M. Senthil Arumugam

On the improved performances of the particle swarm optimization algorithms with adaptive parameters, cross-over operators and root mean square (RMS) variants for computing optimal control of a class of hybrid systems

This paper deals with the concept of including the popular genetic algorithm operator, cross-over and root mean square (RMS) variants into particle swarm optimization (PSO) algorithm to make the convergence faster. Two different PSO algorithms are considered in this paper: the first one is the conventional PSO (cPSO) and the second is the global-local best values based PSO (GLbest-PSO). The GLbest-PSO includes global-local best inertia weight (GLbestIW) with global-local best acceleration coefficient (GLbestAC), whereas the cPSO has a time varying inertia weight (TVIW) and either time varying acceleration coefficient (TVAC) or fixed AC (FAC). The effectiveness of the cross-over operator with both PSO algorithms is tested through a constrained optimal control problem of a class of hybrid systems. The experimental results illustrate the advantage of PSO with cross-over operator, which sharpens the convergence and tunes to the best solution. In order to compare and verify the validity and effectiveness of the new approaches for PSO, several statistical analyses are carried out. The results clearly demonstrate that the GLbest-PSO with the cross-over operator is a very promising optimization technique. Similar conclusions can be made for the GLbest-PSO with RMS variants also.

New hybrid genetic operators for real coded genetic algorithm to compute optimal control of a class of hybrid systems

This paper introduces new hybrid cross-over methods and new hybrid selection methods for real coded genetic algorithm (RCGA), to solve the optimal control problem of a class of hybrid system, which is motivated by the structure of manufacturing environments that integrate process and optimal control. In this framework, the discrete entities have a state characterized by a temporal component whose evolution is described by event-driven dynamics and a physical component whose evolution is described by continuous time-driven systems. The proposed RCGA with hybrid genetic operators can outperform the conventional RCGA and the existing Forward Algorithms for this class of systems. The hybrid genetic operators improve both the quality of the solution and the actual optimum value of the objective function. A typical numerical example of the optimal control problem with the number of jobs varying from 5 to 25 is included to illustrate the efficacy of the proposed algorithm. Several statistical analyses are done to compare the betterment of the proposed algorithm over the conventional RCGA and Forward Algorithm. Hypothesis t-test and Analysis of Variance (ANOVA) test are also carried out to validate the effectiveness of the proposed algorithm.

A novel and effective particle swarm optimization like algorithm with extrapolation technique

A novel competitive approach to particle swarm optimization (PSO) algorithms is proposed in this paper. The proposed method uses extrapolation technique with PSO (ePSO) for solving optimization problems. By considering the basics of the PSO algorithm, the current particle position is updated by extrapolating the global best particle position and the current particle positions in the search space. The position equation is formulated with the global best (gbest) position, local best position (pbest) and the current position of the particle. The proposed method is tested with a set of 13 standard optimization benchmark problems and the results are compared with those obtained through two existing PSO algorithms, the canonical PSO (cPSO), the Global-Local best PSO (GLBest PSO). The cPSO includes a time-varying inertia weight (TVIW) and time-varying acceleration co-efficients (TVAC) while the GLBest PSO consists of Global-Local best inertia weight (GLBest IW) with Global-Local best acceleration co-efficient (GLBestAC). The simulation results clearly elucidate that the proposed method produces the near global optimal solution. It is also observed from the comparison of the proposed method with cPSO and GLBest PSO, the ePSO is capable of producing a quality of optimal solution with faster convergence rate. To strengthen the comparison and prove the efficacy of the proposed method a real time application of steel annealing processing (SAP) is also considered. The optimal control objectives of SAP are computed through the above said three PSO algorithms and also through two versions of genetic algorithms (GA), namely, real coded genetic algorithm (RCGA) and hybrid real coded genetic algorithm (HRCGA) and the results are analyzed with the proposed method. From the results obtained through benchmark problems and the real time application of SAP, it is clearly seen that the proposed ePSO method is competitive to the existing PSO algorithms and also to GAs.

A new and improved version of particle swarm optimization algorithm with global–local best parameters

This paper presents a new and improved version of particle swarm optimization algorithm (PSO) combining the global best and local best model, termed GLBest-PSO. The GLBest-PSO incorporates global–local best inertia weight (GLBest IW) with global–local best acceleration coefficient (GLBest Ac). The velocity equation of the GLBest-PSO is also simplified. The ability of the GLBest-PSO is tested with a set of bench mark problems and the results are compared with those obtained through conventional PSO (cPSO), which uses time varying inertia weight (TVIW) and acceleration coefficient (TVAC). Fine tuning variants such as mutation, cross-over and RMS variants are also included with both cPSO and GLBest-PSO to improve the performance. The simulation results clearly elucidate the advantage of the fine tuning variants, which sharpen the convergence and tune to the best solution for both cPSO and GLBest-PSO. To compare and verify the validity and effectiveness of the GLBest-PSO, a number of statistical analyses are carried out. It is also observed that the convergence speed of GLBest-PSO is considerably higher than cPSO. All the results clearly demonstrate the superiority of the GLBest-PSO.

