Population-based Stochastic Method Research Articles

A study of equivalent electrical circuit fitting to electrochemical impedance using a stochastic method

Modeling electrochemical impedance spectroscopy is usually done using equivalent electrical circuits. These circuits have parameters that need to be estimated properly in order to make possible the simulation of impedance data. Despite the fitting procedure is an optimization problem solved recurrently in the literature, rarely statistical significance of the estimated parameters is evaluated. In this work, the optimization process for the equivalent electrical circuit fitting to the impedance data is detailed. First, a mathematical development regarding the minimization of residual least squares is presented in order to obtain a statistically valid objective function of the complex nonlinear regression problem. Then, the optimization method used in this work is presented, the Differential Evolution, a global search stochastic method. Furthermore, it is shown how a population-based stochastic method like this can be used directly to obtain confidence regions to the estimated parameters. A sensitivity analysis was also conducted. Finally, the equivalent circuit fitting is done to model synthetic experimental data, in order to demonstrate the adopted procedure.

Firefly Algorithm for Finding Optimal Shapes of Electromagnetic Devices

Many real-world optimization problems have to be treated as multi-objective optimization problems. An approach, well established in recent years, is to find Pareto optimal configurations of the trial variables by detecting nondominated solutions with the help of a suitable vector optimization method. Alternatively, relying on scalar optimization methods (both stochastic or deterministic), a suitable objective function taking all objectives into account simultaneously has to be defined. Depending on the number of trial variables, a scalar objective function of that type will exhibit a considerable number of feasible local solutions besides the global one. Therefore, a useful scalar optimization strategy should be able to end up (with a high probability) in the best of all possible solutions in the given search space and additionally detect as many local solutions as possible. Some population-based stochastic methods are implicitly suited for that task; others can be enhanced to fulfill these requirements. Higher order evolution strategies have successfully been tuned for that kind of problem by introducing cluster sensitive recombination [niching higher order evolution strategy (NES)]. The firefly algorithm (FFA) mimics the behavior of fireflies, which use a kind of flashing light to communicate with other members of their species. Since the intensity of the light of a single firefly diminishes with increasing distance, the FFA is implicitly able to detect local solutions on its way to the best solution for a given scalar objective function. The FFA will be applied to the well-known Rastrigin test function and to a shielding/shunting electromagnetic problem with two and three objectives, respectively, and its results will be compared with the ones obtained with an NES.

Algorithms and tools for protein–protein interaction networks clustering, with a special focus on population-based stochastic methods

Protein-protein interaction (PPI) networks are powerful models to represent the pairwise protein interactions of the organisms. Clustering PPI networks can be useful for isolating groups of interacting proteins that participate in the same biological processes or that perform together specific biological functions. Evolutionary orthologies can be inferred this way, as well as functions and properties of yet uncharacterized proteins. We present an overview of the main state-of-the-art clustering methods that have been applied to PPI networks over the past decade. We distinguish five specific categories of approaches, describe and compare their main features and then focus on one of them, i.e. population-based stochastic search. We provide an experimental evaluation, based on some validation measures widely used in the literature, of techniques in this class, that are as yet less explored than the others. In particular, we study how the capability of Genetic Algorithms (GAs) to extract clusters in PPI networks varies when different topology-based fitness functions are used, and we compare GAs with the main techniques in the other categories. The experimental campaign shows that predictions returned by GAs are often more accurate than those produced by the contestant methods. Interesting issues still remain open about possible generalizations of GAs allowing for cluster overlapping. We point out which methods and tools described here are publicly available. simona.rombo@math.unipa.it Supplementary data are available at Bioinformatics online.

Optimal Finite-Thrust Rendezvous Trajectories Found via Particle Swarm Algorithm

The particle swarm optimization technique is a population-based stochastic method developed in recent years and successfully applied in several fields of research. The particle swarm optimization methodology aims at taking advantage of the mechanism of information sharing that affects the overall behavior of a swarm, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. This research applies the technique to determining optimal continuous-thrust rendezvous trajectories in a rotating Euler–Hill frame. Five distinct applications, both in two dimensions and in three dimensions, are considered. Hamiltonian methods are employed to translate the related optimal control problems into parameter optimization problems. The transversality condition, which is an analytical condition that arises from the calculus of variations, is proven to be ignorable for these problems, and this property greatly simplifies the solution process. For each of the five applications considered in the paper, despite its simplicity, the swarming algorithm successfully finds the optimal control law corresponding to the minimum-time trajectory with great accuracy.

Particle swarm optimization applied to impulsive orbital transfers

The particle swarm optimization (PSO) technique is a population-based stochastic method developed in recent years and successfully applied in several fields of research. It mimics the unpredictable motion of bird flocks while searching for food, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. At the end of the process, the best particle (i.e. the best solution with reference to the objective function) is expected to contain the globally optimal values of the unknown parameters. The central idea underlying the method is contained in the formula for velocity updating. This formula includes three terms with stochastic weights. This research applies the particle swarm optimization algorithm to the problem of optimizing impulsive orbital transfers. More specifically, the following problems are considered and solved with the PSO algorithm: (i) determination of the globally optimal two- and three-impulse transfer trajectories between two coplanar circular orbits; (ii) determination of the optimal transfer between two coplanar, elliptic orbits with arbitrary orientation; (iii) determination of the optimal two-impulse transfer between two circular, non-coplanar orbits; (iv) determination of the globally optimal two-impulse transfer between two non-coplanar elliptic orbits. Despite its intuitiveness and simplicity, the particle swarm optimization method proves to be capable of effectively solving the orbital transfer problems of interest with great numerical accuracy.

