Abstract
<title>Abstract</title> <p>This paper studies a quantum-inspired exploratory variant of improved particle swarm optimization (IPSO) for constrained nonlinear programs handled through a quadratic penalty formulation. The study is motivated by the broader view that PSO-type algorithms may benefit from quantum-inspired movement when classical velocity-based search loses exploratory strength on penalized landscapes with multiple local attraction regions. Instead of treating any particular improved PSO scheme as exceptional, the present work uses a representative IPSO baseline from the wider PSO class and replaces its velocity-driven movement with bounded-potential quantum displacement laws. The resulting quantum-inspired PSO (QI-PSO) variants use Lorentz (LR), Rosen--Morse (RM), and Coulomb-like square-root (CS) potential fields to generate probability-controlled exploratory motion around the local attractor while retaining attraction toward personal and global best positions. Numerical experiments are performed on ten two-dimensional constrained benchmark functions using four penalty constants, c ϵ {10,100,1000,10000}, with 30 independent replications for each algorithm--function--penalty setting. Across eleven improving function--penalty cases, all concentrated on the selected multimodal benchmarks, the best quantum variant reduces the mean absolute error of the IPSO baseline by approximately 42.24% to 99.96%. Feasible-trial rates are reported with these rows because some Rastrigin and Griewank improvements involve a strict-feasibility trade-off. The results also show that the classical IPSO baseline remains preferable on exploitation-dominant cases where it already reaches the known optimum to machine precision. This balanced behaviour indicates that quantum-inspired movement is particularly useful as a controlled nonlocal search mechanism for plateau-prone constrained multimodal landscapes, rather than as a universal replacement for all PSO searches.</p>