Renato Tinós

Renato Tinós, Liang Zhao, Francisco Chicano et al.

The NK hybrid genetic algorithm for clustering is proposed in this paper. In order to evaluate the solutions, the hybrid algorithm uses the NK clustering validation criterion 2 (NKCV2). NKCV2 uses information about the disposition of $N$ small groups of objects. Each group is composed of $K+1$ objects of the dataset. Experimental results show that density-based regions can be identified by using NKCV2 with fixed small $K$. In NKCV2, the relationship between decision variables is known, which in turn allows us to apply gray box optimization. Mutation operators, a partition crossover, and a local search strategy are proposed, all using information about the relationship between decision variables. In partition crossover, the evaluation function is decomposed into $q$ independent components; partition crossover then deterministically returns the best among $2^q$ possible offspring with computational complexity $O(N)$. The NK hybrid genetic algorithm allows the detection of clusters with arbitrary shapes and the automatic estimation of the number of clusters. In the experiments, the NK hybrid genetic algorithm produced very good results when compared to another genetic algorithm approach and to state-of-art clustering algorithms.

M. W. Przewozniczek, F. Chicano, R. Tinós et al.

Gray-box optimization employs Walsh decomposition to obtain non-linear variable dependencies and utilize them to propose masks of variables that have a joint non-linear influence on fitness value. These masks significantly improve the effectiveness of variation operators. In some problems, all variables are non-linearly dependent, making the aforementioned masks useless. We analyze the features of the real-world instances of such problems and show that many of their dependencies may have noise-like origins. Such noise-caused dependencies are irrelevant to the optimization process and can be ignored. To identify them, we propose extending the use of Walsh decomposition by measuring variable dependency strength that allows the construction of the weighted dynamic Variable Interaction Graph (wdVIG). wdVIGs adjust the dependency strength to mixed individuals. They allow the filtering of irrelevant dependencies and re-enable using dependency-based masks by variation operators. We verify the wdVIG potential on a large benchmark suite. For problems with noise, the wdVIG masks can improve the optimizer's effectiveness. If all dependencies are relevant for the optimization, i.e., the problem is not noised, the influence of wdVIG masks is similar to that of state-of-the-art structures of this kind.

J. Piatek, M. W. Przewozniczek, F. Chicano et al.

Gray-box optimization proposes effective and efficient optimizers of general use. To this end, it leverages information about variable dependencies and the subfunction-based problem representation. These approaches were already shown effective by enabling \textit{tunnelling} between local optima even if these moves require the modification of many dependent variables. Tunnelling is useful in solving the maximum satisfiability problem (MaxSat), which can be reformulated to Max3Sat. Since many real-world problems can be brought to solving the MaxSat/Max3Sat instances, it is important to solve them effectively and efficiently. Therefore, we focus on Max3Sat instances for which tunnelling fails to introduce improving moves between locally optimal high-quality solutions and the region of globally optimal solutions. We analyze the features of such instances on the ground of phase transitions. Based on these observations, we propose manipulating clause-satisfiability characteristics that allow connecting high-quality solutions distant in the solution space. We utilize multi-satisfiability characteristics in the optimizer built from typical gray-box mechanisms. The experimental study shows that the proposed optimizer can solve those Max3Sat instances that are out of the grasp of state-of-the-art gray-box optimizers. At the same time, it remains effective for instances that have already been successfully solved by gray-box.

Filipe Alves Neto Verri, Renato Tinós, Liang Zhao

Data and knowledge representation are fundamental concepts in machine learning. The quality of the representation impacts the performance of the learning model directly. Feature learning transforms or enhances raw data to structures that are effectively exploited by those models. In recent years, several works have been using complex networks for data representation and analysis. However, no feature learning method has been proposed for such category of techniques. Here, we present an unsupervised feature learning mechanism that works on datasets with binary features. First, the dataset is mapped into a feature--sample network. Then, a multi-objective optimization process selects a set of new vertices to produce an enhanced version of the network. The new features depend on a nonlinear function of a combination of preexisting features. Effectively, the process projects the input data into a higher-dimensional space. To solve the optimization problem, we design two metaheuristics based on the lexicographic genetic algorithm and the improved strength Pareto evolutionary algorithm (SPEA2). We show that the enhanced network contains more information and can be exploited to improve the performance of machine learning methods. The advantages and disadvantages of each optimization strategy are discussed.

Francisco Chicano, Darrell Whitley, Renato Tinos

Local search algorithms and iterated local search algorithms are a basic technique. Local search can be a stand along search methods, but it can also be hybridized with evolutionary algorithms. Recently, it has been shown that it is possible to identify improving moves in Hamming neighborhoods for k-bounded pseudo-Boolean optimization problems in constant time. This means that local search does not need to enumerate neighborhoods to find improving moves. It also means that evolutionary algorithms do not need to use random mutation as a operator, except perhaps as a way to escape local optima. In this paper, we show how improving moves can be identified in constant time for multiobjective problems that are expressed as k-bounded pseudo-Boolean functions. In particular, multiobjective forms of NK Landscapes and Mk Landscapes are considered.

Darrell Whitley, Renato Tinós, Francisco Chicano

This paper introduces the NK Echo State Network. The problem of learning in the NK Echo State Network is reduced to the problem of optimizing a special form of a Spin Glass Problem known as an NK Landscape. No weight adjustment is used; all learning is accomplished by spinning up (turning on) or spinning down (turning off) neurons in order to find a combination of neurons that work together to achieve the desired computation. For special types of NK Landscapes, an exact global solution can be obtained in polynomial time using dynamic programming. The NK Echo State Network is applied to a reinforcement learning problem requiring a recurrent network: balancing two poles on a cart given no velocity information. Empirical results shows that the NK Echo State Network learns very rapidly and yields very good generalization.