Exploratory Toolkit for Evolutionary and Swarm-Based Optimization

Abstract

Optimization of parameters or "systems" in general plays an ever-increasing role in mathematics, economics, engineering, and the life sciences. As a result, a wide variety of both traditional mathematical and nontraditional algorithmic approaches have been introduced to solve challenging and practically relevant optimization problems. Evolutionary optimization methods~in the form of genetic algorithms, genetic programming, and evolution strategies~represent nontraditional optimization algorithms that draw inspiration from the processes of natural evolution. Particle swarm optimization is another set of more recently developed algorithmic optimizers inspired by social behaviors of organisms such as birds [1] and social insects. These new evolutionary approaches in optimization are now entering the stage and are becoming very successful tools for solving real-world optimization problems [2]. We present Visplore and Evolvica as a toolkit to investigate, explore, and visualize evolutionary and swarm-based optimization techniques. A webMathematica interface is also available. ‡ 1. IntroductionThe evolutionary optimization methods of the genetic algorithm (GA) [3], genetic programming (GP) [4], and evolution strategy (ES) [5] are a branch of nontraditional optimization methods drawing inspiration from the processes of natural evolution. The particle swarm optimizer (PSO), on the other hand, is inspired by the social behavior of bird flocking [6]. Recently, we have been investigating the performance of evolution-and swarm-based optimizers in the domain of biomechanics, which we developed with the Human Performance Laboratory at the Faculty of Kinesiology, University of Calgary [7|9]. In this particular biomechanical application, numerical optimization algorithms are used to design equipment for sports activities. The involved simulations of muscle movements are very time consuming and high dimensional, thus making their evaluation costly and difficult. Simulating a soccer kick is an example of a model that investigates muscle activation patterns within the leg and foot when kicking a soccer ball toward the goal. The specific objective in this case is to obtain a high ball speed, in order to minimize the goal keeper's chances of catching the ball. In 1998, Cole applied a (1+ l) ES to this model [7,8]. More recently, we presented improved adaptations of the model parameters through a PSO [2,10].

Mathematical modeling of the dynamics of the bladder cancer and the immune response applied to a patient: Evolution and short‐term prediction

“…For model calibration in the second stage, we minimize the function F 2 using the rPSO algorithm, and the model parameter values are given in Table .…”

“…Now, for model calibration in the third stage, the model parameter values k , λ 1 , d 1 , b 1 , d 2 , b 2 , τ 1 , τ 2 , τ 3 have been calculated and only λ 2 , τ 4 , τ 5 have to be calibrated again, using the fitting function F 2 where, now, the unknown model parameters are only λ 2 , τ 4 , τ 5 . Then, using the rPSO algorithm, the calibrated model parameters are given in Table . It can be seen that the model parameter values satisfy the restrictions stated through this section.…”

The Application of an Improved Particle Swarm Optimization (PSO) Algorithm in Pairwise Sequence Alignment

“…The following processes give an outline of the basic Particle swarm optimization [10][11]: a) Initialize the particle population by stochastically assigning locations and velocities. b) Calculate the fitness value of the individual particle (pbest B.…”

Optimum topological design of negative permeability dielectric metamaterial using a new binary particle swarm algorithm

“…Indeed, these optimization methods can converge to local optima, calculating the sensibilities. So, even if there is no mathematical proof of the global convergence of the metaheuristic methods, they can be used to very efficiently solve the difficult optimization problems [44].…”