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Binary representation suffers from the problem of positional dependence, where the amplitude of phenotype variation is dependent on the position of the altered genotype bits. However, this is contrary to conventional variation operations that treat each genotype bit equally. Positional dependence can be attributed to the poor locality, which results in neighboring genotypes having low correlation in the phenotype space, reducing the effectiveness of systematic local search and evolutionary search based on small mutation steps. For this purpose, this paper will propose an alternative genotype--phenotype mapping for binary representation that introduces redundancy into the mapping and removes the exponential orderings between the alleles, hence improving the locality between the genotype and phenotype search space. Empirical study conducted based on distribution, locality, and mutation innovation revealed key algorithmic characteristics of the proposed code, and its practicality is validated by comparative studies based on different benchmark optimization problems. Possible approaches to resolve the overrepresentation problem due to redundancy will be suggested, exhibiting its flexibility and variability in implementation. Index Terms--Binary representation, evolutionary algorithm (EA), positional dependence, redundancy.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2005.12.029 Byline: K.C. Tan, C.Y. Cheong, C.K. Goh Keywords: Vehicle routing problems; Evolutionary algorithms; Multiobjective optimization; Stochastic Abstract: This paper considers the routing of vehicles with limited capacity from a central depot to a set of geographically dispersed customers where actual demand is revealed only when the vehicle arrives at the customer. The solution to this vehicle routing problem with stochastic demand (VRPSD) involves the optimization of complete routing schedules with minimum travel distance, driver remuneration, and number of vehicles, subject to a number of constraints such as time windows and vehicle capacity. To solve such a multiobjective and multi-modal combinatorial optimization problem, this paper presents a multiobjective evolutionary algorithm that incorporates two VRPSD-specific heuristics for local exploitation and a route simulation method to evaluate the fitness of solutions. A new way of assessing the quality of solutions to the VRPSD on top of comparing their expected costs is also proposed. It is shown that the algorithm is capable of finding useful tradeoff solutions for the VRPSD and the solutions are robust to the stochastic nature of the problem. The developed algorithm is further validated on a few VRPSD instances adapted from Solomon's vehicle routing problem with time windows (VRPTW) benchmark problems. Author Affiliation: Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Singapore Article History: Received 23 March 2005; Accepted 19 December 2005

In this paper, a new memetic algorithm (MA) for multiobjective (MO) optimization is proposed, which combines the global search ability of particle swarm optimization with a synchronous local search heuristic for directed local fine-tuning. A new particle updating strategy is proposed based upon the concept of fuzzy global-best to deal with the problem of premature convergence and diversity maintenance within the swarm. The proposed features are examined to show their individual and combined effects in MO optimization. The comparative study shows the effectiveness of the proposed MA, which produces solution sets that are highly competitive in terms of convergence, diversity, and distribution. Index Terms--Memetic algorithm (MA), multiobjective (MO) optimization, particle swarm optimization (PSO).

In this letter, we attempt to quantify the significance of increasing the number of neurons in the hidden layer of a feedforward neural network architecture using the singular value decomposition (SVD). Through this, we extend some well-known properties of the SVD in evaluating the generalizability of single hidden layer feedforward networks (SLFNs) with respect to the number of hidden layer neurons. The generalization capability of the SLFN is measured by the degree of linear independency of the patterns in hidden layer space, which can be indirectly quantified from the singular values obtained from the SVD, in a postlearning step. A pruning/growing technique based on these singular values is then used to estimate the necessary number of neurons in the hidden layer. More importantly, we describe in detail properties of the SVD in determining the structure of a neural network particularly with respect to the robustness of the selected model.

