A novel method for automatically creating an optimum direction-of-arrival (DOA) estimation algorithm for a given radio environment using a genetic algorithm (GA) is proposed. DOA estimation algorithms are generally described by parameters and operators. The performance of a DOA estimation algorithm is evaluated using root mean square error (RMSE) through computer simulations. A GA searches for the combination of parameters and operators that gives the lowest RMSE. Because a GA can treat only bit strings, Polish notation is used to convert bit strings into a DOA estimation algorithm. A computer simulation showed that the proposed method can create a new angle spectrum function. The created angle spectrum function has higher resolution than the Capon method.

Ant Colony Optimization (ACO) is one of the most recent techniques for solving combinatorial optimization problems, and has been unexpectedly successful. Therefore, many improvements have been proposed to improve the performance of the ACO algorithm. In this paper an ant colony optimization with memory is proposed, which is applied to the classical traveling salesman problem (TSP). In the proposed algorithm, each ant searches the solution not only according to the pheromone and heuristic information but also based on the memory which is from the solution of the last iteration. A large number of simulation runs are performed, and simulation results illustrate that the proposed algorithm performs better than the compared algorithms.

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).

Ant Colony Optimization (ACO) algorithms are a new branch of swarm intelligence. They have been applied to solve different combinatorial optimization problems successfully. Their performance is very promising when they solve small problem instances. However, the algorithms' time complexity increase and solution quality decrease for large problem instances. So, it is crucial to reduce the time requirement and at the same time to increase the solution quality for solving large combinatorial optimization problems by the ACO algorithms. This paper introduces a Local Search based ACO algorithm (LSACO), a new algorithm to solve large combinatorial optimization problems. The basis of LSACO is to apply an adaptive local search method to improve the solution quality. This local search automatically determines the number of edges to exchange during the execution of the algorithm. LSACO also applies pheromone updating rule and constructs solutions in a new way so as to decrease the convergence time. The performance of LSACO has been evaluated on a number of benchmark combinatorial optimization problems and results are compared with several existing ACO algorithms. Experimental results show that LSACO is able to produce good quality solutions with a higher rate of convergence for most of the problems.

Ant colony optimization (ACO) algorithms are a recently developed, population-based approach which has been successfully applied to optimization problems. However, in the ACO algorithms it is difficult to adjust the balance between intensification and diversification and thus the performance is not always very well. In this work, we propose an improved ACO algorithm in which some of ants can evolve by performing genetic operation, and the balance between intensification and diversification can be adjusted by numbers of ants which perform genetic operation. The proposed algorithm is tested by simulating the Traveling Salesman Problem (TSP). Experimental studies show that the proposed ACO algorithm with genetic operation has superior performance when compared to other existing ACO algorithms.

In this paper, we propose a computationally efficient method to solve the large dimension Adaptive Subcarrier Assignment and Bit Allocation (ASABA) problem of multiuser orthogonal frequency division multiplexing system. Our algorithm consists of three Ordinal Optimization (OO) stages to find a good enough solution to the considered problem. First of all, we reformulate the considered problem to separate it into subcarrier assignment and bit allocation problem such that the objective function of a feasible subcarrier assignment pattern is the corresponding optimal bit allocation for minimizing the total consumed power. Then in the first stage, we develop an approximate objective function to evaluate the performance of a subcarrier assignment pattern and use a genetic algorithm to search through the huge solution space and select s best subcarrier assignment patterns based on the approximate objective values. In the second stage, we employ an off-line trained artificial neural network to estimate the objective values of the s subcarrier assignment patterns obtained in stage 1 and select the l best patterns. In the third stage, we use the exact objective function to evaluate the l subcarrier assignment patterns obtained in stage 2, and the best one associated with the corresponding optimal bit allocation is the good enough solution that we seek. We apply our algorithm to numerous cases of large-dimension ASABA problems and compare the results with those obtained by four existing algorithms. The test results show that our algorithm is the best in both aspects of solution quality and computational efficiency.

A branch-and-bound algorithm (BB for short) is the most general technique to deal with various combinatorial optimization problems. Even if it is used, computation time is likely to increase exponentially. So we consider its parallelization to reduce it. It has been reported that the computation time of a parallel BB heavily depends upon node-variable selection strategies. And, in case of a parallel BB, it is also necessary to prevent increase in communication time. So, it is important to pay attention to how many and what kind of nodes are to be transferred (called sending-node selection strategy). In this paper, for the graph coloring problem, we propose some sending-node selection strategies for a parallel BB algorithm by adopting MPI for parallelization and experimentally evaluate how these strategies affect computation time of a parallel BB on a PC cluster network.

Many researchers have attempted to solve the combinatorial optimization problems, that are NP-hard or NP-complete problems, by using neural networks. Though the method used in a neural network has some advantages, the local minimum problem is not solved yet. It has been shown that the Inverse Function Delayed (ID) model, which is a neuron model with a negative resistance on its dynamics and can destabilize an intended region, can be used as the powerful tool to avoid the local minima. In our previous paper, we have shown that the ID network can separate local minimum states from global minimum states in case that the energy function of the embed problem is zero. It can achieve 100% success rate in the N-Queen problem with the certain parameter region. However, for a wider parameter region, the ID network cannot reach a global minimum state while all of local minimum states are unstable. In this paper, we show that the ID network falls into a particular permanent oscillating state in this situation. Several neurons in the network keep spiking in the particular permanent oscillating state, and hence the state transition never proceed for global minima. However, we can also clarify that the oscillating state is controlled by the parameter α which affects the negative resistance region and the hysteresis property of the ID model. In consequence, there is a parameter region where combinatorial optimization problems are solved at the 100% success rate.

