Weak Population–Empowered Large-Scale Multiobjective Immune Algorithm

The multiobjective immune optimization algorithms (MOIAs) utilize the principle of clonal selection, iteratively evolving by replicating a small number of superior solutions to optimize decision vectors. However, this method often leads to a lack of diversity and is particularly ineffective when facing large-scale optimization problems. Moreover, an overemphasis on elite solutions may result in a large number of redundant offspring, reducing evolutionary efficiency. By delving into the causes of these issues, we find that a key factor is that existing algorithms overlook the role of weak solutions during the evolutionary process. With this in mind, we propose a weak population–empowered large-scale multiobjective immune algorithm (WP–MOIA). The core of this algorithm is to construct, in addition to the traditional elite population, a cooperative evolutionary population based on a portion of the remaining solutions, referred to as the weak population. During the evolution, both populations work together: the elite population maximizes its advantageous status for local searches, focusing on exploitation, while the weak population seeks greater variation to escape its disadvantaged position, engaging in broader exploration. At the same time, the sizes of both populations are dynamically adjusted to collaboratively maintain the balance of evolution. Through comparisons with nine state-of-the-art multiobjective evolutionary algorithms (MOEAs) and four powerful MOIAs on 30 benchmark problems, the proposed algorithm demonstrates superior performance in both small-scale and large-scale multiobjective optimization problems (MOPs), and exhibits better convergence efficiency. Especially in large-scale MOPs, the new algorithm’s performance nearly surpasses all 13 advanced algorithms being compared.