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Original Hebbian encoding scheme of bidirectional associative memory (BAM) provides a poor pattern capacity and recall performance. Based on Rosenblatt's perceptron learning algorithm, the pattern capacity of BAM is enlarged, and perfect recall of all training pattern pairs is guaranteed. However, these methods put their emphases on pattern capacity, rather than error correction capability which is another critical point of BAM. This paper analyzes the sensitivity to noise in BAM and obtains an interesting idea to improve noise immunity of BAM. Some researchers have found that the noise sensitivity of BAM relates to the minimum absolute value of net inputs (MAV). However, in this paper, the analysis on failure association shows that it is related not only to MAV but also to the variance of weights associated with synapse connections. In fact, it is a positive monotone increasing function of the quotient of MAV divided by the variance of weights. This idea provides an useful principle of improving error correction capability of BAM. Some revised encoding schemes, such as small variance learning for BAM (SVBAM), evolutionary pseudorelaxation learning for BAM (EPRLAB) and evolutionary bidirectional learning (EBL), have been introduced to illustrate the performance of this principle. All these methods perform better than their original versions in noise immunity. Moreover, these methods have no negative effect on the pattern capacity of BAM. The convergence of these methods is also discussed in this paper. If there exist solutions, EPRLAB and EBL always converge to a global optimal solution in the senses of both pattern capacity and noise immunity. However, the convergence of SVBAM may be affected by a preset function. Index Terms--Associative memory, bidirectional associative memory (BAM), genetic algorithm (GA), neural network, noise immunity, pattern recognition.

This paper considers the stochastic capacitated are routing problem (SCARP), obtained by taking random demands in the CARP. For real-world problems, it is important to create solutions that are insensitive to changes in demand, because these quantities are not deterministic but randomly distributed. This paper provides the basic concept of a new technique to compute such solutions, based upon the best method published for CARP: a hybrid genetic algorithm (HGA). The simulation analysis was achieved with the well-known DeArmon's, Eglese's and Belenguer's instances. This intensive evaluation process was carried out with 1000 replications providing high-quality statistical data. The results obtained prove that there is a great interest to optimize not only the solution cost but also the robustness of solutions. This work is a step forward to treat more realistic problems including industrial goals and constraints linked to demand variations. Keywords: vehicle routeing; genetic algorithms; optimisation; stochastic capacitated arc routing problem; sensitivity analysis; robustness

Type-2 fuzzy logic system (FLS) cascaded with neural network, type-2 fuzzy neural network (T2FNN), is presented in this paper to handle uncertainty with dynamical optimal learning. A T2FNN consists of a type-2 fuzzy linguistic process as the antecedent part, and the two-layer interval neural network as the consequent part. A general T2FNN is computational-intensive due to the complexity of type 2 to type 1 reduction. Therefore, the interval T2FNN is adopted in this paper to simplify the computational process. The dynamical optimal training algorithm for the two-layer consequent part of interval T2FNN is first developed. The stable and optimal left and right learning rates for the interval neural network, in the sense of maximum error reduction, can be derived for each iteration in the training process (back propagation). It can also be shown both learning rates cannot be both negative. Further, due to variation of the initial MF parameters, i.e., the spread level of uncertain means or deviations of interval Gaussian MFs, the performance of back propagation training process may be affected. To achieve better total performance, a genetic algorithm (GA) is designed to search optimal spread rate for uncertain means and optimal learning for the antecedent part. Several examples are fully illustrated. Excellent results are obtained for the truck backing-up control and the identification of nonlinear system, which yield more improved performance than those using type-1 FNN. Index Terms--Back propagation, dynamic optimal learning rate, genetic algorithm, interval type-2 FNN.

