain measurements associated with several response variables. Both the design and analysis of multi-response experiments with a focus on quality control and improvement have received little at...
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Quite often, engineers obtain measurements associated with several response variables. Both the design and analysis of multi-response experiments with a focus on quality control and improvement have received little attention although they are sorely needed. In a multi-response case the optimization problem is more complex than in the single-response situation. In this paper we present a method to optimize multiple quality characteristics based on the mean square error (MSE) criterion when the data are collected from a combined array. The proposed method will generate more alternative solutions. The string of solutions and the trade-offs aid in determining the underlying mechanism of a system or process. The procedure is illustrated with an example, using the generalized reduced gradient (GRG) algorithm for nonlinear programming. (C) 2007 Elsevier Inc. All rights reserved.
We propose a system of differential equations to find a Kuhn-Tucker point of a nonlinear programming problem with both equality and inequality constraints. It is proven that the Kuhn-Tucker point of the nonlinear prog...
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We propose a system of differential equations to find a Kuhn-Tucker point of a nonlinear programming problem with both equality and inequality constraints. It is proven that the Kuhn-Tucker point of the nonlinear programming problem is an asymptotically stable equilibrium point of the proposed differential system. An iterate algorithm is constructed to find an equilibrium point of the differential system, the global convergence and local quadratic convergence rate of this algorithm are demonstrated, and illustrative examples are given. (c) 2006 Elsevier Inc. All rights reserved.
Recently, Gulati and Craven and Mond and Egudo established strict converse duality theorems for some of Mond-Weir duals for nonlinear programming problems. Here, we establish various duality theorems under weaker conv...
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Recently, Gulati and Craven and Mond and Egudo established strict converse duality theorems for some of Mond-Weir duals for nonlinear programming problems. Here, we establish various duality theorems under weaker convexity conditions that are different from those of Gulati and Craven, Mond and Weir, and Mond and Egudo.
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