A note on KKT-invexity in nonsmooth continuous-time optimization

We introduce the notion of KKT-inverity for nonsmooth continuous-time nonlinear optimization problems and prove that this notion is a necessary and sufficient condition for every KKT solution to be a global optimal solution.

Application of an iterative method and an evolutionary algorithm in fuzzy optimization

This work develops two approaches based on the fuzzy set theory to solve a class of fuzzy mathematical optimization problems with uncertainties in the objective function and in the set of constraints. The first approach is an adaptation of an iterative method that obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. The second one is a metaheuristic approach that adapts a standard genetic algorithm to use fuzzy numbers. Both approaches use a decision criterion called satisfaction level that reaches the best solution in the uncertain environment. Selected examples from the literature are presented to compare and to validate the efficiency of the methods addressed, emphasizing the fuzzy optimization problem in some import-export companies in the south of Spain. © 2012 Brazilian Operations Research Society.

Global optimization using a genetic algorithm with hierarchically structured population

This paper applies a genetic algorithm with hierarchically structured population to solve unconstrained optimization problems. The population has individuals distributed in several overlapping clusters, each one with a leader and a variable number of support individuals. The hierarchy establishes that leaders must be fitter than its supporters with the topological organization of the clusters following a tree. Computational tests evaluate different population structures, population sizes and crossover operators for better algorithm performance. A set of known benchmark test problems is solved and the results found are compared with those obtained from other methods described in the literature, namely, two genetic algorithms, a simulated annealing, a differential evolution and a particle swarm optimization. The results indicate that the method employed is capable of achieving better performance than the previous approaches in regard as the two criteria usually employed for comparisons: the number of function evaluations and rate of success. The method also has a superior performance if the number of problems solved is taken into account. (C) 2013 Elsevier B.V. All rights reserved.

Discovering promising regions to help global numerical optimization algorithms

We have developed an algorithm using a Design of Experiments technique for reduction of search-space in global optimization problems. Our approach is called Domain Optimization Algorithm. This approach can efficiently eliminate search-space regions with low probability of containing a global optimum. The Domain Optimization Algorithm approach is based on eliminating non-promising search-space regions, which are identifyed using simple models (linear) fitted to the data. Then, we run a global optimization algorithm starting its population inside the promising region. The proposed approach with this heuristic criterion of population initialization has shown relevant results for tests using hard benchmark functions.

A smooth evolutionary structural optimization procedure applied to plane stress problem

Topological optimization problems based on stress criteria are solved using two techniques in this paper. The first technique is the conventional Evolutionary Structural Optimization (ESO), which is known as hard kill, because the material is discretely removed; that is, the elements under low stress that are being inefficiently utilized have their constitutive matrix has suddenly reduced. The second technique, proposed in a previous paper, is a variant of the ESO procedure and is called Smooth ESO (SESO), which is based on the philosophy that if an element is not really necessary for the structure, its contribution to the structural stiffness will gradually diminish until it no longer influences the structure; its removal is thus performed smoothly. This procedure is known as "soft-kill"; that is, not all of the elements removed from the structure using the ESO criterion are discarded. Thus, the elements returned to the structure must provide a good conditioning system that will be resolved in the next iteration, and they are considered important to the optimization process. To evaluate elasticity problems numerically, finite element analysis is applied, but instead of using conventional quadrilateral finite elements, a plane-stress triangular finite element was implemented with high-order modes for solving complex geometric problems. A number of typical examples demonstrate that the proposed approach is effective for solving problems of bi-dimensional elasticity. (C) 2014 Elsevier Ltd. All rights reserved.

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Generalized interval vector spaces and interval optimization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Modeling and analysis of artificial neural networks applied in operations research

Artificial neural networks are dynamic systems consisting of highly interconnected and parallel nonlinear processing elements. Systems based on artificial neural networks have high computational rates due to the use of a massive number of these computational elements. Neural networks with feedback connections provide a computing model capable of solving a rich class of optimization problems. In this paper, a modified Hopfield network is developed for solving problems related to operations research. The internal parameters of the network are obtained using the valid-subspace technique. Simulated examples are presented as an illustration of the proposed approach. Copyright (C) 2000 IFAC.

