Mixture-of-Experience for Population Initialization

• MPI is a methodology that enhances evolutionary algorithm performance by combining individuals from multiple seeding methods to improve diversity and exploration.
• It applies a dual subpopulation strategy with brief evolutionary runs to generate rich candidate solutions for tasks like neural architecture search and game planning.
• MPI leverages adaptive experience transfer through techniques like VAE-based surrogate ranking and fine-tuning to ensure robust initialization across diverse, high-dimensional optimization problems.

Mixture-of-Experience for Population Initialization (MPI) is a general methodology for enhancing the initial population in evolutionary algorithms (EAs) by combining individuals generated through diverse or adaptive mechanisms, rather than relying solely on random or single-method generation. MPI aims to overcome the limitations of homogeneous initialization—such as reduced diversity, premature convergence, and poor early exploration—by seeding the EA with individuals that represent a breadth of structural or experiential perspectives informed by prior optimization runs, distinct heuristics, or latent experience transfer. This technique has seen successful instantiations in evolutionary neural architecture search (Tallón-Ballesteros et al., 9 Feb 2024), Rolling Horizon Evolutionary Algorithms for game playing (Gaina et al., 2017), and general-purpose binary optimization via cross-instance transfer (Wang et al., 29 Nov 2025).

1. Motivation and Theoretical Underpinnings

Conventional population initialization methods in EAs (including GAs, neuroevolution, and evolutionary planning) typically involve purely random sampling or, at most, simple heuristic seeding. This strategy often leads to insufficient diversity, weak coverage of high-potential regions in the search space, and a higher risk of stagnation in local optima. Mixture-of-Experience for Population Initialization was introduced to address these deficiencies by engineering the initial generation as a union or mixture of individuals derived from multiple, possibly orthogonal, sources or brief prior evolutionary runs. The essential hypothesis is that aggregating "experiences"—each defined by its construction method or sourcing context—yields a richer collective search ability during early EA iterations and increases the probability of evolving superior solutions under stringent evaluation budgets. The theoretical rationale draws on principles from ensemble learning, transfer learning, and exploration-exploitation trade-offs.

2. Canonical Instantiation in Evolutionary Neural Networks

The two-stage algorithm for evolutionary design of Product Unit Neural Networks (PUNNs) embodies a prototypical MPI implementation (Tallón-Ballesteros et al., 9 Feb 2024). The process is defined as follows:

1. Dual Subpopulation Creation: Two large subpopulations are independently generated using random initialization, but each is constrained to a distinct maximum hidden-layer size (neu vs. neu+1).
2. Preliminary Short Evolutions: Each subpopulation undergoes a brief evolutionary micro-run, utilizing EA operators—elitist selection (top 10%), temperature-controlled parametric and structural mutation (node-add, node-del, connection-add, connection-del, node-fusion), and no crossover. Short runs last $G_s = \lfloor 0.1G \rfloor$ generations, where $G$ is the main EA budget.
3. Selection and Mixing: From each subpopulation, the top $N/2$ individuals (according to softmax-cross-entropy fitness) are selected and merged, forming the initial population $P_{\text{new}}$ for the main EA as $P_{\text{new}} = S_1 \cup S_2$.
4. Main Evolution: The combined population serves as the seed for a standard evolutionary optimization loop, with variable hidden-layer sizes allowed between neu and neu+1.

The rationale is that brief, divergent evolutionary "experiences" in constrained topological regimes enable tentative exploration of distinct structural classes. Their union as the launchpad for the main EA increases both genetic and architectural diversity, reducing convergence to suboptimal basins (Tallón-Ballesteros et al., 9 Feb 2024).

3. MPI in General Video Game Playing and Rolling Horizon Evolution

In Rolling Horizon Evolutionary Algorithms for General Video Game Playing, MPI facilitates robust seeding by combining individuals created via distinct rollout-based planning heuristics (Gaina et al., 2017):

• 1-Step Look Ahead (1SLA): Sequentially greedy action selection, constructing a candidate solution by locally optimal choices at each step.
• Monte Carlo Tree Search (MCTS): Root-level MCTS rollouts used to generate action subsequences by traversing the most-visited children in the search tree.
• Random: Purely random action sequences for baseline coverage.

The MPI protocol prescribes drawing population members according to a mixture distribution $(\pi_1, \pi_2, \pi_3)$ over 1SLA, MCTS, and Random seeds. By tuning these mixture weights according to empirical or domain-specific rules—e.g., favoring MCTS when $P \leq 5$ and sequence length $L \leq 10$—MPI ensures that the initial population reflects a deliberate exploration-exploitation balance. Performance gains are pronounced when function evaluation budgets are tight (low $P, L$), and mixture strategies can be dynamically adapted according to current empirical win rates or problem stochasticity (Gaina et al., 2017).

4. Adaptive Experience Transfer in Binary Optimization

A recent development in general-purpose binary optimization introduces a data-driven, cross-instance MPI framework that leverages variational autoencoder (VAE)-based experience transfer (Wang et al., 29 Nov 2025):

• Experience Representation: Solving experiences on source problems are encoded into compact VAEs (encoder, decoder, scorer) trained on large sampled pairs $(x_j^i, y_j^i)$.
• Repository Formation: All trained surrogate models $M_i$ constitute an experience pool.
• Instance-Adaptive Mixture Selection: Given a new instance $s^{\text{new}}$, random probes are launched; prediction rank-correlations between probe labels and surrogate outputs are computed. A learned gating network $G(\cdot; w^G)$ ranks surrogates for selection based on these correlations.
• Decoder Fine-Tuning: Chosen surrogates undergo decoder-only adaptation, learning to reconstruct good solutions on the new instance by aligning rank-grouped source-target pairs.
• High-Quality Population Generation: The adapted surrogates produce many candidate solutions by latent sampling; the best (according to predicted and then exact evaluations) form the initial GA population, supplemented by interpolated individuals for diversity.

This generalizes MPI beyond hand-selected or algorithmically distinct experiences, enabling scalable, black-box transfer across heterogeneous binary optimization tasks—including unseen domains and high-dimensional settings—at modest function evaluation and time overhead. The use of correlation-based gating ensures that only structurally relevant experiences are transferred, avoiding negative transfer and maintaining population quality under aggressive evaluation constraints ($132$ FEs for PI within a total budget of $800$) (Wang et al., 29 Nov 2025).

5. Experimental Performance and Empirical Insights

Empirical validations across diverse domains demonstrate the effectiveness of MPI-based initialization. Some representative findings:

Domain/Study	Baselines	Highlighted Gains	Evaluation Metric
PUNN classification (Tallón-Ballesteros et al., 9 Feb 2024)	EDD, MLP, RBF	Mean CCR increased from 87.38% (EDD) to 87.85% (MPI); highest mean CCR on 9/14 datasets; ