Application Of Different Operators Research Articles

New Probabilistic, Dynamic Multi-Method Ensembles for Optimization Based on the CRO-SL

In this paper, new probabilistic and dynamic (adaptive) strategies for creating multi-method ensembles based on the coral reef optimization with substrate layers (CRO-SL) algorithm are proposed. CRO-SL is an evolutionary-based ensemble approach that is able to combine different search procedures for a single population. In this work, two different probabilistic strategies to improve the algorithm are analyzed. First, the probabilistic CRO-SL (PCRO-SL) is presented, which substitutes the substrates in the CRO-SL population with tags associated with each individual. Each tag represents a different operator which will modify the individual in the reproduction phase. In each generation of the algorithm, the tags are randomly assigned to the individuals with similar probabilities, obtaining this way an ensemble that sees more intense changes with the application of different operators to a given individual than CRO-SL. Second, the dynamic probabilistic CRO-SL (DPCRO-SL) is presented, in which the probability of tag assignment is modified during the evolution of the algorithm, depending on the quality of the solutions generated in each substrate. Thus, the best substrates in the search process will be assigned higher probabilities than those which showed worse performance during the search. The performances of the proposed probabilistic and dynamic ensembles were tested for different optimization problems, including benchmark functions and a real application of wind-turbine-layout optimization, comparing the results obtained with those of existing algorithms in the literature.

Solving multi-objective optimization problem using cuckoo search algorithm based on decomposition

In recent years, cuckoo search (CS) algorithm has been successfully applied in single-objective optimization problems. In addition, decomposition-based multi-objective evolutionary algorithms (MOEA/D) have high performance for multi-objective optimization problems (MOPs). Inspired by this, a new decomposition-based multi-objective CS algorithm is proposed in this paper. Two reproduction operators with different characteristics derived from the CS algorithm are constructed and they compose an operator pool. Then, a bandit-based adaptive operator selection method is used to determine the application of different operators. An angle-based selection strategy that achieves a better balance between convergence and diversity is adopted to preserve diversity. Compared with other improved strategies designed for MOEA/D on two suits of test instances, the proposed algorithm was demonstrated to be effective and competitive for MOPs.

Proximate fixed point property and operations

Klee introduced the proximate fixed point property for compacta which is stronger than fixed point property. We consider relations between proximate fixed point property of spaces being result of application of different operations to continua. As an application we show this property for products, cones, suspensions and joins of span 0 continua.

Bayesian Scheme for Interactive Colourization, Recolourization and Image/Video Editing

We propose a general image and video editing method based on a Bayesian segmentation framework. In the first stage, classes are established from scribbles made by a user on the image. These scribbles can be considered as a multi-map (multi-label map) that defines the boundary conditions of a probability measure field to be computed for each pixel. In the second stage, the global minima of a positive definite quadratic cost function with linear constraints, is calculated to find the probability measure field. The components of such a probability measure field express the degree of each pixel belonging to spatially smooth classes. Finally, the computed probabilities (memberships) are used for defining the weights of a linear combination of user provided colours or effects associated to each class. The proposed method allows the application of different operators, selected interactively by the user, over part or the whole image without needing to recompute the memberships. We present applications to colourization, recolourization, editing and photomontage tasks.

SOME ASPECTS OF FUZZY DECISION‐MAKING

The paper deals with some problems of decision‐making by the use of fuzzy set theory. The application of different operators from a wide class of intersection connectives makes it possible to modelize the process of decision‐making in a very flexible manner. The method of calculation of final non‐fuzzy decision from fuzzy set of decision D is discussed in detail and the problem of the choice of a threshold level presented as appropriate to the intersection operator applied before. The notion of sensitivity of any of intersection operators discussed is introduced and considered in detail.