Quantum-inspired evolutionary algorithms on continuous space multiobjective problems

Multiobjective optimization has a wide range of applications in science and engineering. Various multiobjective optimization algorithms work fine for bi-objective problems with few variables. However, many problems involve several functions that handle many variables each, and there is no efficient mathematical method to solve these types of problems. Quantum computers offer an exponential speed-up for such problems when they take full advantage of quantum phenomena. At present, quantum multiobjective problem solvers for quantum computers do not exist. This paper presents a formal statistical analysis of two state-of-the-art classical multiobjective evolutionary algorithms and three quantum-inspired multiobjective optimization algorithms to determine whether quantum solvers can provide comparatively optimal quality solutions or if they are limited. One of the quantum-inspired algorithms tested is a novel proposal that uses fewer qubits. The paper also presents contributions to the state of the art by modifying two original, quantum-inspired algorithms to perform in continuous search spaces. The purpose of this paper is to settle the first step of multiobjective quantum optimization for quantum computers from quantum-inspired algorithms by providing valuable results that can assist in future research along the way in this field. The results indicated that the quantum-inspired algorithms tested performed as well as the NSGA-II, and the proposed method outperforms the other quantum-inspired algorithms in problems with constraints and complicated Pareto sets.