Learning cellular automata rules for binary classification problem

This paper proposes a cellular automata-based solution of a binary classification problem. The proposed method is based on a two-dimensional, three-state cellular automaton (CA) with the von Neumann neighborhood. Since the number of possible CA rules (potential CA-based classifiers) is huge, searching efficient rules is conducted with use of a genetic algorithm (GA). Experiments show an excellent performance of discovered rules in solving the classification problem. The best found rules perform better than the heuristic CA rule designed by a human and also better than one of the most widely used statistical method: the k-nearest neighbors algorithm (k-NN). Experiments show that CAs rules can be successfully reused in the process of searching new rules.     

Kingfisher: an efficient algorithm for searching for both positive and negative dependency rules with statistical significance measures

Statistical dependency analysis is the basis of all empirical science. A commonly occurring problem is to find the most significant dependency rules, which describe either positive or negative dependencies between categorical attributes. In medical science, for example, one is interested in genetic factors, which can either predispose or prevent diseases. The requirement of statistical significance is essential, because the discoveries should hold also in future data. Typically, the significance is estimated either by Fisher??s exact test or the ?? ²-measure. The problem is computationally very difficult, because the number of all possible dependency rules increases exponentially with the number of attributes. As a solution, different kinds of restrictions and heuristics have been applied, but a general, scalable search method has been missing. In this paper, we introduce an efficient algorithm, called Kingfisher, for searching for the best non-redundant dependency rules with statistical significance measures. The rules can express either positive or negative dependencies between a set of positive attributes and a single consequent attribute. The algorithm itself is independent from the used goodness measure, but we concentrate on Fisher??s exact test and the ?? ²-measure. The algorithm is based on an application of the branch-and-bound search strategy, supplemented by several pruning properties. Especially, we prove a new lower bound for Fisher??s p and introduce a new effective pruning principle. According to our experiments on classical benchmark data, the algorithm is well scalable and can efficiently handle even dense and high-dimensional data sets. An interesting observation was that Fisher??s exact test did not only produce more reliable rules than the ?? ²-measure, but it also performed the search much faster.     

Linguistic fuzzy model identification based on PSO with different length of particles

To generate the structure and parameters of fuzzy rule base automatically, a particle swarm optimization algorithm with different length of particles (DLPPSO) is proposed in the paper. The main finding of the proposed approach is that the structure and parameters of a fuzzy rule base can be generated automatically by the proposed PSO. In this method, the best fitness (f_gbest) and the number (N_gbest) of active rules of the best particle in current generation, the best fitness (f_pbesti) which ith particle has achieved so far and the number (N_pbesti) of active rules of it when the best position emerged are utilized to determine the active rules of ith particle in each generation. To increase the diversity of structure, mutation operator is used to change the number of active rules for particles. Compared with some other PSOs with different length of particles, the algorithm has good adaptive performance. To indicate the effectiveness of the give algorithm, a nonlinear function and two time series are used in the simulation experiments. Simulation results demonstrate that the proposed method can approximate the nonlinear function and forecast the time series efficiently.     

Taking advantage of solving the resource constrained multi-project scheduling problems using multi-modal genetic algorithms

In this paper, for the first time, multi-modal genetic algorithms (MMGAs) are proposed to optimize the resource constrained multi-project scheduling problem (RCMPSP). In problems where the landscape has both multiple local and global optima, such as the RCMPSP, a MMGAs approach can provide managers with an advantage in decision-making because they can choose between alternative solutions equally good. Alternative optima are achieved because the diversification techniques of MMGAs introduce diversity in population, decreasing the possibility of the optimization process getting caught in a unique local or global optimum. To compare the performance of a MMGAs approach with other alternative approaches, commonly accepted by researchers to solve the RCMPSP such as classical genetic algorithms and dispatching heuristics based on priority rules, we analyse two time-based objective functions (makespan and average percent delay) and three coding systems [random keys (RK), activity list (AL), and a new proposal called priority rule (PR)]. We have found that MMGAs significantly improve the efficacy (the algorithm’s capability to find the best optimum) and the multi-solution-based efficacy (the algorithm’s capability to find multiple optima) of the other two approaches. For makespan the PR is the best code in terms of the efficacy and multi-solution-based efficacy, and the RK is the best code for the average percent delay.     

