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

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

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

Combined mutation differential evolution to solve systems of nonlinear equations

This paper presents a differential evolution heuristic to compute a solution of a system of nonlinear equations through the global optimization of an appropriate merit function. Three different mutation strategies are combined to generate mutant points. Preliminary numerical results show the effectiveness of the presented heuristic.Fundação para a Ciência e a Tecnologia (FCT

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

Modified differential evolution based on global competitive ranking for engineering design optimization problems

Engineering design optimization problems are formulated as large-scale mathematical programming problems with nonlinear objective function and constraints. Global optimization finds a solution while satisfying the constraints. Differential evolution is a population-based heuristic approach that is shown to be very efficient to solve global optimization problems with simple bounds. In this paper, we propose a modified differential evolution introducing self-adaptive control parameters, modified mutation, inversion operation and modified selection for obtaining global optimization. To handle constraints effectively, in modified selection we incorporate global competitive ranking which strikes the right balance between the objective function and the constraint violation. Sixteen well-known engineering design optimization problems are considered and the results compared with other solution methods. It is shown that our method is competitive when solving these problems.Fundação para a Ciência e a Tecnologia (FCT