Branching evolution for unknown objective optimization in biclustering

Biclusters hold significant importance in microarray analysis. Given the EA algorithm's efficacy in tackling nonlinear problems, it has become a prevalent choice for evolutionary biclustering in microarray analysis. However, in conventional approaches, the objective of bicluster volume remains elusive, as it heavily relies on the yet-to-be-discovered real bicluster. This discrepancy introduces a novel research problem termed “unknown objective optimization” in our study. To address this issue, our paper introduces an innovative branching evolution strategy within a multi-objective framework. This strategy aims to resolve the challenge of unknown objectives. Throughout the biclustering search process, we meticulously observe the evolution of optimal bicluster individuals. Stability in both mean squared residue (MSR) and volume suggests a high likelihood of reaching an optimal solution, whether local or global. If a global optimal solution is attained at the end of the final evolution, our initial assumption is validated; otherwise, it necessitates an update. The proposed branching strategy is subsequently implemented to bifurcate the original evolution into two branches. One continues the original evolution with an unknown objective of bicluster volume, while the other pursues a new evolution with an estimated objective of bicluster volume. Our algorithm's performance is assessed through comparisons with various traditional and evolutionary biclustering algorithms. The experimental results affirm its enhanced efficacy on both synthetic datasets and real gene datasets.