Mauro Campos

Gaussian basis set of double zeta quality for atoms Rb through Xe: application in non-relativistic and relativistic calculations of atomic and molecular properties

The all-electron contracted Gaussian basis set of double zeta valence quality plus polarization functions (DZP) for the atoms from Rb to Xe is presented. The Douglas–Kroll–Hess (DKH) basis set for fourth-row elements is also reported. The original DZP basis set has been recontracted, i.e. the values of the contraction coefficients were re-optimized using the relativistic DKH Hamiltonian. This extends earlier works on segmented contracted DZ basis set for atoms H-Kr. These sets along with ab initio methods were used to calculate ionization energies of some atoms and spectroscopic constants of a sample of molecules and, then, comparison with results obtained with other basis sets was made. It was shown that experimental and benchmark bond lengths and harmonic vibrational frequencies can be reproduced satisfactorily with DZP-DKZ.

Bare Bones Particle Swarm Optimization With Scale Matrix Adaptation

Bare bones particle swarm optimization (BBPSO) is a swarm algorithm that has shown potential for solving single-objective unconstrained optimization problems over continuous search spaces. However, it suffers of the premature convergence problem that means it may get trapped into a local optimum when solving multimodal problems. In order to address this drawback and improve the performance of the BBPSO, we propose a variant of this algorithm, named by us as BBPSO with scale matrix adaptation (SMA), SMA-BBPSO for short reference. In the SMA-BBPSO, the position of a particle is selected from a multivariate t -distribution with a rule for adaptation of its scale matrix. We use the multivariate t -distribution in its hierarchical form, as a scale mixtures of normal distributions. The t -distribution has heavier tails than those of the normal distribution, which increases the ability of the particles to escape from a local optimum. In addition, our approach includes the normal distribution as a particular case. As a consequence, the t -distribution can be applied during the optimization process by maintaining the proper balance between exploration and exploitation. We also propose a simple update rule to adapt the scale matrix associated with a particle. Our strategy consists of adapting the scale matrix of a particle such that the best position found by any particle in its neighborhood is sampled with maximum likelihood in the next iteration. A theoretical analysis was developed to explain how the SMA-BBPSO works, and an empirical study was carried out to evaluate the performance of the proposed algorithm. The experimental results show the suitability of the proposed approach in terms of effectiveness to find good solutions for all benchmark problems investigated. Nonparametric statistical tests indicate that SMA-BBPSO shows a statistically significant improvement compared with other swarm algorithms.

Swarm algorithms with chaotic jumps applied to noisy optimization problems

In this paper, we investigate the use of some well-known versions of particle swarm optimization (PSO): the canonical PSO with gbest model and lbest model with ring topology, the Bare bones PSO (BBPSO) and the fully informed particle swarm (FIPS) on noisy optimization problems. As far as we know, some of these versions like BBPSO and FIPS had not been previously applied to noisy functions yet. A hybrid approach which consists of the swarm algorithms combined with a jump strategy has been developed for static environments. Here, we focus on investigating the introduction of the jump strategy to the swarm algorithms now applied to noisy optimization problems. The hybrid approach is compared experimentally on different noisy benchmark functions. Simulation results indicate that the addition of the jump strategy to the swarm algorithms is beneficial in terms of robustness.

Bare Bones Particle Swarm Applied to Parameter Estimation of Mixed Weibull Distribution

An approach for estimating the parameters of mixed Weibull distributions is presented. The problem is formulated as maximization of the likelihood function of the corresponding mixture model. For the solution of the optimization problem, Bare Bones Particle Swarm Optimization (BBPSO) algorithm is applied. Illustrative example for a case study using censored data are provided in order to show the suitability of the BBPSO algorithm for this kind of problem very common in lifetime modelling.