Application of reinforcement learning for agent-based production scheduling

Reinforcement learning (RL) has received some attention in recent years from agent-based researchers because it deals with the problem of how an autonomous agent can learn to select proper actions for achieving its goals through interacting with its environment. Although there have been several successful examples demonstrating the usefulness of RL, its application to manufacturing systems has not been fully explored yet. In this paper, Q-learning, a popular RL algorithm, is applied to a single machine dispatching rule selection problem. This paper investigates the application potential of Q-learning, a widely used RL algorithm to a dispatching rule selection problem on a single machine to determine if it can be used to enable a single machine agent to learn commonly accepted dispatching rules for three example cases in which the best dispatching rules have been previously defined. This study provided encouraging results that show the potential of RL for application to agent-based production scheduling.     

On approximation algorithms for the terminal Steiner tree problem

The terminal Steiner tree problem is a special version of the Steiner tree problem, where a Steiner minimum tree has to be found in which all terminals are leaves. We prove that no polynomial time approximation algorithm for the terminal Steiner tree problem can achieve an approximation ratio less than (1−o(1))lnn unless NP has slightly superpolynomial time algorithms. Moreover, we present a polynomial time approximation algorithm for the metric version of this problem with a performance ratio of 2ρ, where ρ denotes the best known approximation ratio for the Steiner tree problem. This improves the previously best known approximation ratio for the metric terminal Steiner tree problem of ρ+2.     

A hybrid algorithm for the single-machine total tardiness problem

We propose a hybrid algorithm based on the ant colony optimization (ACO) meta-heuristic, in conjunction with four well-known elimination rules, to tackle the NP$\mathit{NP}$-hard single-machine scheduling problem to minimize the total job tardiness. The hybrid algorithm has the same running time as that of ACO. We conducted extensive computational experiments to test the performance of the hybrid algorithm and ACO. The computational results show that the hybrid algorithm can produce optimal or near-optimal solutions quickly, and its performance compares favourably with that of ACO for handling standard instances of the problem.     

A <Emphasis Type="Italic">Q</Emphasis>-learning-based swarm optimization algorithm for economic dispatch problem

In this paper, we treat optimization problems as a kind of reinforcement learning problems regarding an optimization procedure for searching an optimal solution as a reinforcement learning procedure for finding the best policy to maximize the expected rewards. This viewpoint motivated us to propose a Q-learning-based swarm optimization (QSO) algorithm. The proposed QSO algorithm is a population-based optimization algorithm which integrates the essential properties of Q-learning and particle swarm optimization. The optimization procedure of the QSO algorithm proceeds as each individual imitates the behavior of the global best one in the swarm. The best individual is chosen based on its accumulated performance instead of its momentary performance at each evaluation. Two data sets including a set of benchmark functions and a real-world problem—the economic dispatch (ED) problem for power systems—were used to test the performance of the proposed QSO algorithm. The simulation results on the benchmark functions show that the proposed QSO algorithm is comparable to or even outperforms several existing optimization algorithms. As for the ED problem, the proposed QSO algorithm has found solutions better than all previously found solutions.     

Numerical quadratures for singular and hypersingular integrals

We present a procedure for the design of high-order quadrature rules for the numerical evaluation of singular and hypersingular integrals; such integrals are frequently encountered in solution of integral equations of potential theory in two dimensions. Unlike integrals of both smooth and weakly singular functions, hypersingular integrals are pseudo-differential operators, being limits of certain integrals; as a result, standard quadrature formulae fail for hypersingular integrals. On the other hand, such expressions are often encountered in mathematical physics (see, for example, [1]), and it is desirable to have simple and efficient “quadrature” formulae for them. The algorithm we present constructs high-order “quadratures” for the evaluation of hypersingular integrals. The additional advantage of the scheme is the fact that each of the quadratures it produces can be used simultaneously for the efficient evaluation of hypersingular integrals, Hilbert transforms, and integrals involving both smooth and logarithmically singular functions; this results in significantly simplified implementations. The performance of the procedure is illustrated with several numerical examples.     

An Algorithm for the Exact Numerical Integration of a Special Class of Functions

The classical Gaussian quadrature rules yield very inaccurate results when they are used for the integration of functions of the form f(x)=P(x,\cos(cx+d))\exp(-a^{2}x^{2}+bx) over the infinite interval (-\infty, \infty) , where a\gt 0, b, c, d are real numbers and P is a polynomial. In this paper we propose a new algorithm that computes this type of integrals without error in the machine precision. The algorithm can also be used for the multiple integrals. We give some numerical examples to compare the results obtained by the new algorithm and those obtained by some other methods including the classical Gauss-Hermite integration rules.     

Performance enhancement of extreme learning machine for multi-category sparse data classification problems

This paper presents a performance enhancement scheme for the recently developed extreme learning machine (ELM) for multi-category sparse data classification problems. ELM is a single hidden layer neural network with good generalization capabilities and extremely fast learning capacity. In ELM, the input weights are randomly chosen and the output weights are analytically calculated. The generalization performance of the ELM algorithm for sparse data classification problem depends critically on three free parameters. They are, the number of hidden neurons, the input weights and the bias values which need to be optimally chosen. Selection of these parameters for the best performance of ELM involves a complex optimization problem.In this paper, we present a new, real-coded genetic algorithm approach called ‘RCGA-ELM’ to select the optimal number of hidden neurons, input weights and bias values which results in better performance. Two new genetic operators called ‘network based operator’ and ‘weight based operator’ are proposed to find a compact network with higher generalization performance. We also present an alternate and less computationally intensive approach called ‘sparse-ELM’. Sparse-ELM searches for the best parameters of ELM using K-fold validation. A multi-class human cancer classification problem using micro-array gene expression data (which is sparse), is used for evaluating the performance of the two schemes. Results indicate that the proposed RCGA-ELM and sparse-ELM significantly improve ELM performance for sparse multi-category classification problems.     

A novel soft subspace clustering algorithm with noise detection for high dimensional datasets

When dealing with high dimensional data, clustering faces the curse of dimensionality problem. In such data sets, clusters of objects exist in subspaces rather than in whole feature space. Subspace clustering algorithms have already been introduced to tackle this problem. However, noisy data points present in this type of data can have great impact on the clustering results. Therefore, to overcome these problems simultaneously, the fuzzy soft subspace clustering with noise detection (FSSC-ND) is proposed. The presented algorithm is based on the entropy weighting soft subspace clustering and noise clustering. The FSSC-ND algorithm uses a new objective function and update rules to achieve the mentioned goals and present more interpretable clustering results. Several experiments have been conducted on artificial and UCI benchmark datasets to assess the performance of the proposed algorithm. In addition, a number of cancer gene expression datasets are used to evaluate the performance of the proposed algorithm when dealing with high dimensional data. The results of these experiments demonstrate the superiority of the FSSC-ND algorithm in comparison with the state of the art clustering algorithms developed in earlier research.     

A note on “A new method for ranking discovered rules from data mining by DEA”, and a full ranking approach

In a recent paper by Toloo et al. [Toloo, M., Sohrabi, B., & Nalchigar, S. (2009). A new method for ranking discovered rules from data mining by DEA. Expert Systems with Applications, 36, 8503–8508], they proposed a new integrated data envelopment analysis model to find most efficient association rule in data mining. Then, utilizing this model, an algorithm is developed for ranking association rules by considering multiple criteria. In this paper, we show that their model only selects one efficient association rule by chance and is totally depended on the solution method or software is used for solving the problem. In addition, it is shown that their proposed algorithm can only rank efficient rules randomly and will fail to rank inefficient DMUs. We also refer to some other drawbacks in that paper and propose another approach to set up a full ranking of the association rules. A numerical example illustrates some contents of the paper.     

Association rule mining using binary particle swarm optimization

In this paper, we developed a binary particle swarm optimization (BPSO) based association rule miner. Our BPSO based association rule miner generates the association rules from the transactional database by formulating a combinatorial global optimization problem, without specifying the minimum support and minimum confidence unlike the a priori algorithm. Our algorithm generates the best M rules from the given database, where M is a given number. The quality of the rule is measured by a fitness function defined as the product of support and confidence. The effectiveness of our algorithm is tested on a real life bank dataset from commercial bank in India and three transactional datasets viz. books database, food items dataset and dataset of the general store taken from literature. Based on the results, we infer that our algorithm can be used as an alternative to the a priori algorithm and the FP-growth algorithm.     

