Kaushik Suresh

Multi-objective optimization with artificial weed colonies

Invasive Weed Optimization (IWO) was recently proposed as a simple but powerful metaheuristic algorithm for real parameter optimization. IWO draws inspiration from the ecological process of weeds colonization and distribution and is capable of solving general multi-dimensional, linear and nonlinear optimization problems with appreciable efficiency. This article extends the basic IWO for tackling multi-objective optimization problems that aim at achieving two or more objectives (very often conflicting) simultaneously. The concept of fuzzy dominance has been used to sort the promising candidate solutions at each iteration. The new algorithm has been shown to be statistically significantly better than some state of the art existing evolutionary multi-objective algorithms, namely NSGAIILS, DECMOSA-SQP, MOEP, Clustering MOEA, GDE3, and MOEADGM on a 12-function test-suite (including both unconstrained and constrained problems) from the IEEE CEC (Congress on Evolutionary Computation) 2009 competition and special session on multi-objective optimization algorithms. The following performance metrics were considered: IGD, Spacing, and Minimum Spacing. Our experimental results suggest that IWO holds immense promise to appear as an efficient metaheuristic for multi-objective optimization.

On Convergence of Differential Evolution Over a Class of Continuous Functions With Unique Global Optimum

Differential evolution (DE) is arguably one of the most powerful stochastic real-parameter optimization algorithms of current interest. Since its inception in the mid 1990s, DE has been finding many successful applications in real-world optimization problems from diverse domains of science and engineering. This paper takes a first significant step toward the convergence analysis of a canonical DE (DE/rand/1/bin) algorithm. It first deduces a time-recursive relationship for the probability density function (PDF) of the trial solutions, taking into consideration the DE-type mutation, crossover, and selection mechanisms. Then, by applying the concepts of Lyapunov stability theorems, it shows that as time approaches infinity, the PDF of the trial solutions concentrates narrowly around the global optimum of the objective function, assuming the shape of a Dirac delta distribution. Asymptotic convergence behavior of the population PDF is established by constructing a Lyapunov functional based on the PDF and showing that it monotonically decreases with time. The analysis is applicable to a class of continuous and real-valued objective functions that possesses a unique global optimum (but may have multiple local optima). Theoretical results have been substantiated with relevant computer simulations.

Inter-particle communication and search-dynamics of lbest particle swarm optimizers: An analysis

Particle Swarm Optimization (PSO) is arguably one of the most popular nature-inspired algorithms for real parameter optimization at present. The existing theoretical research on PSO focuses on the issues like stability, convergence, and explosion of the swarm. However, all of them are based on the gbest (global best) communication topology, which usually is susceptible to false or premature convergence over multi-modal fitness landscapes. The present standard PSO (SPSO 2007) uses an lbest (local best) topology, where a particle is stochastically attracted not towards the best position found in the entire swarm, but towards the best position found by any particle in its topological neighborhood. This article presents a first step towards a probabilistic analysis of the particle interaction and information exchange in an lbest PSO with variable random neighborhood topology (as found in SPSO 2007). It addresses issues like the distribution of particles over neighborhoods, the probability distributions of the social and cognitive terms in lbest model, and the explorative power of the lbest PSO. It also presents a state-space model of the lbest PSO and draws important conclusions regarding the stability and convergence of the particle dynamics in the light of control theory.

Inertia-Adaptive Particle Swarm Optimizer for Improved Global Search

This paper describes a method for improving the final accuracy and the convergence speed of Particle Swarm Optimization (PSO) by adapting its inertia factor in the velocity updating equation and also by adding a new coefficient to the position updating equation. These modifications do not impose any serious requirements on the basic algorithm in terms of the number of Function Evaluations (FEs). The new algorithm has been shown to be statistically significantly better than four recent variants of PSO on an eight-function test-suite for the following performance matrices: Quality of the final solution, time to find out the solution, frequency of hitting the optima, and scalability.

Multi-Objective Differential Evolution for Automatic Clustering with Application to Micro-Array Data Analysis

This paper applies the Differential Evolution (DE) algorithm to the task of automatic fuzzy clustering in a Multi-objective Optimization (MO) framework. It compares the performances of two multi-objective variants of DE over the fuzzy clustering problem, where two conflicting fuzzy validity indices are simultaneously optimized. The resultant Pareto optimal set of solutions from each algorithm consists of a number of non-dominated solutions, from which the user can choose the most promising ones according to the problem specifications. A real-coded representation of the search variables, accommodating variable number of cluster centers, is used for DE. The performances of the multi-objective DE-variants have also been contrasted to that of two most well-known schemes of MO clustering, namely the Non Dominated Sorting Genetic Algorithm (NSGA II) and Multi-Objective Clustering with an unknown number of Clusters K (MOCK). Experimental results using six artificial and four real life datasets of varying range of complexities indicate that DE holds immense promise as a candidate algorithm for devising MO clustering schemes.

