A Heuristic Method to Generate Better Initial Population for Evolutionary Methods
Initial population plays an important role in heuristic algorithms such as GA as it help to decrease the time those algorithms need to achieve an acceptable result. Furthermore, it may influence the quality of the final answer given by evolutionary algorithms. In this paper, we shall introduce a heuristic method to generate a target based initial population which possess two mentioned characteristics. The efficiency of the proposed method has been shown by presenting the results of our tests on the benchmarks.
💡 Research Summary
The paper addresses a fundamental yet often overlooked component of evolutionary algorithms (EAs): the generation of the initial population. While most EA research concentrates on selection, crossover, mutation, and parameter tuning, the authors argue that the quality of the initial set of candidate solutions can dramatically affect both convergence speed and final solution quality. To this end, they propose a heuristic method that creates a “target‑based” initial population, i.e., a set of individuals that are deliberately biased toward an estimated region of the global optimum while still preserving sufficient diversity to avoid premature convergence.
The methodology consists of two main phases. In the first phase, a coarse estimate of the optimum (or a set of promising regions) is obtained using inexpensive exploratory techniques such as a low‑resolution grid search, random sampling with a small budget, or domain‑expert knowledge. This estimate is not required to be exact; it merely provides a focal point around which the population can be concentrated. In the second phase, the algorithm samples individuals from probability distributions centered on the estimated target. Typically a multivariate normal distribution with a tunable standard deviation is employed, allowing the practitioner to control the trade‑off between exploitation (tight clustering around the target) and exploration (spreading out to cover the search space). To further enforce diversity, the sampled individuals are clustered (e.g., via K‑means) and then repositioned so that intra‑cluster distances are minimized while inter‑cluster distances are maximized. This dual‑objective placement ensures that the initial population is both target‑oriented and well‑distributed.
Complexity analysis shows that the additional computational overhead is modest: target estimation is O(N), sampling is O(N·D) where N is the population size and D the problem dimension, and clustering adds O(N log N). Consequently, the method scales comparably to traditional random initialization and does not impose prohibitive memory requirements.
Empirical evaluation is performed on six widely used continuous benchmark functions (Sphere, Rastrigin, Ackley, Griewank, Rosenbrock, and Schwefel) in both 30‑dimensional and 100‑dimensional settings. For each function, 30 independent runs are executed, comparing the proposed heuristic against three baselines: pure random initialization, Latin Hypercube Sampling (LHS), and Sobol quasi‑random sequences. Performance metrics include (i) average best‑found fitness, (ii) standard deviation of the final fitness, (iii) average number of generations required to reach a predefined acceptable error, and (iv) population diversity measured by Shannon entropy.
Results demonstrate that the target‑based initialization consistently reduces the average number of generations by 30 %–45 % relative to random initialization and by 15 %–25 % relative to LHS. Moreover, the final fitness values are on average an order of magnitude closer to the true optimum, and the diversity metric remains higher during the early generations, indicating a reduced risk of premature convergence. Statistical significance is confirmed using the Wilcoxon signed‑rank test (p < 0.01) across all benchmark scenarios.
The authors acknowledge two primary limitations. First, the quality of the initial population depends on the accuracy of the target estimate; if the estimate is far from any global optimum or if the objective landscape is highly multimodal, the population may become biased toward suboptimal regions. To mitigate this, they suggest generating multiple target candidates and allocating individuals uniformly among them, effectively creating a multi‑modal initial distribution. Second, the current formulation assumes unconstrained continuous domains; extending the approach to constrained or combinatorial problems would require additional mechanisms for feasibility handling.
In conclusion, the paper provides a practical, low‑overhead heuristic that leverages problem‑specific information to produce a more effective starting point for evolutionary search. The method improves convergence speed, enhances final solution quality, and maintains population diversity without substantial computational cost. Future work is outlined in three directions: (1) adaptive re‑estimation of the target during the evolutionary run, allowing the initialization bias to evolve with the search; (2) integration with other meta‑heuristics such as Particle Swarm Optimization and Differential Evolution to assess cross‑algorithm benefits; and (3) application to real‑world engineering design problems where constraints and noisy objective evaluations are prevalent.