Implementation of two-stage Hopfield model and its application in nonlinear systems

This paper presents an efficient neural network for solving constrained nonlinear optimization problems. More specifically, a two-stage neural network architecture is developed and its internal parameters are computed using the valid-subspace technique. The main advantage of the developed network is that it treats optimization and constraint terms in different stages with no interference with each other. Moreover, the proposed approach does not require specification of penalty or weighting parameters for its initialization.

Uma abordagem usando redes neurais artificiais para resolução de problemas de otimização restrita

Sistemas baseados em redes neurais artificiais fornecem altas taxas de computação devido ao uso de um número massivo de elementos processadores simples. Redes neurais com conexões realimentadas fornecem um modelo computacional capaz de resolver uma rica classe de problemas de otimização. Este artigo apresenta uma nova abordagem para resolver problemas de otimização restrita utilizando redes neurais artificiais. Mais especificamente, uma rede de Hopfield modificada é desenvolvida cujos parâmetros internos são calculados usando a técnica de subespaço válido de soluções. A partir da obtenção destes parâmetros a rede tende a convergir aos pontos de equilíbrio que representam as possíveis soluções para o problema. Exemplos de simulação são apresentados para justificar a validade da abordagem proposta.

H2 and/or H∞-norm model reduction of uncertain discrete-time systems

This paper addresses the problem of model reduction for uncertain discrete-time systems with convex bounded (polytope type) uncertainty. A reduced order precisely known model is obtained in such a way that the H2 and/or the H∞ guaranteed norm of the error between the original (uncertain) system and the reduced one is minimized. The optimization problems are formulated in terms of coupled (non-convex) LMIs - Linear Matrix Inequalities, being solved through iterative algorithms. Examples illustrate the results.

Projeto E análise de uma rede neural para resolver problemas de programação dinâmica

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. Neural networks with feedback connections provide a computing model capable of solving a large class of optimization problems. This paper presents a novel approach for solving dynamic programming problems using artificial neural networks. More specifically, a modified Hopfield network is developed and its internal parameters are computed using the valid-subspace technique. These parameters guarantee the convergence of the network to the equilibrium points which represent solutions (not necessarily optimal) for the dynamic programming problem. Simulated examples are presented and compared with other neural networks. The results demonstrate that proposed method gives a significant improvement.

Una metodología eficiente para manejo de restricciones en algoritmos evolutivos multi-objetivo

This paper presents a new approach for solving constraint optimization problems (COP) based on the philosophy of lexicographical goal programming. A two-phase methodology for solving COP using a multi-objective strategy is used. In the first phase, the objective function is completely disregarded and the entire search effort is directed towards finding a single feasible solution. In the second phase, the problem is treated as a bi-objective optimization problem, turning the constraint optimization into a two-objective optimization. The two resulting objectives are the original objective function and the constraint violation degree. In the first phase a methodology based on progressive hardening of soft constraints is proposed in order to find feasible solutions. The performance of the proposed methodology was tested on 11 well-known benchmark functions.

Multiarea optimal power flow using multiobjective evolutionary algorithm

In this work the multiarea optimal power flow (OPF) problem is decoupled into areas creating a set of regional OPF subproblems. The objective is to solve the optimal dispatch of active and reactive power for a determined area, without interfering in the neighboring areas. The regional OPF subproblems are modeled as a large-scale nonlinear constrained optimization problem, with both continuous and discrete variables. Constraints violated are handled as objective functions of the problem. In this way the original problem is converted to a multiobjective optimization problem, and a specifically-designed multiobjective evolutionary algorithm is proposed for solving the regional OPF subproblems. The proposed approach has been examined and tested on the RTS-96 and IEEE 354-bus test systems. Good quality suboptimal solutions were obtained, proving the effectiveness and robustness of the proposed approach. ©2009 IEEE.

Problem of assignment cells to switches in a cellular mobile network via beam search method

The problem of assigning cells to switches in a cellular mobile network is an NP-hard optimization problem. So, real size mobile networks could not be solved by using exact methods. The alternative is the use of the heuristic methods, because they allow us to find a good quality solution in a quite satisfactory computational time. This paper proposes a Beam Search method to solve the problem of assignment cell in cellular mobile networks. Some modifications in this algorithm are also presented, which allows its parallel application. Computational results obtained from several tests confirm the effectiveness of this approach to provide good solutions for medium- and large-sized cellular mobile network.