Multiple Global Peaks Big Bang-Big Crunch Algorithm for Multimodal Optimization

TL;DR

The paper tackles multimodal optimization by extending the Big Bang-Big Crunch framework to identify multiple global peaks. It introduces MGP-BBBC, a cluster-based, mean-shift driven extension that maintains an archive of elites and employs a survival stage with distance-based filtering, a big-crunch phase to form centers of mass, and a big-bang phase with adaptive expansion to balance exploration and exploitation. Key contributions include automatic cluster determination via mean-shift, niche-aware offspring allocation, and extensive parameter analyses to guide practical settings. Empirical results on the CEC'2013 benchmark show competitive or superior peak-finding performance across 20 multimodal functions, highlighting the method's robustness and potential for real-world multimodal search tasks.

Abstract

The main challenge of multimodal optimization problems is identifying multiple peaks with high accuracy in multidimensional search spaces with irregular landscapes. This work proposes the Multiple Global Peaks Big Bang-Big Crunch (MGP-BBBC) algorithm, which addresses the challenge of multimodal optimization problems by introducing a specialized mechanism for each operator. The algorithm expands the Big Bang-Big Crunch algorithm, a state-of-the-art metaheuristic inspired by the universe's evolution. Specifically, MGP-BBBC groups the best individuals of the population into cluster-based centers of mass and then expands them with a progressively lower disturbance to guarantee convergence. During this process, it (i) applies a distance-based filtering to remove unnecessary elites such that the ones on smaller peaks are not lost, (ii) promotes isolated individuals based on their niche count after clustering, and (iii) balances exploration and exploitation during offspring generation to target specific accuracy levels. Experimental results on twenty multimodal benchmark test functions show that MGP-BBBC generally performs better or competitively with respect to other state-of-the-art multimodal optimizers.

Figures (6)

• Figure 1: Basic framework of MGP-BBBC.
• Figure 2: Distribution of elites (green and blue circles) around the global peaks (red crosses) for Vincent with 2D function ($F_7$ of CEC'2013 benchmark set). The plot shows that more elites tend to surround the prominent peaks (up-right area) due to the higher density of high fitness points rather than the smaller sharper ones (down-left area) -- and many peaks in the down-left area are missed. The filtering procedure will remove points close to each other (blue circles), allowing MGP-BBBC to explore surroundings in low-density areas when producing new offspring.
• Figure 3: Reduction of the bang extent of expansion over generations. In the example, the extent starts from $2.0$ and decreases logarithmically until the $60\%$ of the total number of generations (exploration phase) when it reaches a value of $1.0E-01$. After that, it decreases with constant steps to target the other levels of accuracy ($1.0E-02$, $1.0E-03$, $1.0E-04$, and $1.0E-05$) in an equal number of generations (exploitation phase). Zoomed-in plots allow readers to appreciate the details of the exploitation phase.
• Figure 4: Changes in the PR values (at the accuracy level $\varepsilon=1.0E-04$) with different Population Size (n) and Clustering Kernel Bandwidth (h) on CEC'2013 benchmark set.
• Figure 5: Changes in the PR values (at the accuracy level $\varepsilon=1.0E-04$) with different Population Size (n) and the ratio between Clustering Kernel Bandwidth Volume and Search Space Volume on CEC'2013 benchmark set.