Enhancing the Multiverse Optimizer through Symmetry-Guided Search Operators

Introduction:

Metaheuristic algorithms are widely used to solve nonlinear optimization problems, but their search dynamics can still suffer from premature convergence and limited exploration of regions outside the search domain. This study proposes a Symmetry-Guided Multiverse Optimizer (SGMVO) in which candidate universes generate reflected alternatives around the search space center, the current best solution, and selected mirrored dimensions. The novelty lies in using symmetry as an active search operator rather than as a post-processing descriptor.

Methods:

The SGMVO was benchmarked against GA, PSO, and the standard Multiverse Optimizer. A small-scale experimental campaign was conducted using five continuous objective functions: Sphere, Rosenbrock, Rastrigin, Ackley, and Griewank. All algorithms were evaluated under the same conditions: 30 dimensions, 40 search agents, 250 iterations, and 30 independent runs. In the SGMVO, each candidate universe generates symmetric alternatives through reflections about the search space center and the current best universe, as well as partial coordinate mirroring. These reflected candidates compete with the original solution, and the best one is retained for the next iteration. This mechanism increases exploration of opposite regions and improves local refinement near promising solutions. Performance was assessed using the best, mean, median, worst, standard deviation, execution time, and convergence behavior.

Results:

The SGMVO obtained the best single-run solution across four functions: Sphere, Rosenbrock, Ackley, and Griewank. Regarding mean performance, the SGMVO achieved the best values on Sphere (0.0490) and Griewank (0.2216). Compared with standard MVOs, the SGMVO reduced the mean objective value by 98.69% in Sphere, 78.53% in Griewank, 42.37% in Ackley, and 1.88% in Rosenbrock. The method was less competitive in Rastrigin, where GA achieved the lowest mean value.

Conclusions:

The results indicate that symmetry-based candidate reflection improves MVO performance across several benchmark functions, particularly in unimodal and moderately multimodal landscapes. The SGMVO offers a simple, reproducible modification for enhancing search diversification in population-based optimization.