Chaotic Quantum Double Delta Swarm Algorithm using Chebyshev Maps: Theoretical Foundations, Performance Analyses and Convergence Issues

Quantum Double Delta Swarm (QDDS) Algorithm is a new metaheuristic algorithm inspired by the convergence mechanism to the center of potential generated within a single well of a spatially co-located double-delta well setup. It mimics the wave nature of candidate positions in solution spaces and draws upon quantum mechanical interpretations much like other quantum-inspired computational intelligence paradigms. In this work, we introduce a Chebyshev map driven chaotic perturbation in the optimization phase of the algorithm to diversify weights placed on contemporary and historical, socially-optimal agents' solutions. We follow this up with a characterization of solution quality on a suite of 23 single-objective functions and carry out a comparative analysis with eight other related nature-inspired approaches. By comparing solution quality and successful runs over dynamic solution ranges, insights about the nature of convergence are obtained. A two-tailed t-test establishes the statistical significance of the solution data whereas Cohen's d and Hedge's g values provide a measure of effect sizes. We trace the trajectory of the fittest pseudo-agent over all function evaluations to comment on the dynamics of the system and prove that the proposed algorithm is theoretically globally convergent under the assumptions adopted for proofs of other closely-related random search algorithms.Comment: 27 pages, 4 figures, 19 table

A Comprehensive Survey on Particle Swarm Optimization Algorithm and Its Applications

Particle swarm optimization (PSO) is a heuristic global optimization method, proposed originally by Kennedy and Eberhart in 1995. It is now one of the most commonly used optimization techniques. This survey presented a comprehensive investigation of PSO. On one hand, we provided advances with PSO, including its modifications (including quantum-behaved PSO, bare-bones PSO, chaotic PSO, and fuzzy PSO), population topology (as fully connected, von Neumann, ring, star, random, etc.), hybridization (with genetic algorithm, simulated annealing, Tabu search, artificial immune system, ant colony algorithm, artificial bee colony, differential evolution, harmonic search, and biogeography-based optimization), extensions (to multiobjective, constrained, discrete, and binary optimization), theoretical analysis (parameter selection and tuning, and convergence analysis), and parallel implementation (in multicore, multiprocessor, GPU, and cloud computing forms). On the other hand, we offered a survey on applications of PSO to the following eight fields: electrical and electronic engineering, automation control systems, communication theory, operations research, mechanical engineering, fuel and energy, medicine, chemistry, and biology. It is hoped that this survey would be beneficial for the researchers studying PSO algorithms

Quantum Particle Swarm Optimization Algorithm Based on Dynamic Adaptive Search Strategy

The particle swarm system simulates the evolution of the social mechanism. In this system, the individual particle representing the potential solution flies in the multidimensional space in order to find the better or the optimal solution. But because of the search path and limited speed, it's hard to avoid local best and the premature phenomenon occurs easily. Based on the uncertain principle of the quantum mechanics, the global search ability of the quantum particle swarm optimization (QPSO) algorithms are better than the particle swarm optimization algorithm (PSO). On the basis of the fundamental quantum PSO algorithm, this article introduces the grouping optimization strategy, and meanwhile adopts the dynamic adjustment, quantum mutation and possibility acceptance criteria to improve the global search capability of the algorithm and avoid premature convergence phenomenon. By optimizing the test functions, the experimental simulation shows that the proposed algorithm has better global convergence and search ability

A novel multi-objective quantum particle swarm algorithm for suspension optimization

In this paper, a novel multi-objective archive-based Quantum Particle Optimizer (MOQPSO) is proposed for solving suspension optimization problems. The algorithm has been adapted from the well-knownsingle objectiveQPSOby substantialmodifications in the core equations and implementation of new multi-objectivemechanisms. The novel algorithmMOQPSO and the long-establishedNSGA-II andCOGA-II (Compressed-ObjectiveGenetic Algorithm with Convergence Detection) are compared. Two situations are considered in this paper: a simple half-car suspension model and a bus suspension model. The numerical model of the bus allows complex dynamic interactions not considered in previous studies. The suitability of the solution is evaluated based on vibration-related ISO Standards, and the efficiency of the proposed algorithm is tested by dominance comparison. For a specifically chosen Pareto front solution found by MOQPSO in the second case, the passengers and driver accelerations attenuated about 50% and 33%, respectively, regarding non-optimal suspension parameters. All solutions found by NSGA-II are dominated by those found byMOQPSO,which presented a Pareto front noticeably wider for the same number of objective function calls

Quantum behaved artificial bee colony based conventional controller for optimum dispatch

Since a multi area system (MAS) is characterized by momentary overshoot, undershoot and intolerable settling time so, neutral copper conductors are replaced by multilayer zigzag graphene nano ribbon (MLGNR) interconnects that are tremendously advantageous to copper interconnects for the future transmission line conductors necessitated for economic and emission dispatch (EED) of electric supply system giving rise to reduced overshoots and settling time and greenhouse effect as well. The recent work includes combinatorial algorithm involving proportional integral and derivative controller and heuristic swarm optimization; we say it as Hybrid- particle swarm optimization (PSO) controller. The modeling of two multi area systems meant for EED is carried out by controlling the conventional proportional integral and derivative (PID) controller regulated and monitored by quantum behaved artificial bee colony (ABC) optimization based PID (QABCOPID) controller in MATLAB/Simulink platform. After the modelling and simulation of QABCOPID controller it is realized that QABCOPID is better as compared to multi span double display (MM), neural network based PID (NNPID), multi objective constriction PSO (MOCPSO) and multi objective PSO (MOPSO). The real power generation fixed by QABCOPID controller is used to estimate the combined cost and emission objectives yielding optimal solution, minimum losses and maximum efficiency of transmission line

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment

A Self-Adaptive Chaos Particle Swarm Optimization Algorithm

As a new evolutionary algorithm, particle swarm optimization (PSO) achieves integrated evolution through the information between the individuals. All the particles have the ability to adjust their own speed and remember the optimal positions they have experienced. This algorithm has solved many practical engineering problems and achieved better optimization effect. However, PSO can easily get trapped in local extremum, making it fail to get the global optimal solution and reducing its convergence speed. To settle these deficiencies, this paper has proposed an adaptive chaos particle swarm optimization (ACPSO) based on the idea of chaos optimization after analyzing the basic principles of PSO. This algorithm can improve the population diversity and the ergodicity of particle search through the property of chaos; adjust the inertia weight according to the premature convergence of the population and the individual fitness; consider the global optimization and local optimization; effectively avoid premature convergence and improve algorithm efficiency. The experimental simulation has verified its effectiveness and superiority