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.

A novel approach based on recurrent neural networks applied to nonlinear systems optimization

This paper presents an efficient approach based on recurrent neural network for solving nonlinear optimization. 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 that represent an optimal feasible solution. 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 and weighting parameters for its initialization. A study of the modified Hopfield model is also developed to analyze its stability and convergence. Simulation results are provided to demonstrate the performance of the proposed neural network. (c) 2005 Elsevier B.V. All rights reserved.

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.

Polynomials generated by a three term recurrence relation: bounds for complex zeros

This paper deals with the zeros of polynomials generated by a certain three term recurrence relation. The main objective is to find bounds, in terms of the coefficients of the recurrence relation, for the regions where the zeros are located. In most part, the zeros are explored through an Eigenvalue representation associated with a corresponding Hessenberg rnatrix. Applications to Szego polynomials, para-orthogonal polynomials and polynomials with non-zero complex coefficients are considered. (C) 2004 Elsevier B.V. All rights reserved.

Nonlinear optimization using a modified Hopfield model

Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing 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 constrained nonlinear optimization problems. The internal parameters of the network are obtained using the valid-subspace technique. Simulated examples are presented as an illustration of the proposed approach.

Global optimization for the ℋ∞-norm model reduction problem

A branch and bound algorithm is proposed to solve the [image omitted]-norm model reduction problem for continuous and discrete-time linear systems, with convergence to the global optimum in a finite time. The lower and upper bounds in the optimization procedure are described by linear matrix inequalities (LMI). Also proposed are two methods with which to reduce the convergence time of the branch and bound algorithm: the first one uses the Hankel singular values as a sufficient condition to stop the algorithm, providing to the method a fast convergence to the global optimum. The second one assumes that the reduced model is in the controllable or observable canonical form. The [image omitted]-norm of the error between the original model and the reduced model is considered. Examples illustrate the application of the proposed method.

Environmental evaluation of cogeneration scenarios in sugar industry

The development of new techniques that allow the analysis and optimization of energy systems bearing in mind environmental issues is indispensable in a world with finite natural resources and growing demand of energy. Among the energy systems that deserve special attention, cogeneration in the sugar industry must be pointed out, because it uses efficiently a common fuel for generation of useful heat and power. Within this frame, thermoeconomical optimization - 2nd Law of Thermodynamics analysis by exergy function and economic evaluation of the thermal system - gradually is taking importance as a powerful tool to assist to the decision making process. Also, the explicit consideration of environmental issues offers a better way to explore trade-offs between different aspects to support the decisions that must be made. In this work it is used the technique of Life Cycle Analysis (LCA) which allows to consider environmental matters as an integral part of the problem, in opposite to most of the environmental approaches that only reduce residuals generation , without taking into account impacts associated to other related processes. On the other hand, the consideration of environmental issues in optimization of energy systems is a novel and promissory contribution in the state of the art of energy optimization and LCA. The system under study is a sugar plant of Tucumán (Argentina) given the particular importance that this industry had inside the regional economy of the Argentinean Northwest. Although cogeneration comes being used a while ago in sugar industry, being the main objective the generation of heat and as secondary objective the electric power generation and mechanic power to cover several needs of working machineries, to the date it is no available a versatile tool that allows to analyze economical feasible alternatives bearing in mind environmental issues. At sugar plants, steam is generated in boilers using as fuel bagasse - cellulosic fiber waste obtained crushing the sugar cane- and it is used to give useful heat and shaft work to the plant, but it can also be used to generate electricity with export opportunities to the electrical network. The great number of process alternatives outlines a serious decision making problem in order to take advantage of the resources. Although the problem turns out to be a mixed non-linear problem (MINLP), the main contribution of this work is the development of a hybrid strategy to evaluate cogeneration alternatives that combines optimization approaches with environmental indicators. This powerful tool for its versatility and robustness to analyze cogeneration systems, will be of great help in the decision making process, because of their easy implementation to analyze the kind of problems presented in the sugar industry.

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.

