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

Fundação para a Ciência e a Tecnologia (FCT

Numerical experiments with nonconvex MINLP problems

We present a methodology to solve nonconvex Mixed-Integer Nonlinear Programming problems, that combines the Branch-and-Bound and simulated annealing type methods, which was implemented in MATLAB. A set of benchmark functions with simple bounds and different dimensions was used to analyze its practical behaviour. We exhibit computational results showing the good performance of the method.Fundação para a Ciência e a Tecnologia (FCT

A derivative-free filter driven multistart technique for global optimization

A stochastic global optimization method based on a multistart strategy and a derivative-free filter local search for general constrained optimization is presented and analyzed. In the local search procedure, approximate descent directions for the constraint violation or the objective function are used to progress towards the optimal solution. The algorithm is able to locate all the local minima, and consequently, the global minimum of a multi-modal objective function. The performance of the multistart method is analyzed with a set of benchmark problems and a comparison is made with other methods.This work was financed by FEDER funds through COMPETE-Programa Operacional Fatores de Competitividade and by portuguese funds through FCT-Fundação para a Ciência e a Tecnologia within projects PEst-C/MAT/UI0013/2011 and FCOMP- 01-0124-FEDER-022674

Interrupted searches in the BBMCSFilter context for MINLP problems

The BBMCSFilter method was developed to solve mixed integer nonlinear programming problems. This kind of problems have integer and continuous variables and they appear very frequently in process engineering problems. The objective of this work is to analyze the performance of the method when the coordinate searches are interrupted in the context of the multistart strategy. From the numerical experiments, we observed a reduction on the number of function evaluations and on the CPU time

A deterministic-stochastic method for nonconvex MINLP problems

A mixed-integer programming problem is one where some of the variables must have only integer values. Although some real practical problems can be solved with mixed-integer linear methods, there are problems occurring in the engineering area that are modelled as mixed-integer nonlinear programming (MINLP) problems. When they contain nonconvex functions then they are the most difficult of all since they combine all the difficulties arising from the two sub-classes: mixed-integer linear programming and nonconvex nonlinear programming (NLP). Efficient deterministic methods for solving MINLP are clever combinations of Branch-and-Bound (B&B) and Outer-Approximations classes. When solving nonconvex NLP relaxation problems that arise in the nodes of a tree in a B&B algorithm, using local search methods, only convergence to local optimal solutions is guaranteed. Pruning criteria cannot be used to avoid an exhaustive search in the solution space. To address this issue, we propose the use of a simulated annealing algorithm to guarantee convergence, at least with probability one, to a global optimum of the nonconvex NLP relaxation problem. We present some preliminary tests with our algorithm.Fundação para a Ciência e a Tecnologi

Practical evaluation of an interior point three-D filter line search method using engineering design problems

We present a primal-dual interior point method for nonlinear optimization that relies on a line search filter strategy to allow convergence from poor starting points. The filter technique has already been adapted to interior point methods in different ways. Our filter relies on three components. Each entry in the filter includes the feasibility measure, the centrality measure and the barrier objective function value as the optimality measure. Numerical experiments carried out with a set of engineering design problems show that our filter approach is effective in reaching the solution. A comparison with other well-known methods is also reported

Incorporating a four-dimensional filter line search method into an interior point framework

Here we incorporate a four-dimensional filter line search method into an infeasible primal-dual interior point framework for nonlinear programming. Each entry in the filter has four components measuring dual feasibility, complementarity, primal feasibility and optimality. Three measures arise directly from the first order optimality conditions of the problem and the fourth is the objective function, so that convergence to a stationary point that is a minimizer is guaranteed. The primary assessment of the method has been done with a well-known collection of small problems

Practical implementation of an interior point nonmonotone line search filter method

Versão não definitiva do artigoHere we present a primal-dual interior point nonmonotone line search filter method for nonlinear programming. The filter relies on three measures, the feasibility, the centrality and the optimality presented in the optimality conditions, considers relaxed acceptability criteria for the step size and includes a feasibility restoration phase. The evaluation of the method is until now made on small problems and a comparison is provided with a merit function approach

A three-D filter line search method within an interior point framework

Here we present a primal-dual interior point three-dimensional filter line search method for nonlinear programming. The three components of the filter aim to measure adequacy of feasibility, centrality and optimality of trial iterates. The algorithm also relies on a monotonic barrier parameter reduction and it includes a feasibility/centrality restoration phase. Numerical experiments with a set of well-known problems are carried out and a comparison with a previous implementation that differs on the optimality measure is presented

Comparison of filter line search algorithms in the primal-dual barrier approach for nonlinear programming

In this paper, we present a new filter line search method based on two measures that is integrated into the primal-dual barrier method developed by Wachter and Biegler [Mathematical Programming 106 (2006), pp. 25--57] for nonlinear programming. One measure arises directly from the first order optimality conditions of the problem and the other is the barrier function. Primary assessment of the method has been done with a well-known collection of problems and compared with the solver IPOPT.Fundação para a Ciência e a Tecnologia (FCT