Modified constrained differential evolution for solving nonlinear global optimization problems

Nonlinear optimization problems introduce the possibility of multiple local optima. The task of global optimization is to find a point where the objective function obtains its most extreme value while satisfying the constraints. Some methods try to make the solution feasible by using penalty function methods, but the performance is not always satisfactory since the selection of the penalty parameters for the problem at hand is not a straightforward issue. Differential evolution has shown to be very efficient when solving global optimization problems with simple bounds. In this paper, we propose a modified constrained differential evolution based on different constraints handling techniques, namely, feasibility and dominance rules, stochastic ranking and global competitive ranking and compare their performances on a benchmark set of problems. A comparison with other solution methods available in literature is also provided. The convergence behavior of the algorithm to handle discrete and integer variables is analyzed using four well-known mixed-integer engineering design problems. It is shown that our method is rather effective when solving nonlinear optimization problems.Fundação para a Ciência e a Tecnologia (FCT

A modified differential evolution based solution technique for economic dispatch problems

Economic dispatch (ED) plays one of the major roles in power generation systems. The objective of economic dispatch problem is to find the optimal combination of power dispatches from different power generating units in a given time period to minimize the total generation cost while satisfying the specified constraints. Due to valve-point loading effects the objective function becomes nondifferentiable and has many local minima in the solution space. Traditional methods may fail to reach the global solution of ED problems. Most of the existing stochastic methods try to make the solution feasible or penalize an infeasible solution with penalty function method. However, to find the appropriate penalty parameter is not an easy task. Differential evolution is a population-based heuristic approach that has been shown to be very efficient to solve global optimization problems with simple bounds. In this paper, we propose a modified differential evolution based solution technique along with a tournament selection that makes pair-wise comparison among feasible and infeasible solutions based on the degree of constraint violation for economic dispatch problems. We reformulate the nonsmooth objective function to a smooth one and add nonlinear inequality constraints to original ED problems. We consider five ED problems and compare the obtained results with existing standard deterministic NLP solvers as well as with other stochastic techniques available in literature.Fundação para a Ciência e a Tecnologia (FCT

Modified differential evolution based on global competitive ranking for engineering design optimization problems

Engineering design optimization problems are formulated as large-scale mathematical programming problems with nonlinear objective function and constraints. Global optimization finds a solution while satisfying the constraints. Differential evolution is a population-based heuristic approach that is shown to be very efficient to solve global optimization problems with simple bounds. In this paper, we propose a modified differential evolution introducing self-adaptive control parameters, modified mutation, inversion operation and modified selection for obtaining global optimization. To handle constraints effectively, in modified selection we incorporate global competitive ranking which strikes the right balance between the objective function and the constraint violation. Sixteen well-known engineering design optimization problems are considered and the results compared with other solution methods. It is shown that our method is competitive when solving these problems.Fundação para a Ciência e a Tecnologia (FCT

Global competitive ranking for constraints handling with modified differential evolution

Constrained nonlinear programming problems involving a nonlinear objective function with inequality and/or equality constraints introduce the possibility of multiple local optima. The task of global optimization is to find a solution where the objective function obtains its most extreme value while satisfying the constraints. Depending on the nature of the involved functions many solution methods have been proposed. Most of the existing population-based stochastic methods try to make the solution feasible by using a penalty function method. However, to find the appropriate penalty parameter is not an easy task. Population-based differential evolution is shown to be very efficient to solve global optimization problems with simple bounds. To handle the constraints effectively, in this paper, we propose a modified constrained differential evolution that uses self-adaptive control parameters, a mixed modified mutation, the inversion operation, a modified selection and the elitism in order to progress efficiently towards a global solution. In the modified selection, we propose a fitness function based on the global competitive ranking technique for handling the constraints. We test 13 benchmark problems. We also compare the results with the results found in literature. It is shown that our method is rather effective when solving constrained problemsFundação para a Ciência e a Tecnologia (FCT

Endogenous n-3 fatty acids protect ovariectomy induced bone loss by attenuating osteoclastogenesis

