A study of simulated annealing variants

This work presents a study of some variants of simulated annealing method

Caracterização da função de penalidade exponencial na resolução de problemas de programação semi-infinita

Os problemas de programação semi-infinita (PSI) são caracterizados por terem um conjunto finito de variáveis e um número infinito de restrições. A classe de métodos de redução é baseada na ideia que, sob certas condições, é possível substituir as infinitas restrições por um conjunto finito de restrições que, localmente, é suficiente para definir a região admissível do problema PSI. Neste trabalho é proposto um novo método de redução que combina o método simulated annealing para a optimização multilocal, e o método de penalidade para a optimização não linear com restrições

Solving SIP by penalty techniques: merit functions and filter method

We present a review of reduction type methods to solve nonlinear semi-infinite programming problems. In the last years a large type of techniques were presented in literature to solve SIP problems based on reduction method. These reduction type methods presented are based on merit functions and filter method combined with penalty techniques. Some comparations are made

A stretched simulated annealing algorithm for locating all global maximizers

Work partially supported by FCT grant POCTI/MAT/58957/2004.In this work we consider the problem of finding all the global maximizers of a given multimodal optimization problem. We propose a new algorithm that combines the simulated annealing (SA) method with a function stretching technique to generate a sequence of global maximization problems that are defined whenever a new maximizer is identified. Each global maximizer is located through a variant of the SA algorithm. Results of numerical experiments with a set of well-known test problems show that the proposed method is effective. We also compare the performance of our algorithm with other multi-global optimizers

Reduction method with simulated annealing for semi-infinite programming

Semi-infinite programming (SIP) problems are characterized by a finite number of variables and an infinite number of constraints. The class of the reduction methods is based on the idea that, under certain conditions, it is possible to replace the infinite constraints by a finite set of constraints, that are locally sufficient to define the feasible region of the SIP problem. We propose a new reduction method based on a simulated annealing algorithm for multi-local optimization and the penalty method for solving the finite problem

Comparative study of penalty simulated annealing methods for multiglobal programming

In a multiglobal optimization problem we aim to find all the global solutions of a constrained nonlinear programming problem where the objective function is multimodal. This class of global optimization problems is very important and frequently encountered in engineering applications, such as, process synthesis, design and control in chemical engineering. The most common method for solving this type of problems uses a local search method to refine a set of approximations, which are obtained by comparing objective function values at points of a predefined mesh. This type of method can be very expensive numerically. On the other hand, the success of local search methods depends on the starting point being at the neighbourhood of a solution. Stochastic methods are appropriate alternatives to find global solutions, in which convergence to a global solution can be guaranteed, with probability one. This is the case of the simulated annealing (SA) method. To compute the multiple solutions, a function stretching technique that transforms the objective function at each step is herein combined with SA to be able to force, step by step, convergence to each one of the required global solutions. The constraints of the problem are dealt with a penalty technique. This technique transforms the constrained problem into a sequence of unconstrained problems by penalizing the objective function when constraints are violated. Numerical experiments are shown with three penalty functions

Experiences with reduction method to solve semi-infinite programming problems

In this talk, some variants of reduction-type method combined with a line search filter method to solve nonlinear semi-infinite programming problems are presented. We use the stretched simulated annealing method and the branch and bound technique to compute the maximizers of the constraint. The filter method is used as an alternative to merit functions to promote convergence from poor starting points

Particle swarm and simulated annealing for multi-local optimization

Particle swarm and simulated annealing optimization algorithms proved to be valid in finding a global optimum in the bound constrained optimization context. However, their original versions can only detect one global optimum even if the problem has more than one solution. In this paper we propose modifications to both algorithms. In the particle swarm optimization algorithm we introduce gradient information to enable the computation of all the global and local optima. The simulated annealing algorithm is combined with a stretching technique to be able to compute all global optima. The numerical experiments carried out with a set of well-known test problems illustrate the effectiveness of the proposed algorithms.Work partially supported by FCT grant POCTI/MAT/58957/ 2004 and by the Algoritmi research center

Solving semi-infinite programming problems using filter method

Semi-infinite programming problems can be efficiently solved by reduction type methods. Here, we present a new global reduction method for Semi-infinite programming, where the multi-local optimization is carried out with a stretched simulated annealing algorithm, the reduced problem is approximately solved by a primal-dual interior point method combined with a three-dimensional filter line search strategy, and the global convergence is promoted through a two-dimensional filter line search. Numerical experiments with a set of well-known problems are shown

Stopping rules effect on a derivative-free filter multistart algorithm for multilocal programming

Multilocal programming aims to identify all the local solutions of constrained optimization problems. The purpose of this paper is to analyze the effect of stopping rules on the performance of a particular multistart method, which relies on a derivative-free local search procedure to converge to a solution, when solving multilocal optimization problems. The method herein presented implements the approximate descent direction method combined with a filter methodology to handle the constraints by forcing the local search towards the feasible region. Two stopping rules are tested on five classical multimodal problems.FC