Constrained and unconstrained Gibbs free energy minimization in reactive systems using genetic algorithm and differential evolution with tabu list

Phase equilibrium modeling plays an important role in design, optimization and control of separation processes. The global optimization problem involved in phase equilibrium calculations is very challenging due to the high non-linearity of thermodynamic models especially for multi-component systems subject to chemical reactions. To date, a few attempts have been made in the application of stochastic methods for reactive phase equilibrium calculations compared to those reported for non-reactive systems. In particular, the population-based stochastic methods are known for their good exploration abilities and, when optimal balance between the exploration and exploitation is found, they can be reliable and efficient global optimizers. Genetic algorithms (GAs) and differential evolution with tabu list (DETL) have been very successful for performing phase equilibrium calculations in non-reactive systems. However, there are no previous studies on the performance of both these strategies to solve the Gibbs free energy minimization problem for systems subject to chemical equilibrium. In this study, the constrained and unconstrained Gibbs free energy minimization in reactive systems have been analyzed and used to assess the performance of GA and DETL. Specifically, the numerical performance of these stochastic methods have been tested using both conventional and transformed composition variables as the decision vector for free energy minimization in reactive systems, and their relative strengths are discussed. The results of these strategies are compared with those obtained using SA, which has shown competitive performance in reactive phase equilibrium calculations. To the best of our knowledge, there are no studies in the literature on the comparison of reactive phase equilibrium using both the formulations with stochastic global optimization methods. Our results show that the effectiveness of the stochastic methods tested depends on the stopping criterion, the type of decision variables, and the use of local optimization for intensification stage. Overall, unconstrained Gibbs free energy minimization involving transformed composition variables requires more computational time compared to constrained minimization, and DETL has better performance for both constrained and unconstrained Gibbs free energy minimization in reactive systems.

Particle Swarm Optimization Applied to Space Trajectories

The particle swarm optimization technique is a population-based stochastic method developed in recent years and successfully applied in several fields of research. It represents a very intuitive (and easy to program) methodology for global optimization, inspired by the behavior of bird flocks while searching for food. The particle swarm optimization technique attempts to take advantage of the mechanism of information sharing that affects the overall behavior of a swarm, with the intent of determining the optimal values of the unknown parameters of the problem under consideration. In this research the method is applied to a variety of space trajectory optimization problems, i.e., the determination of periodic orbits in the context of the circular restricted three-body problem, and the optimization of (impulsive and finite thrust) orbital transfers. Despite its simplicity and intuitiveness, the particle swarm algorithm proves to be quite effective in finding the optimal solution to all of the applications considered in the paper, with great numerical accuracy.

Swarms and Swarm Intelligence

Nature-inspired intelligent swarm technologies deals with complex problems that might be impossible to solve using traditional technologies and approaches. Swarm intelligence techniques (note the difference from intelligent swarms) are population-based stochastic methods used in combinatorial optimization problems in which the collective behavior of relatively simple individuals arises from their local interactions with their environment to produce functional global patterns. Swarm intelligence represents a meta heuristic approach to solving a variety of problems

A Population-based Approach for Hard Global Optimization Problems based on Dissimilarity Measures

When dealing with extremely hard global optimization problems, i.e. problems with a large number of variables and a huge number of local optima, heuristic procedures are the only possible choice. In this situation, lacking any possibility of guaranteeing global optimality for most problem instances, it is quite difficult to establish rules for discriminating among different algorithms. We think that in order to judge the quality of new global optimization methods, different criteria might be adopted like, e.g.: <ol%gt; efficiency – measured in terms of the computational effort necessary to obtain the putative global optimum robustness – measured in terms of “percentage of successes”, i.e. of the number of times the algorithm, re-started with different seeds or starting points, is able to end up at the putative global optimum discovery capability – measured in terms of the possibility that an algorithm discovers, for the first time, a putative optimum for a given problem which is better than the best known up to now. </ol%gt; Of course the third criterion cannot be considered as a compulsory one, as it might be the case that, for a given problem, the best known putative global optimum is indeed the global one, so that no algorithm will ever be able to discover a better one. In this paper we present a computational framework based on a population-based stochastic method in which different candidate solutions for a single problem are maintained in a population which evolves in such a way as to guarantee a sufficient diversity among solutions. This diversity enforcement is obtained through the definition of a dissimilarity measure whose definition is dependent on the specific problem class. We show in the paper that, for some well known and particularly hard test classes, the proposed method satisfies the above criteria, in that it is both much more efficient and robust when compared with other published approaches. Moreover, for the very hard problem of determining the minimum energy conformation of a cluster of particles which interact through short-range Morse potential, our approach was able to discover four new putative optima.