Anupam Yadav

An efficient co-swarm particle swarm optimization for non-linear constrained optimization

Abstract This paper proposes a new co-swarm PSO (CSHPSO) for constrained optimization problems, which is obtained by hybridizing the recently proposed shrinking hypersphere PSO (SHPSO) with the differential evolution (DE) approach. The total swarm is subdivided into two sub swarms in such a way that the first sub swarms uses SHPSO and second sub swarms uses DE. Experiments are performed on a state-of-the-art problems proposed in IEEE CEC 2006. The results of the CSHPSO is compared with SHPSO and DE in a variety of fashions. A statistical approach is applied to provide the significance of the numerical experiments. In order to further test the efficacy of the proposed CSHPSO, an economic dispatch (ED) problem with valve points effects for 40 generating units is solved. The results of the problem using CSHPSO is compared with SHPSO, DE and the existing solutions in the literature. It is concluded that CSHPSO is able to give the minimal cost for the ED problem in comparison with the other algorithms considered. Hence, CSHPSO is a promising new co-swarm PSO which can be used to solve any real constrained optimization problem.

An efficient algorithm based on artificial neural networks and particle swarm optimization for solution of nonlinear Troesch's problem

Abstract In this article, a simple and efficient approach for the approximate solution of a nonlinear differential equation known as Troesch’s problem is proposed. In this article, a mathematical model of the Troesch’s problem is described which arises in confinement of plasma column by radiation pressure. An artificial neural network (ANN) technique with gradient descent and particle swarm optimization is used to obtain the numerical solution of the Troesch’s problem. This method overcomes the difficulty arising in the solution of Troesch’s problem in the literature for eigenvalues of higher magnitude. The results obtained by the ANN method have been compared with the analytical solutions as well as with some other existing numerical techniques. It is observed that our results are more approximate and solution is provided on continuous finite time interval unlike the other numerical techniques. The main advantage of the proposed approach is that once the network is trained, it allows evaluating the solution at any required number of points for higher magnitude of eigenvalues with less computing time and memory.

Shrinking hypersphere based trajectory of particles in PSO

This paper proposes a new Shrinking Hypersphere PSO (SHPSO) for continuous function optimization. The global best and personal best fly in the search space in the form of a hypersphere instead of particles. The hyperspheres keep on shrinking as the iterations proceed and the velocity and position update equations are applied at each iteration. The theoretical convergence of the SHPSO is proved. Then the performance of the proposed SHPSO is compared with five well known PSO variants namely basic PSO, Trelea I PSO, Trelea II PSO, Clerc PSO and SPSO 2011. The basis of comparison is 24 benchmark problems selected from collection of CEC benchmark problem set. The analysis is performed with t-Test, performance index, empirical cumulative distribution and time complexity. It is concluded that the proposed SHPSO is a promising new variant of PSO which will open new doors of research in this area.

Gravitational swarm optimizer for global optimization

Abstract In this paper, a new meta-heuristic method is proposed by combining Particle Swarm Optimization (PSO) and gravitational search in a coherent way. The advantage of swarm intelligence and the idea of a force of attraction between two particles are employed collectively to propose an improved meta-heuristic method for constrained optimization problems. Excellent constraint handling is always required for the success of any constrained optimizer. In view of this, an improved constraint-handling method is proposed which was designed in alignment with the constitutional mechanism of the proposed algorithm. The design of the algorithm is analyzed in many ways and the theoretical convergence of the algorithm is also established in the paper. The efficiency of the proposed technique was assessed by solving a set of 24 constrained problems and 15 unconstrained problems which have been proposed in IEEE-CEC sessions 2006 and 2015, respectively. The results are compared with 11 state-of-the-art algorithms for constrained problems and 6 state-of-the-art algorithms for unconstrained problems. A variety of ways are considered to examine the ability of the proposed algorithm in terms of its converging ability, success, and statistical behavior. The performance of the proposed constraint-handling method is judged by analyzing its ability to produce a feasible population. It was concluded that the proposed algorithm performs efficiently with good results as a constrained optimizer.

