A gradient ascent learning algorithm of the Hopfield neural networks for graph planarization is presented. This learning algorithm uses the Hopfield neural network to get a near-maximal planar subgraph, and increases the energy by modifying parameters in a gradient ascent direction to help the network escape from the state of the near-maximal planar subgraph to the state of the maximal planar subgraph or better one. The proposed algorithm is applied to several graphs up to 150 vertices and 1064 edges. The performance of our algorithm is compared with that of Takefuji/Lee's method. Simulation results show that the proposed algorithm is much better than Takefuji/Lee's method in terms of the solution quality for every tested graph.

The Clonal Selection Algorithm (CSA) is employed by the natural immune system to define the basic features of an immune response to an antigenic stimulus. In the immune response, according to Burnet's clonal selection principle, the antigen imposes a selective pressure on the antibody population by allowing only those cells which specifically recognize the antigen to be selected for proliferation and differentiation. However ongoing investigations indicate that receptor editing, which refers to the process whereby antigen receptor engagement leads to a secondary somatic gene rearrangement event and alteration of the receptor specificity, is occasionally found in affinity maturation process. In this paper, we extend the traditional CSA approach by incorporating the receptor editing method, named RECSA, and applying it to the Traveling Salesman Problem. Thus, both somatic hypermutation (HM) of clonal selection theory and receptor editing (RE) are utilized to improve antibody affinity. Simulation results and comparisons with other general algorithms show that the RECSA algorithm can effectively enhance the searching efficiency and greatly improve the searching quality within reasonable number of generations.

This paper presents a new multi-layered artificial immune system architecture using the ideas generated from the biological immune system for solving combinatorial optimization problems. The proposed methodology is composed of five layers. After expressing the problem as a suitable representation in the first layer, the search space and the features of the problem are estimated and extracted in the second and third layers, respectively. Through taking advantage of the minimized search space from estimation and the heuristic information from extraction, the antibodies (or solutions) are evolved in the fourth layer and finally the fittest antibody is exported. In order to demonstrate the efficiency of the proposed system, the graph planarization problem is tested. Simulation results based on several benchmark instances show that the proposed algorithm performs better than traditional algorithms.

A calibrating analog-to digital (A/D) converter employing a T-Model neural network is described. The T-Model neural-based A/D converter architecure is presented with particular emphasis on the elimination of local minimum of the Hopfield neural network. Furthermore, a teacher forcing algorithm is presented and used to synthesize the A/D converter and correct errors of the converter due to offset and device mismatch. An experimental A/D converter using standard 5-µm CMOS discrete IC circuits demonstrates high-performance analog-to-digital conversion and calibrating.

In this paper, based on maximum neural network, we propose a new parallel algorithm that can escape from local minima and has powerful ability of searching the globally optimal or near-optimum solution for the maximum clique problem (MCP). In graph theory a clique is a completely connected subgraph and the MCP is to find a clique of maximum size of a graph. The MCP is a classic optimization problem in computer science and in graph theory with many real-world applications, and is also known to be NP-complete. Lee and Takefuji have presented a very powerful neural approach called maximum neural network for this NP-complete problem. The maximum neural model always guarantees a valid solution and greatly reduces the search space without a burden on the parameter-tuning. However, the model has a tendency to converge to the local minimum easily because it is based on the steepest descent method. By adding a negative self-feedback to the maximum neural network, we proposed a parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm is then fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the maximum neural network and the chaotic neurodynamics. A large number of instances have been simulated to verify the proposed algorithm.

A technique for pulse code modulation (PCM) encoding using a T-Model neural network is described. Performance evaluation on both the T-Model and the Hopfield model neural-based PCM encoders is carried out with PSpice simulations. The PSpice simulations also show that the T-Model neural-based PCM encoder computes to a global minimum much more effectively and more quickly than the Hopfield one.

Breast cancer is a serious disease across the world, and it is one of the largest causes of cancer death for women. The traditional diagnosis is not only time consuming but also easily affected. Hence, artificial intelligence (AI), especially neural networks, has been widely used to assist to detect cancer. However, in recent years, the computational ability of a neuron has attracted more and more attention. The main computational capacity of a neuron is located in the dendrites. In this paper, a novel neuron model with dendritic nonlinearity (NMDN) is proposed to classify breast cancer in the Wisconsin Breast Cancer Database (WBCD). In NMDN, the dendrites possess nonlinearity when realizing the excitatory synapses, inhibitory synapses, constant-1 synapses and constant-0 synapses instead of being simply weighted. Furthermore, the nonlinear interaction among the synapses on a dendrite is defined as a product of the synaptic inputs. The soma adds all of the products of the branches to produce an output. A back-propagation-based learning algorithm is introduced to train the NMDN. The performance of the NMDN is compared with classic back propagation neural networks (BPNNs). Simulation results indicate that NMDN possesses superior capability in terms of the accuracy, convergence rate, stability and area under the ROC curve (AUC). Moreover, regarding ROC, for continuum values, the existing 0-connections branches after evolving can be eliminated from the dendrite morphology to release computational load, but with no influence on the performance of classification. The results disclose that the computational ability of the neuron has been undervalued, and the proposed NMDN can be an interesting choice for medical researchers in further research.