An inertia-adaptive particle swarm system with particle mobility factor for improved global optimization

Particle Swarm Optimization (PSO) has recently emerged as a nature-inspired algorithm for real parameter optimization. This article describes a method for improving the final accuracy and the convergence speed of PSO by firstly adding a new coefficient (called mobility factor) to the position updating equation and secondly modulating the inertia weight according to the distance between a particle and the globally best position found so far. The two-fold modification tries to balance between the explorative and exploitative tendencies of the swarm with an objective of achieving better search performance. We also mathematically analyze the effect of the modifications on the dynamics of the PSO algorithm. The new algorithm has been shown to be statistically significantly better than the basic PSO and four of its state-of-the-art variants on a twelve-function test-suite in terms of speed, accuracy, and robustness.

On Some Properties of the lbest Topology in Particle Swarm Optimization

Particle Swarm Optimization (PSO) is arguably one of the most popular nature- inspired algorithms for real parameter optimization at present. The existing theoretical research on PSO is mostly based on the gbest (global best) particle topology, which usually is susceptible to false or premature convergence over multi-modal fitness landscapes. The present standard PSO (SPSO 2007) uses an lbest (local best) topology where a particle is stochastically attracted not towards the best position found in the entire swarm, but towards the best position found by any particle in its topological neighborhood. This paper presents a first step towards a probabilistic analysis of the lbest PSO with variable random neighborhood topology by addressing issues like inter-particle interaction and probabilities of selection based on particle ranks.

Designing Fractional-order PI λ D μ controller using a modified invasive Weed Optimization algortihm

Invasive weed optimization (IWO) has been found to be a simple but powerful algorithm for function optimization over continuous spaces. It has reportedly outperformed many types of evolutionary algorithms and other search heuristics when tested over both benchmark and real-world problems. This article describes the design of Fractional-Order Proportional-Integral-Derivative (FOPID) controllers, using a newly developed variant of IWO, known as IWOSS (Invasive Weed Optimization with Stochastic Selection). Parameters for FOPID controllers include the proportionality constant, integral constant, derivative constant, derivative order and, integral order; and, its design is more complex than that of conventional integer-order proportional-integral-derivative (PID) controller since the latter involves only three variables. Controller synthesis is based on user specifications like peak overshoot and, rise time; which are used to formulate a single objective optimization problem. Tustin operator-based continuous fraction expansion (CFE) scheme was used to digitally realize fractional-order closed loop transfer function of the designed plant-controller setup. Simulation results for some real life analog plants and, comparison of the same for IWOSS and few established optimization techniques (Particle Swarm Optimization (PSO) and Genetic Algorithm (GA)) have been presented to support the claim of superiority of the proposed design technique.

Design of optimal digital IIR filters by using a Bandwidth Adaptive Harmony Search algorithm

Evolutionary optimization algorithms have been recently applied to optimal digital IIR filter design. In this paper, we apply a Bandwidth Adaptive Harmony Search (BAHS) algorithm to the design of 1-dimensional IIR filters. Harmony Search is an evolutionary algorithm, which emulates the improvisation process of musicians. We have modified the algorithm by setting the bandwidth equal to the standard deviation of the vectors in the harmony memory, and by introducing a penalty function to ensure IIR filter stability. The proposed variant has been applied to the design of low-pass, high-pass, band pass and band stop filters, by minimizing the L1 and L2 norm approximation errors and the maximum pass band and stop band ripples. The algorithm has been compared with the TIA approach. The harmony search variant has been found to outperform the TIA approach in designing IIR filters having near-desired frequency responses.

Automatic Clustering Using a Synergy of Genetic Algorithm and Multi-objective Differential Evolution

This paper applies the Differential Evolution (DE) and Genetic Algorithm (GA) to the task of automatic fuzzy clustering in a Multi-objective Optimization (MO) framework. It compares the performance a hybrid of the GA and DE (GADE) algorithms over the fuzzy clustering problem, where two conflicting fuzzy validity indices are simultaneously optimized. The resultant Pareto optimal set of solutions from each algorithm consists of a number of non-dominated solutions, from which the user can choose the most promising ones according to the problem specifications. A real-coded representation of the search variables, accommodating variable number of cluster centers, is used for GADE. The performance of GADE has also been contrasted to that of two most well-known schemes of MO.