This paper presents a genetic algorithm (GA)-based economic contracting strategy for optimal selection of tenders in the England and Wales standing reserve market. The aim of the contracting strategy is three fold--first, to identify potential tenders to be contracted, second, to determine the volume of electric power that each tender should supply, and thirdly how often they should provide the service. The third issue is easy to deal with using a contracting strategy where all tenders bid for a full service window (fixed tenders); however, it becomes troublesome if tenders are allowed to bid for a flexible, partial service window (flexible tenders). In this paper, a GA strategy with a special encoding scheme, order-based crossover and mutation operators (OBGA), has been developed to deal with flexible tenders within the tender selection process. The proposed method has been investigated using four test cases, with different tender flexibility and constraints. The test results clearly demonstrate that the OBGA performs as well as the conventional GA when all tenders bid for fixed contracts; however, OBGA gradually outperforms the conventional GA as the number of flexible tenders progressively increases. Index Terms--Contracting strategy, genetic algorithms (GAs), standing reserve, tender selection process.

In this paper, a cooperative agent algorithm, the ant colony system (ACS), for optimum switch relocation is proposed. Switch relocation is a useful tool for distribution automation, since it can reduce the interruption costs without additional capital investments. The formulation of switch relocation is a combinatorial optimization problem with nonlinear and nondifferential objective functions. In this paper, the authors choose the ACS to solve the problem since the ACS has the characteristics of positive feedback, distributed computation, and the use of a constructive greedy heuristic. One of the main goals of this paper is to investigate the applicability of the ACS-based algorithm in the power system optimization problems. Test results show that the proposed ACS-based algorithm can offer a near-optimum solution for switch relocation. The comparisons of the proposed method with a genetic-algorithm (GA)-based method are also shown in the test results to demonstrate the values of the proposed method. Index Terms--Ant colony system, customer interruption cost, distribution automation, genetic algorithm, reliability improvement, switch relocation.

The graph partitioning problem is defined as that of dividing the vertices of an undirected graph into a set of balanced parts through the removal of a set of edges, whose size is to be minimized. A number of researchers have investigated multilevel schemes, which coarsen the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partitioning of the original graph. In this paper, a genetic algorithm for the coarsening phase of a multilevel scheme for graph partitioning is presented. The proposed approach has been demonstrated to improve the solution quality at the expense of running time. Keywords: graph partitioning problem; multilevel graph partitioning; genetic algorithms

Design of an optimal controller minimizing the integral of squared error (ISE) of the closed-loop system for an interval plant via evolutionary approaches is proposed in this paper. Based on a worst-case design philosophy, the design problem is formulated as a minimax optimization problem from the signal energy point of view, and subsequently solved by two interactive genetic algorithms. To ensure robust stability of the closed-loop system, root locations of the Kharitonov polynomials associated with the characteristic polynomial are used to establish a constraint handling mechanism for incorporation into the fitness function to effectively evaluate chromosomes in the current population. To accelerate the derivation process to obtain the optimal controller, alternative approaches based on the two-phase evolutionary scheme are also proposed, in which the worst-case ISE is suitably estimated via information provided by the Kharitonov plants. Thus, the derived controller not only stabilizes the interval plant, but also minimizes the ISE criterion of the closed-loop system. Constraints on higher order plants and controller order commonly encountered by conventional design methods are therefore removed by using the proposed approach. Index Terms--Genetic algorithms, integral of squared error (ISE), interval plants, minimax optimization, robust controllers, signal energy.

In this paper, two robust decentralized control design methodologies for load frequency control (LFC) are proposed. The first one is based on [H.sub.[infinity]] control design using linear matrix inequalities (LMI) technique in order to obtain robustness against uncertainties. The second controller has a simpler structure, which is more appealing from an implementation point of view, and it is tuned by a proposed novel robust control design algorithm to achieve the same robust performance as the first one. More specifically, genetic algorithms (GAs) optimization is used to tune the control parameters of the proportional-integral (PI) controller subject to the [H.sub.[infinity]] constraints in terms of LMI. Hence, the second control design is called GALMI. Both proposed controllers are tested on a three-area power system with three scenarios of load disturbances to demonstrate their robust performances. Index Terms--Automatic generation control, decentralized control, genetic algorithms, [H.sub.[infinity]], linear matrix inequalities, load frequency control, robust control.

