QDDS – A Novel Quantum-inspired Swarm Optimizer: Theoretical Foundations, Convergence Analyses and Application Perspectives

Abstract

With sensor fusion and data-driven approaches taking center stage in ubiquitous computing, customized and application-specific optimization methods are increasingly important. The interest follows in part from the limitations of specific optimization methods implied by the No Free Lunch Theorem. Applications of computational intelligence are growing exponentially with the widespread availability of increasingly powerful computers. This has made feasible the mimicry of highly interactive multi-agent models of natural systems that solve complicated problems while remaining stable. The emergent behaviors arising in such systems hint at novel methods of optimization that can find solutions to machine learning problems of similar complexity.

This dissertation introduces a social, agent-based (swarm) intelligence algorithm viz. the Quantum Double Delta Swarm (QDDS). It is modeled after the mechanism of convergence, under an attractive potential field, to the center of a single well in a double Dirac delta potential-well problem. The swarming model developed here extends the well-known Quantum-behaved Particle Swarm Optimization (QPSO) algorithm to the more stable, double well configuration for optimal solutions of complex engineering design problems. Theoretical foundations and experimental illustrations lead to applications of the model to find solutions of problems in intrinsically high-dimensional feature spaces. In addition, the effects of chaos on the exploratory capacity of the algorithm are studied by including a Chebyshev map driven exploration (C-QDDS) step and benchmarking the results. Visualization of the process is enabled by tracking the trajectory of the best performing agent in each iteration over all episodes across benchmark contours. Under general assumptions common to random search convergence proofs the dynamical limitations of this model’s convergence are critically analyzed. Finally, results are demonstrated on: a) the multidimensional finite impulse response (FIR) filter design problem and b) Neuro-evolution, specifically using a two-layer neural architecture where the C-QDDS search mutates candidate architectures whose weights and biases are then trained using gradient-free swarming.