A shrinking hypersphere PSO for engineering optimisation problems

Many real-world and engineering design problems can be formulated as constrained optimisation problems (COPs). Swarm intelligence techniques are a good approach to solve COPs. In this paper an efficient shrinking hypersphere-based particle swarm optimisation (SHPSO) algorithm is proposed for constrained optimisation. The proposed SHPSO is designed in such a way that the movement of the particle is set to move under the influence of shrinking hyperspheres. A parameter-free approach is used to handle the constraints. The performance of the SHPSO is compared against the state-of-the-art algorithms for a set of 24 benchmark problems. An exhaustive comparison of the results is provided statistically as well as graphically. Moreover three engineering design problems namely welded beam design, compressed string design and pressure vessel design problems are solved using SHPSO and the results are compared with the state-of-the-art algorithms.

Numerical solution of unsteady advection dispersion equation arising in contaminant transport through porous media using neural networks

A soft computing approach based on artificial neural network (ANN) and optimization is presented for the numerical solution of the unsteady one-dimensional advection-dispersion equation (ADE) arising in contaminant transport through porous media. A length factor ANN method, based on automatic satisfaction of arbitrary boundary conditions (BCs) was chosen for the numerical solution of ADE. The strength of ANN is exploited to construct a trial approximate solution (TAS) for ADE in a way that it satisfies the initial or BCs exactly. An unsupervised error is constructed in approximating the solution of ADE which is minimized by training ANN using gradient descent algorithm (GDA). Two challenging test problems of ADE are considered in this paper, in which, the first problem has steep boundary layers near x = 1 and many numerical methods create non-physical oscillation near steep boundaries. Also for the second problem many numerical schemes suffer from computational noise and instability issues. The proposed method is advantageous as it does not require temporal discretization for the solution of the ADEs as well as it does not suffer from numerical instability. The reliability and effectiveness of the presented algorithm is investigated by sufficient large number of independent runs and comparison of results with other existing numerical methods. The results show that the present method removes the difficulties arising in the solution of the ADEs and provides solution with good accuracy.

A Study of Harmony Search Algorithms: Exploration and Convergence Ability

Harmony Search Algorithm (HSA) has shown to be simple, efficient and strong optimization algorithm. The exploration ability of any optimization algorithm is one of the key points. In this article a new methodology is proposed to measure the exploration ability of the HS algorithm. To understand the searching ability potential exploration range for HS algorithm is designed. Four HS variants are selected and their searching ability is tested based on the choice of improvised harmony. An empirical analysis of the proposed method is tested along with the justification of theoretical findings and experimental results.

History of Neural Networks

Here we are presenting a brief history of neural networks, given in Haykin (Neural networks: a comprehensive foundation, 2002) [7], Zurada (Introduction to artificial neural systems, 2001) [8], Nielsen (Neurocomputing, 1990 [9] in terms of the development of architectures and algorithms that are widely used today. The history of neural networks has been divided in four stages: Beginning of neural networks, First golden age, Quiet Years and Renewed enthusiasm which shows the interplay among biological experimentation, modeling and computer simulation, hardware implementation.

A Niching Co-swarm Gravitational Search Algorithm for Multi-modal Optimization

In this paper, a Niching co-swarm gravitational search algorithm (CoGSA) is designed for solving multi-modal optimization problems. The collective approach of Gravitational Search Algorithm and differential evolution (DE) is used to solve multi-modal optimization problems. A set of twelve multi-modal problems are taken from a benchmark set of CEC 2013. An experimental study has been performed to evaluate the availability of CoGSA over these twelve problems. The performance is measured in an advanced way. It has been observed that CoGSA provides good solution for multi-modal optimization problems.

A Novel Co-swarm Gravitational Search Algorithm for Constrained Optimization

In this article a new co-swarm Gravitational Search Algorithm is proposed to solve the non-linear constrained optimization problems. The idea of Gravitational search algorithm (GSA) and Differential Evolution (DE) is inherited to proposed a new robust search algorithm. The individual influences of GSA and DE over the particles is incorporated collectively to provide a more effective influence in comparison to the individual influences of the GSA and DE. A new velocity update equation is propose to update the positions of the particles. To evaluate the availability of the proposed algorithm a state-of-the-art problems proposed in IEEE CEC 2006 is solved and the results are compared with GSA and DE. The supremacy of the proposed algorithm is benchmarked over the exhaustive simulation results, feasibility rate and success rate.