An assessment of fiscal and regulatory barriers to deployment of energy efficiency and renewable energy technologies in Belize

Belize is currently faced with several critical challenges associated with the production, distribution and use of energy. Despite an abundance of renewable energy resources, the country remains disproportionately dependent on imported fossil fuels, which exposes it to volatile and rising oil prices, limits economic development, and retards its ability to make the investments that are necessary for adapting to climate change, which pose a particularly acute threat to the small island states and low-lying coastal nations of the Caribbean. This transition from energy consumption and supply patterns that are based on imported fossil fuels and electricity towards a more sustainable energy economy that is based on environmentally benign, indigenous renewable energy technologies and more efficient use of energy requires concerted action as the country is already challenged by limited fiscal space which reduces its ability to provide some fiscal incentives, which have been proven to be effective tools for the promotion of sustainable energy markets in a number of countries. This report identifies the fiscal and regulatory barriers to implementation of energy efficiency measures and renewable energy technologies in Belize. Data and information were derived from stakeholder consultations conducted within the country. The major result of the assessment is that the transition of policies and plans into tangible action needs to be increased. In this regard, it is necessary to articulate sub-policies of the National Energy Policy to amend the Public Utilities Commission Act, to develop a grid interconnection policy, to establish minimum energy performance standards for buildings and equipment and to develop a public procurement policy. Finally, decisions on renewable energy and energy efficiency-related incentives from the Government formally requires decision-makers to solve what may be extremely complex optimization problems in order to obtain the lowest-cost provision of energy services to society, thereby weighing the cost of revenue losses with the benefits of fuel and infrastructure expansion savings. The establishment of a management system that is efficient, flexible, and transparent, which will facilitate the implementation of the strategic objectives and outputs in the time available, with the financial resources allocated is recommended. Support is required for additional institutional and capacity strengthening.

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.

Generalized interval vector spaces and interval optimization

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A comparison of deterministic, reliability-based and risk-based structural optimization under uncertainty

In this paper, the effects of uncertainty and expected costs of failure on optimum structural design are investigated, by comparing three distinct formulations of structural optimization problems. Deterministic Design Optimization (DDO) allows one the find the shape or configuration of a structure that is optimum in terms of mechanics, but the formulation grossly neglects parameter uncertainty and its effects on structural safety. Reliability-based Design Optimization (RBDO) has emerged as an alternative to properly model the safety-under-uncertainty part of the problem. With RBDO, one can ensure that a minimum (and measurable) level of safety is achieved by the optimum structure. However, results are dependent on the failure probabilities used as constraints in the analysis. Risk optimization (RO) increases the scope of the problem by addressing the compromising goals of economy and safety. This is accomplished by quantifying the monetary consequences of failure, as well as the costs associated with construction, operation and maintenance. RO yields the optimum topology and the optimum point of balance between economy and safety. Results are compared for some example problems. The broader RO solution is found first, and optimum results are used as constraints in DDO and RBDO. Results show that even when optimum safety coefficients are used as constraints in DDO, the formulation leads to configurations which respect these design constraints, reduce manufacturing costs but increase total expected costs (including expected costs of failure). When (optimum) system failure probability is used as a constraint in RBDO, this solution also reduces manufacturing costs but by increasing total expected costs. This happens when the costs associated with different failure modes are distinct. Hence, a general equivalence between the formulations cannot be established. Optimum structural design considering expected costs of failure cannot be controlled solely by safety factors nor by failure probability constraints, but will depend on actual structural configuration. (c) 2011 Elsevier Ltd. All rights reserved.

A Chaotic Approach of Differential Evolution Optimization Applied to Loudspeaker Design Problem

Over the past few years, the field of global optimization has been very active, producing different kinds of deterministic and stochastic algorithms for optimization in the continuous domain. These days, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. Differential evolution (DE) algorithms are a family of evolutionary optimization techniques that use a rather greedy and less stochastic approach to problem solving, when compared to classical evolutionary algorithms. The main idea is to construct, at each generation, for each element of the population a mutant vector, which is constructed through a specific mutation operation based on adding differences between randomly selected elements of the population to another element. Due to its simple implementation, minimum mathematical processing and good optimization capability, DE has attracted attention. This paper proposes a new approach to solve electromagnetic design problems that combines the DE algorithm with a generator of chaos sequences. This approach is tested on the design of a loudspeaker model with 17 degrees of freedom, for showing its applicability to electromagnetic problems. The results show that the DE algorithm with chaotic sequences presents better, or at least similar, results when compared to the standard DE algorithm and other evolutionary algorithms available in the literature.