Ranking and comparing evolutionary algorithms with Hellinger-TOPSIS

Ranking and comparison of algorithms performance in evolutionary computation is a challenging issue.An alternative novel application of Hellinger TOPSIS has been proposed to ranking and comparison of algorithms performance.Promising results show the feasibility of the approach in terms of effectiveness and easy implementation. When multiple algorithms are applied to multiple benchmarks as it is common in evolutionary computation, a typical issue rises, how can we rank the algorithms? It is a common practice in evolutionary computation to execute the algorithms several times and then the mean value and the standard deviation are calculated. In order to compare the algorithms performance it is very common to use statistical hypothesis tests. In this paper, we propose a novel alternative method based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to support the performance comparisons. In this case, the alternatives are the algorithms and the criteria are the benchmarks. Since the standard TOPSIS is not able to handle the stochastic nature of evolutionary algorithms, we apply the Hellinger-TOPSIS, which uses the Hellinger distance, for algorithm comparisons. Case studies are used to illustrate the method for evolutionary algorithms but the approach is general. The simulation results show the feasibility of the Hellinger-TOPSIS to find out the ranking of algorithms under evaluation.

Swarm algorithms with chaotic jumps for optimization of multimodal functions

In this article, the use of some well-known versions of particle swarm optimization (PSO) namely the canonical PSO, the bare bones PSO (BBPSO) and the fully informed particle swarm (FIPS) is investigated on multimodal optimization problems. A hybrid approach which consists of swarm algorithms combined with a jump strategy in order to escape from local optima is developed and tested. The jump strategy is based on the chaotic logistic map. The hybrid algorithm was tested for all three versions of PSO and simulation results show that the addition of the jump strategy improves the performance of swarm algorithms for most of the investigated optimization problems. Comparison with the off-the-shelf PSO with local topology (l best model) has also been performed and indicates the superior performance of the standard PSO with chaotic jump over the standard both using local topology (l best model).

Hierarchical bare bones particle swarm for solving constrained optimization problems

Bare bones particle swarm optimization (BBPSO) is a well-known swarm algorithm which has shown potential for solving single-objective unconstrained optimization problems. In this paper, firstly, we propose a generalization of the BBPSO, named by us as hierarchical BBPSO, HBBPSO for short. Next a hybrid approach is introduced combining the constraint-handling method based on sum of ranks with the HBBPSO algorithm for solving single-objective constrained optimization problems. In the HBBPSO, the position of a particle is selected from a multivariate t-distribution. The multivariate t-distribution is used in its hierarchical form as a member of the flexible class of scale mixtures of normal distributions. The t-distribution has heavier tails than those of the normal distribution, which increases the ability of the particles to escape from a local optimum. In addition, the t-distribution includes the normal case when the number of degrees of freedom of the t-distribution is sufficiently large. As a result, the t-distribution can be applied during the optimization process, while maintaining the proper equilibrium between exploration and exploitation. An empirical study has been carried out to evaluate the performance of the proposed approach. The experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness to find good solutions for all benchmark problems tested.

Particle Swarm Optimization for Inference Procedures in the Generalized Gamma Family Based on Censored Data

The generalized gamma distribution offers a highly flexible family of models for lifetime data and includes a considerable number of distributions as special cases. This work deals with the use of the particle swarm optimization (PSO) algorithm in the maximum likelihood estimation of distributions of the generalized gamma family (GG-family) based on data with censored observations.We also discuss a procedure for testing whether a distribution that belong to GG-family is appropriate for lifetime data using the generalized likelihood ratio test principle. Finally, we present two illustrative applications using real data sets. For each data set, we use the PSO algorithm to fit several distributions of the GG-family simultaneously. Then, we test the appropriateness of each fitted model and select the most appropriate one using the Bayesian information criterion or the Akaike information criterion.

Bare bones particle swarm with scale mixtures of Gaussians for dynamic constrained optimization

Bare bones particle swarm optimization (BBPSO) is a well-known swarm algorithm which has shown potential for solving single-objective constrained optimization problems in static environments. In this paper, a generalized BBPSO for dynamic single-objective constrained optimization problems is proposed. An empirical study was carried out to evaluate the performance of the proposed approach. Experimental results show the suitability of the proposed algorithm in terms of effectiveness to find good solutions for all benchmark problems investigated. For comparison purposes, experimental results found by other algorithms are also presented.