Numerous power utilities have installed advanced distributed temperature sensing (DTS) systems to measure the temperature of underground cables. This paper presents a general procedure for real-time assessment of underground cable ratings based on DTS. After the identification and location of hot spots on a cable, the cable installation data, load, and DTS-recorded temperature over a period of time are used to estimate soil thermal parameters and assess cable ratings under normal and over-loading conditions. In order to accurately estimate soil thermal parameters, a combined technique of the finite-element method and gradient-based optimization is used. The technique was validated in the laboratory and applied to a rating assessment of a 230-kV/500-MVA cable circuit. The assessed continuous and emergency ratings are helpful in improving the operation of this circuit. Index Terms--Cable rating, distributed temperature sensing, finite-element method (FEM), hot spot, optimization method.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2004.11.019 Byline: K.C. Tan (a), Y.H. Chew (a), L.H. Lee (b) Keywords: Vehicle routing; Evolutionary algorithms; Multi-objective optimization Abstract: This paper considers a transportation problem for moving empty or laden containers for a logistic company. Owing to the limited resource of its vehicles (trucks and trailers), the company often needs to sub-contract certain job orders to outsourced companies. A model for this truck and trailer vehicle routing problem (TTVRP) is first constructed in the paper. The solution to the TTVRP consists of finding a complete routing schedule for serving the jobs with minimum routing distance and number of trucks, subject to a number of constraints such as time windows and availability of trailers. To solve such a multi-objective and multi-modal combinatorial optimization problem, a hybrid multi-objective evolutionary algorithm (HMOEA) featured with specialized genetic operators, variable-length representation and local search heuristic is applied to find the Pareto optimal routing solutions for the TTVRP. Detailed analysis is performed to extract useful decision-making information from the multi-objective optimization results as well as to examine the correlations among different variables, such as the number of trucks and trailers, the trailer exchange points, and the utilization of trucks in the routing solutions. It has been shown that the HMOEA is effective in solving multi-objective combinatorial optimization problems, such as finding useful trade-off solutions for the TTVRP routing problem. Author Affiliation: (a) Department of Electrical and Computer Engineering, National University of Singapore, 4, Engineering Drive 3, Singapore 117576, Singapore (b) Department of Industrial and System Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Article History: Received 18 March 2004; Accepted 9 November 2004

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.ejor.2004.08.038 Byline: K.C. Tan, C.K. Goh, Y.J. Yang, T.H. Lee Keywords: Global optimization; Evolutionary computations; Multiple criteria analysis Abstract: The aim of multi-objective evolutionary optimization is to minimize the distance between the solution set and the true Pareto front, to distribute the solutions evenly and to maximize the spread of solution set. This paper addresses these issues by presenting two features that enhance the optimization ability of multi-objective evolutionary algorithms. The first feature is a variant of the mutation operator that adapts the mutation rate along the evolution process to maintain a balance between the introduction of diversity and local fine-tuning. In addition, this adaptive mutation operator adopts a new approach to strike a compromise between the preservation and disruption of genetic information. The second feature is an enhanced exploration strategy that encourages the exploration towards less populated areas and hence achieves better discovery of gaps in the generated front. The strategy also preserves non-dominated solutions in the evolving population to achieve a good convergence for the optimization. Comparative studies of some well-known diversity operators, mutation operators and multi-objective evolutionary algorithms are performed on different benchmark problems, which illustrate the effectiveness and efficiency of the proposed features. Author Affiliation: Department of Electrical and Computer Engineering, National University of Singapore, 4 Engineering Drive 3, Singapore 117576, Republic of Singapore Article History: Received 12 August 2003; Accepted 13 August 2004

The additive recurrent network structure of linear threshold neurons represents a class of biologically-motivated models, where nonsaturating transfer functions are necessary for representing neuronal activities, such as that of cortical neurons. This paper extends the existing results of dynamics analysis of such linear threshold networks by establishing new and milder conditions for boundedness and asymptotical stability, while allowing for multistability. As a condition for asymptotical stability, it is found that boundedness does not require a deterministic matrix to be symmetric or possess positive off-diagonal entries. The conditions put forward an explicit way to design and analyze such networks. Based on the established theory, an alternate approach to study such networks is through permitted and forbidden sets. An application of the linear threshold (LT) network is analog associative memory, for which a simple design method describing the associative memory is suggested in this paper. The proposed design method is similar to a generalized Hebbian approach, but with distinctions of additional network parameters for normalization, excitation and inhibition, both on a global and local scale. The computational abilities of the network are dependent on its nonlinear dynamics, which in turn is reliant upon the sparsity of the memory vectors. Index Terms--Associative memory, continuous real-valued patterns, dynamics analysis, linear threshold (LT) network.

