Hybrid Evolutionary Algorithms: Methodologies, Architectures, and Reviews

The Collaborative Local Search Based on Dynamic-Constrained Decomposition With Grids for Combinatorial Multiobjective Optimization

The decomposition-based algorithms [e.g., multiobjective evolutionary algorithm based on decomposition (MOEA/D)] transform a multiobjective optimization problem (MOP) into a number of single-objective optimization subproblems and solve them in a collaborative manner. It is a natural framework for using single-objective local search (LS) to solve combinatorial MOPs. However, commonly used decomposition methods, such as weighted sum (WS), Tchebycheff (TCH), and penalty-based boundary intersection (PBI) may not be good at maintaining the population diversity while providing diverse initial solutions for different LS procedures in a collaborative way. Based on our previous work on the constrained decomposition with grids (CDG), this article proposes a dynamic CDG (DCDG) framework used to design a multiobjective memetic algorithm (DCDG-MOMA). DCDG uses grids for maintaining diversity, supporting the collaborative LS. In addition, DCDG dynamically increases the number of grids for obtaining more nondominated solutions as well as the better collaborative search among them. DCDG-MOMA has been compared with several classical and state-of-the-art algorithms on multiobjective traveling salesman problem (MOTSP), multiobjective quadratic assignment problem (MOQAP), and multiobjective capacitated arc routing problem (MOCARP).

A review and experimental study on the application of classifiers and evolutionary algorithms in EEG-based brain-machine interface systems

OBJECTIVE

Considering the importance and the near-future development of noninvasive brain-machine interface (BMI) systems, this paper presents a comprehensive theoretical-experimental survey on the classification and evolutionary methods for BMI-based systems in which EEG signals are used.

APPROACH

The paper is divided into two main parts. In the first part, a wide range of different types of the base and combinatorial classifiers including boosting and bagging classifiers and evolutionary algorithms are reviewed and investigated. In the second part, these classifiers and evolutionary algorithms are assessed and compared based on two types of relatively widely used BMI systems, sensory motor rhythm-BMI and event-related potentials-BMI. Moreover, in the second part, some of the improved evolutionary algorithms as well as bi-objective algorithms are experimentally assessed and compared.

MAIN RESULTS

In this study two databases are used, and cross-validation accuracy (CVA) and stability to data volume (SDV) are considered as the evaluation criteria for the classifiers. According to the experimental results on both databases, regarding the base classifiers, linear discriminant analysis and support vector machines with respect to CVA evaluation metric, and naive Bayes with respect to SDV demonstrated the best performances. Among the combinatorial classifiers, four classifiers, Bagg-DT (bagging decision tree), LogitBoost, and GentleBoost with respect to CVA, and Bagging-LR (bagging logistic regression) and AdaBoost (adaptive boosting) with respect to SDV had the best performances. Finally, regarding the evolutionary algorithms, single-objective invasive weed optimization (IWO) and bi-objective nondominated sorting IWO algorithms demonstrated the best performances.

SIGNIFICANCE

We present a general survey on the base and the combinatorial classification methods for EEG signals (sensory motor rhythm and event-related potentials) as well as their optimization methods through the evolutionary algorithms. In addition, experimental and statistical significance tests are carried out to study the applicability and effectiveness of the reviewed methods.

Evolutionary algorithms with segment-based search for multiobjective optimization problems

This paper proposes a variation operator, called segment-based search (SBS), to improve the performance of evolutionary algorithms on continuous multiobjective optimization problems. SBS divides the search space into many small segments according to the evolutionary information feedback from the set of current optimal solutions. Two operations, micro-jumping and macro-jumping, are implemented upon these segments in order to guide an efficient information exchange among "good" individuals. Moreover, the running of SBS is adaptive according to the current evolutionary status. SBS is activated only when the population evolves slowly, depending on general genetic operators (e.g., mutation and crossover). A comprehensive set of 36 test problems is employed for experimental verification. The influence of two algorithm settings (i.e., the dimensionality and boundary relaxation strategy) and two probability parameters in SBS (i.e., the SBS rate and micro-jumping proportion) are investigated in detail. Moreover, an empirical comparative study with three representative variation operators is carried out. Experimental results show that the incorporation of SBS into the optimization process can improve the performance of evolutionary algorithms for multiobjective optimization problems.

Nature inspired computational technique for the numerical solution of nonlinear singular boundary value problems arising in physiology

We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error of the given nonlinear ordinary differential equation (ODE) and its boundary conditions is formulated. The optimization of the unknown adjustable parameters contained in the fitness function is performed by the hybrid heuristic computation algorithm based on genetic algorithm (GA), interior point algorithm (IPA), and active set algorithm (ASA). The efficiency and the viability of the proposed method are confirmed by solving three examples from physiology. The obtained approximate solutions are found in excellent agreement with the exact solutions as well as some conventional numerical solutions.