QDDS: A Novel Quantum Swarm Algorithm Inspired by a Double Dirac Delta Potential

TL;DR

This paper introduces QDDS, a quantum-inspired swarm algorithm based on double Dirac delta potentials, demonstrating promising results on benchmark functions and FIR filter design, with potential for further refinement in high-dimensional spaces.

Contribution

The paper proposes a novel quantum-inspired swarm algorithm, QDDS, based on double Dirac delta potentials, and provides initial theoretical and experimental validation.

Findings

QDDS outperforms some existing algorithms on benchmark functions.

QDDS shows promise in high-dimensional optimization problems.

Further work is needed for consistent near-optimal solutions at high dimensions.

Abstract

In this paper a novel Quantum Double Delta Swarm (QDDS) algorithm modeled after the mechanism of convergence to the center of attractive potential field generated within a single well in a double Dirac delta well setup has been put forward and the preliminaries discussed. Theoretical foundations and experimental illustrations have been incorporated to provide a first basis for further development, specifically in refinement of solutions and applicability to problems in high dimensional spaces. Simulations are carried out over varying dimensionality on four benchmark functions, viz. Rosenbrock, Rastrigrin, Griewank and Sphere as well as the multidimensional Finite Impulse Response (FIR) Filter design problem with different population sizes. Test results illustrate the algorithm yields superior results to some related reports in the literature while reinforcing the need of substantial future work to deliver near-optimal results consistently, especially if dimensionality scales up.