Hybrid particle swarm optimization algorithm with fine tuning operators

This paper introduces a new approach called hybrid particle swarm optimisation like algorithm (hybrid PSO) with fine tuning operators to solve optimisation problems. This method combines the merits of the parameter-free PSO (pf-PSO) and the extrapolated particle swarm optimisation like algorithm (ePSO). In order to accelerate the PSO algorithms to obtain the global optimal solution, three fine tuning operators, namely mutation, cross-over and root mean square variants are introduced. The effectiveness of the fine tuning elements with various PSO algorithms is tested through three benchmark functions along with a few recently developed state-of-the-art methods and the results are compared with those obtained without the fine tuning elements. From several comparative analyses, it is clearly seen that the performance of all the three PSO algorithms (pf-PSO, ePSO, and hybrid PSO) is considerably improved with various fine tuning operators and sometimes more competitive than the recently developed PSO algorithms.

Competitive approaches to PSO algorithms via new acceleration co-efficient variant with mutation operators

This paper presents a few new competitive approaches to particle swarm optimization (PSO) algorithm in terms of the global and local best values (GLbest-PSO) and the standard PSO along with three set of variants namely, inertia weight (IW), acceleration co-efficient (AC) and mutation operators in this paper. Standard PSO is designed with time varying inertia weight (TVIW) and either time varying AC (TVAC) or fixed AC (FAC) while GLbest-PSO comprises of global-average local best IW (GaLbestIW) with either global-local best AC (GLbestAC) or FAC. The performances of these two algorithms are improved considerably in solving an optimal control problem, by introducing the concept of mutation variants between particles in each generation. The presence of mutation operator sharpens the convergence and tunes to the best solution. In order to compare and verify the validity and effectiveness of the new approaches for PSO, several statistical analyses are carried out. The results clearly demonstrate the improved performances of the proposed PSOs over the standard PSOs.

On the optimal control of the steel annealing processes as a two-stage hybrid systems via PSO algorithms

The computation of optimal control variables for a two-stage steel annealing process which comprises of one or more furnaces is proposed in this paper. The heating and soaking furnaces of the steel annealing line form the two-stage hybrid systems. Three algorithms including particle swarm optimisation (PSO) with globally and locally tuned parameters (GLBest PSO), a parameter free PSO algorithm (pf-PSO) and a PSO-like algorithm via extrapolated PSO (ePSO) are considered to solve this optimal control problem for the two-stage steel annealing processes (SAP). The optimal solutions including optimal line speed, optimal cost and job completion time obtained through these three methods are compared with one another and those obtained via conventional PSO (cPSO) with time varying inertia weight (TVIW) and time varying acceleration coefficient (TVAC). From the results obtained through the five algorithms considered, the efficacy and validity of each algorithm are analysed.

Two New and Useful Defuzzification Methods Based on Root Mean Square Value

This paper presents two novel and useful defuzzification methods for fuzzy set outputs. Two algorithms based on root mean square (RMS) to obtain a new defuzzification procedure are proposed. In order to validate the efficacy of the proposed algorithms the results are compared with the existing defuzzification methods such as weighted average, centroid (COG) and mean of maxima. The satisfaction of a set of essential constraints is also dealt with which motivates a step towards rational defuzzification algorithm. These new methods RMS1and RMS2 stand on par with the most commonly used COG method in every respect. In addition, the value obtained by RMS2 is always higher and hence when a higher value is needed or desirable this can be employed advantageously.

A novel effective particle swarm optimization like algorithm via extrapolation technique

A novel competitive approach to particle swarm optimization (PSO) algorithms is proposed in this paper. The proposed method uses extrapolation technique with PSO (ePSO) for solving optimization problems. By considering the basics of the PSO algorithm, the current particle position is updated by extrapolating the global best particle position and the current particle positions in the search space. The position of the particles in each iteration is updated directly without using the velocity equation. The position equation is formulated with the global best (gbest) position, personal or local best position (pbest) and the current position of the particle. The proposed method is tested with a set of five standard optimization bench mark problems and the results are compared with those obtained through three PSO algorithms, the canonical PSO (cPSO), the global-local best PSO (GLBest-PSO) and the proposed ePSO method. The cPSO includes a time varying inertia weight (TVIW) and time varying acceleration coefficients (TVAC) while the GLBest PSO consists of global-local best inertia weight (GLBest 1W) with global-local best acceleration coefficient (GLBestAC). The simulation results clearly elucidate that the proposed method produces the near global optimal solution. It is also observed from the comparison of the proposed method with cPSO and GLBest-PSO, the ePSO is capable of producing a quality of optimal solution with faster convergence rate. To strengthen the comparison and prove the efficacy of the proposed method, analysis of variance and hypothesis t-test are also carried out. All the results indicate that the proposed ePSO method is competitive to the existing PSO algorithms.

ON A CLASS OF HYBRID SYSTEMS VIA A NOVEL APPROACH FOR REAL-CODED GENETIC ALGORITHM WITH HYBRID SELECTION

A real-coded genetic algorithm (RGA) approach with hybrid selection method to compute the optimal control and cost (fitness) of a single stage hybrid system is investigated. A typical numerical example is included to illustrate the efficacy of the proposed algorithm, which gives the better solution in comparison with forward algorithm. Several statistical tests are also carried out to prove the improved performance of the proposed algorithm. ANOVA test and t-test are also done to verify the betterment of the RGA with hybrid selection. From the experimental approach of the various proportion of the hybrid selection, the right proportions of the hybrid selection is identified and tested.