Harmonic estimation in a distorted signal along with additive noise has been an area of interest for researchers in many disciplines of science and engineering. This paper presents a new algorithm to estimate the harmonics in power systems using genetic algorithms (GAs). The harmonic estimation problem is linear in amplitude and nonlinear in phase. The proposed hybrid algorithm takes advantage of this structure and iterates between linear least squares amplitude estimation and the nonlinear GA-based phase estimation. Improvement in both convergence for solution as well as processing time is demonstrated from this algorithm. Index Terms--Genetic algorithms, harmonic estimation, hybrid algorithm, least squares, performance index.

This paper presents a simple heuristic technique to deal with multiple local minima in nonconvex, nonlinear power system optimization problems by solving a sequence of interior-point subproblems. Both the real-valued and the mixed-integer cases are separately discussed. The method is then applied to the unit commitment problem and its performance on realistic cases is compared with that of a genetic algorithm (GA). Index Terms--Genetic algorithms (GAs), global optimization, interior point algorithms, nonconvex mixed-integer optimization.

This paper considers a phasor measurement unit (PMU) placement problem requiring simultaneous optimization of two conflicting objectives, such as minimization of the number of PMUs and maximization of the measurement redundancy. The objectives are in conflict since the improvement of one of them leads to the deterioration of another. Instead of a unique optimal solution, it exists a set of best tradeoffs between competing objectives, the so-called Pareto-optimal solutions. A specially tailored nondominated sorting genetic algorithm (NSGA) for a PMU placement problem is proposed as a methodology to find these Pareto-optimal solutions. The algorithm is combined with the graph-theoretical procedure and a simple GA to reduce the initial number of the PMU's candidate locations. The NSGA parameters are carefully set by performing a number of trial runs and evaluating the NSGA performances based on the number of distinct Pareto-optimal solutions found in the particular run and distance of the obtained Pareto front from the optimal one. Illustrative results on the 39- and 118-bus IEEE systems are presented. Index Terms--Genetic algorithm (GA), multiobjective optimization, nondominated sorting, Pareto-optimal solutions, phasor measurement unit (PMU), topological observability.

This paper proposes a new formulation for reactive power (VAR) planning problem including the allocation of flexible ac transmission systems (FACTS) devices. A new feature of the formulation lies in the treatment of security issues. Different from existing formulations, we directly take into account the expected cost for voltage collapse and corrective controls, where the control effects by the devices to be installed are evaluated together with the other controls such as load shedding in contingencies to compute an optimal VAR planning. The inclusion of load shedding into the formulation guarantees the feasibility of the problem. The optimal allocation by the proposed method implies that the investment is optimized, taking into account its effects on security in terms of the cost for power system operation under possible events occurring probabilistically. The problem is formulated as a mixed integer nonlinear programming problem of a large dimension. The Benders decomposition technique is tested where the original problem is decomposed into multiple subproblems. The numerical examinations are carried out using AEP-14 bus system to demonstrate the effectiveness of the proposed method. Index Terms--Benders decomposition, FACTS devices, genetic algorithms, VAR planning, voltage stability.

In this paper, a solution to the problem of the multidimensional (m-D) polynomial factorization is attempted by using genetic algorithms (GAs). The proposed method is based on an appropriate minimization of the norm of the difference between the original polynomial and its desirable factorized form. Using GAs, we can obtain better results than with other methods of minimization (numerical techniques, neural networks, etc.). The present methodology, which can also be used for every type of m-D factorization, is illustrated by means of a numerical example. Index Terms--Genetic algorithm (GA), multidimensional (m-D) polynomial factorization, multivariate polynomials.