Beneficial effects of n-3 fatty acids (FA) on bone mineral density (BMD) have been reported in mice, rats and human beings, but the precise mechanisms involved have not been described. This study used the Fat-1 mouse, a transgenic model that synthesizes n-3 FA from n-6 FA to directly determine if outcome of bone health were correlated with n-3 FA. Ovariectomized (Ovx) and sham operated wild-type (WT) and Fat-1 mice were fed an AIN-93M diet containing 10% corn oil for 24 weeks. BMD was analysed by dual energy x-ray absorptiometry. Fat-1 Ovx mice exhibited significantly lower level of osteotropic factors like receptor activator of NF-κB ligand and tartrate-resistant acid phosphatase (TRAP)5b in serum and higher BMD in distal femoral metaphysis, proximal tibial metaphysis, femoral diaphysis and lumbar vertebra as compared to WT Ovx mice. LPS-stimulated bone marrow (BM) cells from Fat-1 Ovx mice produced significantly lower level of pro-inflammatory cytokines like tumour necrosis factor-α, interleukin (IL)-1-β, IL-6 and higher level of anti-inflammatory cytokines like IL-10, IFN-γ and higher level of nitric oxide as compared to BM cells from WT Ovx mice. LPS-stimulated COX-II activity as well as NF-κB activation in BM cells from Fat-1 Ovx mice was significantly less as compared to BM cells from WT Ovx mice. Furthermore, Fat-1 BM cells generated significantly less number of TRAP osteoclast-like cells as compared to WT BM cells. In conclusion, we offer further insight into the mechanisms involved in preventing the BMD loss in Ovx mice by n-3 FA using a Fat-1 transgenic mouse model

Function of circular RNAs in fish and their potential application as biomarkers

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Nonlinear continuous global optimization by modified differential evolution

The task of global optimization is to find a point where the objective function obtains its most extreme value. Differential evolution (DE) is a population-based heuristic approach that creates new candidate solutions by combining several points of the same population. The algorithm has three parameters: amplification factor of the differential variation, crossover control parameter and population size. It is reported that DE is sensitive to the choice of these parameters. To improve the quality of the solution, in this paper, we propose a modified differential evolution introducing self-adaptive parameters, modified mutation and the inversion operator. We test our method with a set of nonlinear continuous optimization problems with simple bounds.Fundação para a Ciência e a Tecnologia (FCT

Solving 0–1 quadratic knapsack problems with a population-based artificial fish swarm algorithm

Fundação para a Ciência e a Tecnologia (FCT

A simplified binary artificial fish swarm algorithm for 0–1 quadratic knapsack problems

Available online 8 October 2013.This paper proposes a simplified binary version of the artificial fish swarm algorithm (S-bAFSA) for solving 0–1 knapsack problems. This is a combinatorial optimization problem, which arises in many fields of optimization. In S-bAFSA, trial points are created by using crossover and mutation. In order to make the points feasible, a random heuristic drop item procedure is used. The heuristic add item is also implemented to improve the quality of the solutions, and a cyclic reinitialization of the population is carried out to avoid convergence to non-optimal solutions. To enhance the accuracy of the solution, a local search is applied on a predefined number of points. The method is tested on a set of benchmark 0–1 knapsack problems.Fundação para a Ciência e a Tecnologia (FCT

A simplified binary artificial fish swarm algorithm for uncapacitated facility location problems

Uncapacitated facility location problem (UFLP) is a combinatorial optimization problem, which has many applications. The artificial fish swarm algorithm has recently emerged in continuous optimization problem. In this paper, we present a simplified binary version of the artificial fish swarm algorithm (S-bAFSA) for solving the UFLP. In S-bAFSA, trial points are created by using crossover and mutation. In order to improve the quality of the solutions, a cyclic reinitialization of the population is carried out. To enhance the accuracy of the solution, a local search is applied on a predefined number of points. The presented algorithm is tested on a set of benchmark uncapacitated facility location problems.Fundação para a Ciência e a Tecnologia (FCT