This paper proposes a probabilistic modeling learning algorithm for the local search approach to the Multiple-Valued Logic (MVL) networks. The learning model (PMLS) has two phases: a local search (LS) phase, and a probabilistic modeling (PM) phase. The LS performs searches by updating the parameters of the MVL network. It is equivalent to a gradient decrease of the error measures, and leads to a local minimum of error that represents a good solution to the problem. Once the LS is trapped in local minima, the PM phase attempts to generate a new starting point for LS for further search. It is expected that the further search is guided to a promising area by the probability model. Thus, the proposed algorithm can escape from local minima and further search better results. We test the algorithm on many randomly generated MVL networks. Simulation results show that the proposed algorithm is better than the other improved local search learning methods, such as stochastic dynamic local search (SDLS) and chaotic dynamic local search (CDLS).

Particle swarm optimizer (PSO) is a stochastic global optimization technique based on a social interaction metaphor. Because of the complexity, dynamics and randomness involved in PSO, it is hard to theoretically analyze the mechanism on which PSO depends. Statistical results have shown that the probability distribution of PSO is a truncated triangle, with uniform probability across the middle that decreases on the sides. The "truncated triangle" is also called the "Maya pyramid" by Kennedy. However, very little is known regarding the sampling distribution of PSO in itself. In this paper, we theoretically analyze the "Maya pyramid" without any assumption and derive its computational formula, which is actually a hybrid uniform distribution that looks like a trapezoid and conforms with the statistical results. Based on the derived density function of the hybrid uniform distribution, the search strategy of PSO is defined and quantified to characterize the mechanism of the search strategy in PSO. In order to show the significance of these definitions based on the derived hybrid uniform distribution, the comparison between the defined search strategies of the classical linear decreasing weight based PSO and the canonical constricted PSO suggested by Clerc is illustrated and elaborated.

Immune system protects living body from various attacks by foreign invades. Based on the immune response principles, we propose an improved lateral interaction artificial immune system model in this paper. Considering that the different epitopes on the surface of antigen can be recognized by a set of different paratopes expressed on the surface of immune cells, we build a neighborhood set that consists of immune cells with different affinities to a certain input antigen. We update all the weights of the immune cells located in neighborhood set according to their affinities. Simulations on noisy pattern recognition illustrate that the proposed artificial immune system model has stronger noise tolerance ability and is more effective at recognizing noisy patterns than that of our previous models.

We introduce a novel neural network called the T-Model and investigates the learning ability of the T-Model neural network. A learning algorithm based on the least mean square (LMS) algorithm is used to train the T-Model and produces a very good result for the T-Model network. We present simulation results on several practical problems to illustrate the efficiency of the learning techniques. As a result, the T-Model network learns successfully, but the Hopfield model fails to and the T-Model learns much more effectively and more quickly than a multi-layer network.

In this paper, we propose a new parallel algorithm for cellular radio channel assignment problem that can help the expanded maximum neural network escape from local minima by introducing a transient chaotic neurodynamics. The goal of the channel assignment problem, which is an NP-complete problem, is to minimize the total interference between the assigned channels needed to satisfy all of the communication needs. The expanded maximum neural model always guarantees a valid solution and greatly reduces search space without a burden on the parameter-tuning. However, the model has a tendency to converge to local minima easily because it is based on the steepest descent method. By adding a negative self-feedback to expanded maximum neural network, we proposed a new parallel algorithm that introduces richer and more flexible chaotic dynamics and can prevent the network from getting stuck at local minima. After the chaotic dynamics vanishes, the proposed algorithm then is fundamentally reined by the gradient descent dynamics and usually converges to a stable equilibrium point. The proposed algorithm has the advantages of both the expanded maximum neural network and the chaotic neurodynamics. Simulations on benchmark problems demonstrate the superior performance of the proposed algorithm over other heuristics and neural network methods.

We present a learning algorithm of the Hopfield neural network for minimizing edge crossings in linear drawings of nonplanar graphs. The proposed algorithm uses the Hopfield neural network to get a local optimal number of edge crossings, and adjusts the balance between terms of the energy function to make the network escape from the local optimal number of edge crossings. The proposed algorithm is tested on a variety of graphs including some "real word" instances of interconnection networks. The proposed learning algorithm is compared with some existing algorithms. The experimental results indicate that the proposed algorithm yields optimal or near-optimal solutions and outperforms the compared algorithms.

