Renato A. Krohling

Fuzzy TOPSIS for group decision making: A case study for accidents with oil spill in the sea

The selection of the best combat responses to oil spill in the sea when several alternatives have to be evaluated with different weights for each criterion consist of a multicriteria decision making (MCDM) problem. In this work, firstly the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is described. Secondly, its expansion known as fuzzy TOPSIS to handle uncertain data is presented. Next, based on fuzzy TOPSIS we propose a fuzzy TOPSIS for group decision making, which is applied to evaluate the ratings of response alternatives to a simulated oil spill. The case study was carried out for one of the largest Brazilian oil reservoirs. The results show the feasibility of the fuzzy TOPSIS framework to find out the best combat responses in case of accidents with oil spill in the sea.

Combining prospect theory and fuzzy numbers to multi-criteria decision making

Many multi-criteria decision making (MCDM) methods have been proposed to handle uncertain decision making problems. Most of them are based on fuzzy numbers and they are not able to cope with risk in decision making. In recent years, some MCDM methods based on prospect theory to handle risk MCDM problems have been developed. In this paper, we propose a hybrid approach combining prospect theory and fuzzy numbers to handle risk and uncertainty in MCDM problems. So, it is possible to tackle more challenging MCDM problems. A case study involving oil spill in the sea illustrates the application of the novel method.

Gaussian particle swarm with jumps

Gaussian particle swarm optimization (GPSO) algorithm has shown promising results for solving multimodal optimization problems in low dimensional search space. But similar to evolutionary algorithms (EAs), GPSO may also get stuck in local minima when optimizing functions with many local minima like the Rastrigin or Riewank functions in high dimensional search space. In this paper, an approach which consists of a GPSO with jumps to escape from local minima is presented. The jump strategy is implemented as a mutation operator based on the Gaussian and Cauchy probability distribution. The new algorithm was tested on a suite of well-known benchmark functions with many local optima and the results were compared with those obtained by the standard PSO algorithm, and PSO with constriction factor. Simulation results show that the GPSO with Gaussian and Cauchy jump outperforms the standard one and presents a very competitive performance compared to PSO with constriction factor and also self-adaptive evolutionary programming.

Bare Bones Particle Swarm Optimization with Gaussian or Cauchy jumps

Bare Bones Particle Swarm Optimization (BBPSO) is a powerful algorithm, which has shown potential to solving multimodal optimization problems. Unfortunately, BBPSO may also get stuck into local optima when optimizing functions with many local optima in high dimensional search space. In previous attempts an approach was developed which consists of a jump strategy combined with PSO in order to escape from local optima and promising results have been obtained. In this paper, we combine BBPSO with a jump strategy when no fitness improvement is observed. The jump strategy is implemented based on the Gaussian or the Cauchy probability distribution. The algorithm was tested on a suite of well-known benchmark multimodal functions and the results were compared with those obtained by the standard BBPSO algorithm and with BBPSO with re-initialization. Simulation results show that the BBPSO with the jump strategy performs well in all functions investigated. We also notice that the improved performance is due to a successful number of Gaussian or Cauchy jumps.

Differential evolution algorithm on the GPU with C-CUDA

Several areas of knowledge are being benefited with the reduction of the computing time by using the technology of Graphics Processing Units (GPU) and the Compute Unified Device Architecture (CUDA) platform. In case of Evolutionary algorithms, which are inherently parallel, this technology may be advantageous for running experiments demanding high computing time. In this paper, we provide an implementation of the Differential Evolution (DE) algorithm in C-CUDA. The algorithm was tested on a suite of well-known benchmark optimization problems and the computing time has been compared with the same algorithm implemented in C. Results demonstrate that the computing time can significantly be reduced using C-CUDA. As far as we know, this is the first implementation of DE algorithm in C-CUDA.

Co-evolutionary particle swarm optimization for min-max problems using Gaussian distribution

Previous work presented an approach based on coevolutionary particle swarm optimization (Co-PSO) to solve constrained optimization problems formulated as min-max problems. Preliminary results demonstrated that Co-PSO constitutes a promising approach to solve constrained optimization problems. However the difficulty to obtain fine tuning of the solution using a uniform distribution became evident. In this paper, a modified PSO using a Gaussian distribution is applied in the context of Co-PSO. The modified Co-PSO is tested on some benchmark optimization problems and the results show a superior performance compared to the standard Co-PSO.

A study of TODIM in a intuitionistic fuzzy and random environment

Nowadays the process of decision making may be very complex. Many methods to support Multi-Criteria Decision Making (MCDM) have been proposed. Recently, the TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) method, which is based on the prospect theory, has received more attention. In this paper we generalize the Fuzzy-TODIM method to deal with intuitionistic fuzzy information and to be capable to consider underlying random vectors that affects the performance of the alternatives. The method makes use of some Bayesian ideas to provide an overall ranking of the alternatives. This work considers information represented by intuitionistic fuzzy number and intuitionistic fuzzy sets (IFS). Also, a new formula of distance between IFS and a new score function to compare IFS are introduced. Examples are discussed and compared with other works, showing the feasibility of the proposed method.

Swarm's flight: Accelerating the particles using C-CUDA

With the development of Graphics Processing Units (GPU) and the Compute Unified Device Architecture (CUDA) platform, several areas of knowledge are being benefited with the reduction of the computing time. Our goal is to show how optimization algorithms inspired by Swarm Intelligence can take profit from this technology. In this paper, we provide an implementation of the Particle Swarm Optimization (PSO) algorithm in C-CUDA. The algorithm was tested on a suite of well-known benchmark optimization problems and the computing time has been compared with the same algorithm implemented in C and Matlab. Results demonstrate that the computing time can significantly be reduced using C-CUDA. As far as we know, this is the first implementation of PSO in C-CUDA.

Short Communication: IF-TODIM: An intuitionistic fuzzy TODIM to multi-criteria decision making

The recently developed fuzzy TODIM (an acronym in Portuguese for iterative multi-criteria decision making) method using fuzzy numbers has been applied to uncertain MCDM problems with promising results. In this paper, a more general approach to the fuzzy TODIM, which takes into account the membership and the non-membership of the fuzzy information is considered. So, the fuzzy TODIM method has been extended to handle intuitionistic fuzzy information. This way, it is possible to tackle more challenging MCDM problems. Two case studies are used to illustrate and show the suitability of the developed method.

The Hellinger distance in Multicriteria Decision Making: An illustration to the TOPSIS and TODIM methods

Due to the difficulty in some situations of expressing the ratings of alternatives as exact real numbers, many well-known methods to support Multicriteria Decision Making (MCDM) have been extended to compute with many types of information. This paper focuses on the information represented as probability distribution. Many of the methods that deal with probability distribution use the concept of stochastic dominance, which imposes very strong restrictions to differentiate two probability distributions, or uses the probability distributions to obtain a quantity that will be used to rank the alternatives. This paper brings the Hellinger distance concept to the MCDM context to assist the models to deal with probability distributions in a direct way without any transformation. Transformations in the data or summary quantities may miss represent the original information. For direct comparisons among probability distributions we use the stochastic dominance degree (SDD). We illustrate how simple it can be to adapt the existing methods to deal with probability distributions through the Hellinger distance and SDD by adapting the TOPSIS and TODIM (an acronym in Portuguese of Interactive and Multicriteria Decision Making) methods.