On the performance of self-organizing maps for the non-Euclidean Traveling Salesman Problem in the polygonal domain

In this paper, two state-of-the-art algorithms for the Traveling Salesman Problem (TSP) are examined in the multi-goal path planning problem motivated by inspection planning in the polygonal domain W. Both algorithms are based on the self-organizing map (SOM) for which an application in W is not typical. The first is Somhom’s algorithm, and the second is the Co-adaptive net. These algorithms are augmented by a simple approximation of the shortest path among obstacles in W. Moreover, the competitive and cooperative rules are modified by recent adaptation rules for the Euclidean TSP, and by proposed enhancements to improve the algorithms’ performance in the non-Euclidean TSP. Based on the modifications, two new variants of the algorithms are proposed that reduce the required computational time of their predecessors by an order of magnitude, therefore making SOM more competitive with combinatorial heuristics. The results show how SOM approaches can be used in the polygonal domain so they can provide additional features over the classical combinatorial approaches based on the complete visibility graph.     

Faster Algorithms for Stable Allocation Problems

We consider a high-multiplicity generalization of the classical stable matching problem known as the stable allocation problem, introduced by Baïou and Balinski in 2002. By leveraging new structural properties and sophisticated data structures, we show how to solve this problem in O(mlog?n) time on a bipartite instance with n vertices and m edges, improving the best known running time of O(mn). Building on this algorithm, we provide an algorithm for the non-bipartite stable allocation problem running in O(mlog?n) time with high probability. Finally, we give a polynomial-time algorithm for solving the “optimal” variant of the bipartite stable allocation problem, as well as a 2-approximation algorithm for the NP-hard “optimal” variant of the non-bipartite stable allocation problem.     

The Little Towers of Antwerpen problem

The Little Towers of Antwerpen problem is a simple variant of the Towers of Hanoi problem requiring the interchanging of two stacks (black, white) of N rings using the third tower as a spare, subject to the usual rules governing ring movement. An optimal algorithm for the problem is presented and its performance is analyzed.     

A differential-based harmony search algorithm for the optimization of continuous problems

The performance of the Harmony Search (HS) algorithm is highly dependent on the parameter settings and the initialization of the Harmony Memory (HM). To address these issues, this paper presents a new variant of the HS algorithm, which is called the DH/best algorithm, for the optimization of globally continuous problems. The proposed DH/best algorithm introduces a new improvisation method that differs from the conventional HS in two respects. First, the random initialization of the HM is replaced with a new method that effectively initializes the harmonies and reduces randomness. Second, the conventional pitch adjustment method is replaced by a new pitch adjustment method that is inspired by a Differential Evolution (DE) mutation strategy known as DE/best/1. Two sets of experiments are performed to evaluate the proposed algorithm. In the first experiment, the DH/best algorithm is compared with other variants of HS based on 12 optimization functions. In the second experiment, the complete CEC2014 problem set is used to compare the performance of the DH/best algorithm with six well-known optimization algorithms from different families. The experimental results demonstrate the superiority of the proposed algorithm in convergence, precision, and robustness.     

The choice of the best among the shortest routes in transparent optical networks

This work introduces the problem of the best choice among M combinations of the shortest paths for dynamic provisioning of lightpaths in all-optical networks. To solve this problem in an optimized way (shortest path and load balance), a new fixed routing algorithm, named Best among the Shortest Routes (BSR), is proposed. The BSR’s performance is compared in terms of blocking probability and network utilization with Dijkstra’s shortest path algorithm and others algorithms proposed in the literature. The evaluated scenarios include several representative topologies for all-optical networking and different wavelength conversion architectures. For all studied scenarios, BSR achieved superior performance.     

An indirect approach to trigonometric quadrature rules

In this paper we establish the existence of quadrature rules of trigonometric degreed usingd+1 abscissas, and we determine a few of their elementary properties, some of which are new. The approach used here does not involve orthogonal trigonometric polynomials but is based on transforming standard algebraic quadrature rules for a doubly infinite interval.