In this paper, a four-quadrant analog multiplier consisting of four neuron-MOS transistors and two load resistors is proposed. The proposed multiplier can be operated at only 1 V. Furthermore, the input range of the multiplier is equal to 100% of the supply voltage. The theoretical harmonic distortion caused by mobility degradation and device mismatchs is derived in detail. The performance of the proposed multiplier is characterized through HSPICE simulations with a standard 2.0 µm CMOS process with a double-poly layer. Simulations of the proposed multiplier demonstrate that the linearity error of 0.77% and a total harmonic distortion of 0.62% are obtained with full-scale input conditions. The maximum power consumption and 3 dB bandwidth are 9.56 µW and 107 MHz, respectively. The active area of the proposed multiplier is 210 µm 140 µm.

The goal of the maximum cut problem is to partition the vertex set of an undirected graph into two parts in order to maximize the cardinality of the set of edges cut by the partition. The maximum cut problem has many important applications including the design of VLSI circuits and communication networks. Moreover, many optimization problems can be formulated in terms of finding the maximum cut in a network or a graph. In this paper, we propose an improved Hopfield neural network algorithm for efficiently solving the maximum cut problem. A large number of instances have been simulated. The simulation results show that the proposed algorithm is much better than previous works for solving the maximum cut problem in terms of the computation time and the solution quality.

This paper proposes a gradient ascent learning algorithm for the elastic net approach to the Traveling Salesman Problem (TSP). The learning model has two phases: an elastic net phase, and a gradient ascent phase. The elastic net phase is equivalent to gradient descent of an energy function, and leads to a local minimum of energy that represents a good solution to the problem. Once the elastic net gets stuck in local minima, the gradient ascent phase attempts to fill up the valley by modifying parameters in a gradient ascent direction of the energy function. Thus, these two phases are iterated until the elastic net gets out of local minima. We test the algorithm on many randomly generated travel salesman problems up to 100 cities. For all problems, the systems are shown to be capable of escaping from the elastic net local minima and generating shorter tour than the original elastic net.

In this paper, introducing a stochastic hill-climbing dynamics into an optimal competitive Hopfield network model (OCHOM), we propose a new algorithm that permits temporary energy increases, which helps the OCHOM escape from local minima. In graph theory, a clique is a completely connected subgraph and the maximum clique problem (MCP) is to find a clique of maximum size of a graph. The MCP is a classic optimization problem in computer science and in graph theory with many real-world applications, and is also known to be NP-complete. Recently, Galan-Marin et al. proposed the OCHOM for the MCP. It can guarantee convergence to a global/local minimum of energy function, and performs better than other competitive neural approaches. However, the OCHOM has no mechanism to escape from local minima. The proposed algorithm introduces stochastic hill-climbing dynamics which helps the OCHOM escape from local minima, and it is applied to the MCP. A number of instances have been simulated to verify the proposed algorithm.

Clonal Selection Algorithm (CSA), based on the clonal selection theory proposed by Burnet, has gained much attention and wide applications during the last decade. However, the proliferation process in the case of immune cells is asexual. That is, there is no information exchange during different immune cells. As a result the traditional CSA is often not satisfactory and is easy to be trapped in local optima so as to be premature convergence. To solve such a problem, inspired by the quantum interference mechanics, an improved quantum crossover operator is introduced and embedded in the traditional CSA. Simulation results based on the traveling salesman problems (TSP) have demonstrated the effectiveness of the quantum crossover-based Clonal Selection Algorithm.

A new arithmetic multiple-valued algebra with functional completeness is introduced. The algebra is called Neuro-Algebra for it has very similar formula and architecture to neural networks. Two canonical forms of multiple-valued functions of this Neuro-Algebra are presented. Since the arithmetic operations of the Neuro-Aglebra are basically a weighted-sum and a piecewise linear operations, their implementations are very simple and straightforward. Furthermore, the multiple-valued networks based on the Neuro-Algebra can be trained by the traditional back-propagation learning algorithm directly.

Kennedy has proposed the bare bones particle swarm (BBPS) by the elimination of the velocity formula and its replacement by the Gaussian sampling strategy without parameter tuning. However, a delicate balance between exploitation and exploration is the key to the success of an optimizer. This paper firstly analyzes the sampling distribution in BBPS, based on which we propose an adaptive BBPS inspired by the cloud model (ACM-BBPS). The cloud model adaptively produces a different standard deviation of the Gaussian sampling for each particle according to the evolutionary state in the swarm, which provides an adaptive balance between exploitation and exploration on different objective functions. Meanwhile, the diversity of the swarms is further enhanced by the randomness of the cloud model itself. Experimental results show that the proposed ACM-BBPS achieves faster convergence speed and more accurate solutions than five other contenders on twenty-five unimodal, basic multimodal, extended multimodal and hybrid composition benchmark functions. The diversity enhancement by the randomness in the cloud model itself is also illustrated.