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

Improved dynamical particle swarm optimization method for structural dynamics

A methodology to the multiobjective structural design of buildings based on an improved particle swarm optimization algorithm is presented, which has proved to be very efficient and robust in nonlinear problems and when the optimization objectives are in conflict. In particular, the behaviour of the particle swarm optimization (PSO) classical algorithm is improved by dynamically adding autoadaptive mechanisms that enhance the exploration/exploitation trade-off and diversity of the proposed algorithm, avoiding getting trapped in local minima. A novel integrated optimization system was developed, called DI-PSO, to solve this problem which is able to control and even improve the structural behaviour under seismic excitations. In order to demonstrate the effectiveness of the proposed approach, the methodology is tested against some benchmark problems. Then a 3-story-building model is optimized under different objective cases, concluding that the improved multiobjective optimization methodology using DI-PSO is more efficient as compared with those designs obtained using single optimization.Peer ReviewedPostprint (published version

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

Dual sub-swarm interaction QPSO algorithm based on different correlation coefficients

A novel quantum-behaved particle swarm optimization (QPSO) algorithm, the dual sub-swarm interaction QPSO algorithm based on different correlation coefficients (DCC-QPSO), is proposed by constructing master-slave sub-swarms with different potential well centres. In the novel algorithm, the master sub-swarm and the slave sub-swarm have different functinons during the evolutionary process through separate information processing strategies. The master subswarm is conducive to maintaining population diversity and enhancing the global search ability of particles. The slave sub-swarm accelerates the convergence rate and strengthens the particles’ local searching ability. With the critical information contained in the search space and results of the basic QPSO algorithm, this new algorithm avoids the rapid disappearance of swarm diversity and enhances searching ability through collaboration between sub-swarms. Experimental results on six test functions show that DCC-QPSO outperforms the traditional QPSO algorithm regarding optimization of multimodal functions, with enhancement in both convergence speed and precision

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

Particle Swarm Optimization with Quantum Infusion for the Design of Digital Filters

In this paper, particle swarm optimization with quantum infusion (PSO-QI) has been applied for the design of digital filters. In PSO-QI, Global best (gbest) particle (in PSO star topology) obtained from particle swarm optimization is enhanced by doing a tournament with an offspring produced by quantum behaved PSO, and selecting the winner as the new gbest. Filters are designed based on the best approximation to the ideal response by minimizing the maximum ripples in passband and stopband of the filter response. PSO-QI, as is shown in the paper, converges to a better fitness. This new algorithm is implemented in the design of finite impulse response (FIR) and infinite impulse response (IIR) filter