Genetic Transfer or Population Diversification? Deciphering the Secret Ingredients of Evolutionary Multitask Optimization

Evolutionary multitasking has recently emerged as a novel paradigm that enables the similarities and/or latent complementarities (if present) between distinct optimization tasks to be exploited in an autonomous manner simply by solving them together with a unified solution representation scheme. An important matter underpinning future algorithmic advancements is to develop a better understanding of the driving force behind successful multitask problem-solving. In this regard, two (seemingly disparate) ideas have been put forward, namely, (a) implicit genetic transfer as the key ingredient facilitating the exchange of high-quality genetic material across tasks, and (b) population diversification resulting in effective global search of the unified search space encompassing all tasks. In this paper, we present some empirical results that provide a clearer picture of the relationship between the two aforementioned propositions. For the numerical experiments we make use of Sudoku puzzles as case studies, mainly because of their feature that outwardly unlike puzzle statements can often have nearly identical final solutions. The experiments reveal that while on many occasions genetic transfer and population diversity may be viewed as two sides of the same coin, the wider implication of genetic transfer, as shall be shown herein, captures the true essence of evolutionary multitasking to the fullest.

💡 Research Summary

The paper investigates the fundamental drivers behind the success of evolutionary multitasking (EM), focusing on two competing hypotheses: (a) implicit genetic transfer (GT) – the exchange of high‑quality genetic material across tasks, and (b) population diversification (PD) – maintaining a diverse set of solutions to improve global search. To explore these ideas, the authors employ the Multi‑Factorial Evolutionary Algorithm (MFEA), a well‑known EM framework that uses a single population with a unified representation, a “skill factor” to associate each individual with a specific task, and a scalar fitness to rank individuals across tasks.

Sudoku puzzles are chosen as the testbed because different puzzle statements can lead to nearly identical final solutions, providing a natural analogue for latent task complementarities. Each puzzle is modeled as a combinatorial optimization problem: rows are hard constraints (must be permutations of 1‑9), while columns and 3×3 sub‑grids are soft constraints whose satisfaction contributes to the objective. The encoding is a 9×9 matrix where each row is a permutation of the digits, fitting directly into the MFEA’s unified search space.

Genetic operators consist of row‑wise Partially Matched Crossover (PMX) and a simple swap mutation that exchanges two non‑fixed cells within a row. When two parents with different skill factors crossover, the offspring inherits genetic material from both tasks, thereby effecting GT automatically. Because each Sudoku instance has its own set of fixed cells, a repair step is added after skill‑factor assignment to ensure that the offspring respects the fixed‑cell constraints of its designated puzzle.

To quantify PD, the authors adopt an entropy‑based measure from information theory. For each matrix locus (row r, column s) they compute the probability distribution of digits across the whole population, calculate the local entropy E(r,s), and sum over all loci to obtain a normalized population entropy E∈