Collaboration of growing self-organizing maps (GSOM) and adaptive resonance theory maps (ART) is considered through traveling sales-person problems (TSP).The ART is used to parallelize the GSOM: it divides the input space of city positions into subspaces automatically. One GSOM is allocated to each subspace and grows following the input data. After all the GSOMs grow sufficiently they are connected and we obtain a tour. Basic experimental results suggest that we can find semi-optimal solution much faster than serial methods.

In this paper, we present a modified genetic algorithm for solving combinatorial optimization problems. The modified genetic algorithm in which crossover and mutation are performed conditionally instead of probabilistically has higher global and local search ability and is more easily applied to a problem than the conventional genetic algorithms. Three optimization problems are used to test the performances of the modified genetic algorithm. Experimental studies show that the modified genetic algorithm produces better results over the conventional one and other methods.

This paper proposes a new class of parallel branch-and-bound (B&B) schemes. The main idea of the scheme is to focus on the functional parallelism instead of conventional data parallelism, and to support such a heterogeneous and irregular parallelism by using a collection of autonomous agents distributed over the network. After examining several implementation issues, we describe a detail of the prototype system implemented over eight PC's connected by a network. The result of experiments conducted over the prototype system indicates that the proposed parallel processing scheme significantly improves the performance of the underlying B&B scheme by adaptively switching exploring policies adopted by each agent participating to the problem solving.

A new edge-coloring algorithm for bipartite graphs is presented. This algorithm, based on the framework of the O(m log d + (m/d) log (m/d) log d) algorithm by Makino-Takabatake-Fujishige and the O(m log m) one by Alon, finds an optimal edge-coloring of a bipartite graph with m edges and maximum degree d in O(m log d + (m/d) log (m/d)) time. This algorithm does not require elaborate data structures, which the best known O(m log d) algorithm due to Cole-Ost-Schirra depends on.

The concepts of M-convexity and L-convexity, introduced by Murota (1996, 1998) for functions on the integer lattice, extract combinatorial structures in well-solved nonlinear combinatorial optimization problems. These concepts are extended to polyhedral convex functions and quadratic functions on the real space by Murota-Shioura (2000, 2001). In this paper, we consider a further extension to general convex functions. The main aim of this paper is to provide rigorous proofs for fundamental properties of general M-convex and L-convex functions.

In this paper, performance of chaos and burst noises injected to the Hopfield Neural Network for quadratic assignment problems is investigated. For the evaluation of the noises, two methods to appreciate finding a lot of nearly optimal solutions are proposed. By computer simulations, it is confirmed that the burst noise generated by the Gilbert model with a laminar part and a burst part achieved the good performance as the intermittency chaos noise near the three-periodic window.

In a previous study about a combinatorial optimization problem solver using neural networks, since the Hopfield method, convergence to the optimum solution sooner and with more certainty is regarded as important. Namely, only static states are considered as the information. However, from a biological point of view, dynamical systems have attracted attention recently. Therefore, we propose a "dynamical" combinatorial optimization problem solver using hysteresis neural networks. In this paper, the proposed system is evaluated by the N-Queen problem.

Digital halftoning is a technique to convert a continuous-tone image into a binary image consisting of black and white dots. It is an important technique for printing machines and printers to output an image with few intensity levels or colors which looks similar to an input image. This paper surveys how algorithm engineering can contribute to digital halftoning or what combinatorial problems are related to digital halftoning. A common criterion on optimal digital halftoning leads to a negative result that obtaining an optimal halftoned image is NP-complete. So, there are two choices: approximation algorithm and polynomial-time algorithm with relaxed condition. Main algorithmic notions related are geometric discrepancy, matrix (or array) rounding problems, and network-flow algorithms.

When solving combinatorial optimization problems with a binary Hopfield-type neural network, the updating process in neural network is an important step in achieving a solution. In this letter, we propose a new updating procedure in binary Hopfield-type neural network for efficiently solving combinatorial optimization problems. In the new updating procedure, once the neuron is in excitatory state, then its input potential is in positive saturation where the input potential can only be reduced but cannot be increased, and once the neuron is in inhibitory state, then its input potential is in negative saturation where the input potential can only be increased but cannot be reduced. The new updating procedure is evaluated and compared with the original procedure and other improved methods through simulations based on N-Queens problem. The results show that the new updating procedure improves the searching capability of neural networks with shorter computation time. Particularly, the simulation results show that the performance of proposed method surpasses the exiting methods for N-queens problem in synchronous parallel computation model.

We propose hysteresis neural network solving combinatorial optimization problems, Box Puzzling Problem. Hysteresis neural network searches solutions of the problem with nonlinear dynamics. The output vector becomes stable only when it corresponds with a solution. This system does never become stable without satisfying constraints of the problem. After estimating hardware calculating time, we obtain that numerical calculating time increases extremely comparing with hardware time as problem's scale increases. However the system has possibility of limit cycle. Though it is very hard to remove limit cycle completely, we propose some methods to remove this phenomenon.

This paper presents a genetic algorithm for designing at minimum cost a two-connected network topology such that the shortest cycle (referred to as a ring) to which each edge belongs does not exceed a given maximum number of hops. The genetic algorithm introduces a solution representation in which constraints such as connectivity and ring constraints are easily encoded. Furthermore, a problem specific crossover operator that ensures solutions generated through genetic evolution are all feasible is also proposed. Hence, both checking of the constraints and repair mechanism can be avoided thus resulting in increased efficiency. Experimental evaluation shows the effectiveness of the proposed GA.

This paper treats meta-heuristics for combinatorial optimization problems. The parallelization of meta-heuristics is then discussed in which we show that parallel processing has possibility of not only speeding up but also improving solution quality. Finally we extend the discussion of the combinatorial optimization into autonomous decentralized systems, say autonomous decentralized optimization. This notion becomes very important with the advancement of the network-connected system architecture.