This paper presents a new approach of task-oriented developmental learning for humanoid robots. It is capable of setting up multiple tasks representation automatically using real-time experiences, thereby enabling a robot to handle various tasks concurrently without the need of predefining the tasks. In the approach, an evolvable partitioned tree structure is used for task representation knowledgebase that is partitioned into different task domains. The search/update of task knowledge is focused on a particular task branch, without considering the whole task knowledgebase that is often large and time consuming in the process. A prototype of the proposed task-oriented developmental learning is designed and implemented using a Khepera robot. Experimental results show that the robot can redirect itself to new tasks through interactions with the environment, and a learned task can be easily updated in order to meet varying specifications in the real world. Index Terms--Humanoid robots, learning systems, task representation.

Multistable networks have attracted much interest in recent years, since multistability is of primary importance for some applications of recurrent neural networks where monostability exhibits some restrictions. This paper focuses on the analysis of dynamical property for a class of additive recurrent neural networks with nonsaturating linear threshold transfer functions. A milder condition is derived to guarantee the boundedness and global attractivity of the networks as compared to that presented in [6]. Dynamical properties of the equilibria of two-dimensional networks are analyzed theoretically, and the relationships between the equilibria features and network parameters (synaptic weights and external inputs) are revealed. In addition, the sufficient and necessary conditions for coexistence of multiple equilibria are obtained, which confirmed the observations in [14] with a cortex-inspired silicon circuit. The results obtained in this paper are applicable to both symmetric and nonsymmetric networks. Simulation examples are used to illustrate the theory developed in this paper. Index Terms--Equilibria, global attractivity, linear threshod (LT) neural network, nonsaturating, multistability.

Parameter setting is a critical step in the Hopfield networks solution of the traveling salesman problem (TSP), which is often prone to extraneous solutions. This paper presents some stability criteria that ensure the convergence of valid solutions and suppression of infeasible solutions. Our theory is based on an enhanced parametric formulation that maps TSP onto a continuous-time Hopfield network (CHN), which is more advantageous than the Hopfield-Tank (H-T) formulation. A set of analytical conditions for optimal parameter settings of the CHN is then derived, and the resulting performance is validated by simulations. Index Terms--Hopfield neural networks, traveling salesman problem (TSP), parameter setting, stability.

This letter presents a new dynamical optimal learning (DOL) algorithm for three-layer linear neural networks and investigates its generalization ability. The optimal learning rates can be fully determined during the training process. The mean squared error (muse) is guaranteed to be stably decreased and the learning is less sensitive to initial parameter settings. The simulation results illustrate that the proposed DOL algorithm gives better generalization performance and faster convergence as compared to standard error back propagation algorithm. Index Terms--Back propagation, dynamical optimal learning (DOL), feedforward neural networks (FNN), stability.

The major drawbacks of the Hopfield network when it is applied to some combinatorial problems, e.g., the traveling salesman problem (TSP), are invalidity of the obtained solutions, trial-and-error setting value process of the network parameters and low-computation efficiency. This letter presents a columnar competitive model (CCM) which incorporates winner-takes-all (WTA) learning rule for solving the TSP. Theoretical analysis for the convergence of the CCM shows that the competitive computational neural network guarantees the convergence to valid states and avoids the onerous procedures of determining the penalty parameters. In addition, its intrinsic competitive learning mechanism enables a fast and effective evolving of the network. The simulation results illustrate that the competitive model offers more and better valid solutions as compared to the original Hopfield network. Index Terms--Convergence analysis, Hopfield networks, traveling salesman problem (TSP), winner-takes-all (WTA).

An overview is presented on rural development in Yuhang, located in China's Zhejiang province. Reform-induced urbanization and industrialization have had significant social, economic and environmental impacts, including income disparities from private enterprise and a shift from agricultural to non-agricultural land use.

This article explores the changes brought on by economic reform and rural development in China. The authors, focusing on the rural area of Yuhang, Zhejiang, maintain the most noticeable changes of reform was the rapid economic growth, privatization of enterprises, and the relationship between peasant and land in which peasants gained more control over the land.