Geometric Particle Swarm Optimization for Multi-objective Optimization Using Decomposition

Multi-objective evolutionary algorithms (MOEAs) based on decomposition are aggregation-based algorithms which transform a multi-objective optimization problem (MOP) into several single-objective subproblems. Being effective, efficient, and easy to implement, Particle Swarm Optimization (PSO) has become one of the most popular single-objective optimizers for continuous problems, and recently it has been successfully extended to the multi-objective domain. However, no investigation on the application of PSO within a multi-objective decomposition framework exists in the context of combinatorial optimization. This is precisely the focus of the paper. More specifically, we study the incorporation of Geometric Particle Swarm Optimization (GPSO), a discrete generalization of PSO that has proven successful on a number of single-objective combinatorial problems, into a decomposition approach. We conduct experiments on manyobjective 1/0 knapsack problems i.e. problems with more than three objectives functions, substantially harder than multi-objective problems with fewer objectives. The results indicate that the proposed multi-objective GPSO based on decomposition is able to outperform two version of the wellknow MOEA based on decomposition (MOEA/D) and the most recent version of the non-dominated sorting genetic algorithm (NSGA-III), which are state-of-the-art multi-objective evolutionary approaches based on decomposition

Impact analysis of crossovers in a multi-objective evolutionary algorithm

Multi-objective optimization has become mainstream because several real-world problems are naturally posed as a Multi-objective optimization problems (MOPs) in all fields of engineering and science. Usually MOPs consist of more than two conflicting objective functions and that demand trade-off solutions. Multi-objective evolutionary algorithms (MOEAs) are extremely useful and well-suited for solving MOPs due to population based nature. MOEAs evolve its population of solutions in a natural way and searched for compromise solutions in single simulation run unlike traditional methods. These algorithms make use of various intrinsic search operators in efficient manners. In this paper, we experimentally study the impact of different multiple crossovers in multi-objective evolutionary algorithm based on decomposition (MOEA/D) framework and evaluate its performance over test instances of 2009 IEEE congress on evolutionary computation (CEC?09) developed for MOEAs competition. Based on our carried out experiment, we observe that used variation operators are considered to main source to improve the algorithmic performance of MOEA/D for dealing with CEC?09 complicated test problems

Optimization of ANN Structure Using Adaptive PSO & GA and Performance Analysis Based on Boolean Identities

In this paper, a novel heuristic structure optimization technique is proposed for Neural Network using Adaptive PSO & GA on Boolean identities to improve the performance of Artificial Neural Network (ANN). The selection of the optimal number of hidden layers and nodes has a significant impact on the performance of a neural network, is decided in an adhoc manner. The optimization of architecture and weights of neural network is a complex task. In this regard the use of evolutionary techniques based on Adaptive Particle Swarm Optimization (APSO) & Adaptive Genetic Algorithm (AGA) is used for selecting an optimal number of hidden layers and nodes of the neural controller, for better performance and low training errors through Boolean identities. The hidden nodes are adapted through the generation until they reach the optimal number. The Boolean operators such as AND, OR, XOR have been used for performance analysis of this technique

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Biochemical systems identification by a random drift particle swarm optimization approach

BACKGROUND: Finding an efficient method to solve the parameter estimation problem (inverse problem) for nonlinear biochemical dynamical systems could help promote the functional understanding at the system level for signalling pathways. The problem is stated as a data-driven nonlinear regression problem, which is converted into a nonlinear programming problem with many nonlinear differential and algebraic constraints. Due to the typical ill conditioning and multimodality nature of the problem, it is in general difficult for gradient-based local optimization methods to obtain satisfactory solutions. To surmount this limitation, many stochastic optimization methods have been employed to find the global solution of the problem. RESULTS: This paper presents an effective search strategy for a particle swarm optimization (PSO) algorithm that enhances the ability of the algorithm for estimating the parameters of complex dynamic biochemical pathways. The proposed algorithm is a new variant of random drift particle swarm optimization (RDPSO), which is used to solve the above mentioned inverse problem and compared with other well known stochastic optimization methods. Two case studies on estimating the parameters of two nonlinear biochemical dynamic models have been taken as benchmarks, under both the noise-free and noisy simulation data scenarios. CONCLUSIONS: The experimental results show that the novel variant of RDPSO algorithm is able to successfully solve the problem and obtain solutions of better quality than other global optimization methods used for finding the solution to the inverse problems in this study

Geometric Generalization of the Nelder-Mead Algorithm

The Nelder-Mead Algorithm (NMA) is an almost half-century old method for numerical optimization, and it is a close relative of Particle Swarm Optimization (PSO) and Differential Evolution (DE). Geometric Particle Swarm Optimization (GPSO) and Geometric Differential Evolution (GDE) are recently introduced formal generalization of traditional PSO and DE that apply naturally to both continuous and combinatorial spaces. In this paper, we generalize NMA to combinatorial search spaces by naturally extending its geometric interpretation to these spaces, analogously as what was done for the traditional PSO and DE algorithms, obtaining the Geometric Nelder-Mead Algorithm (GNMA)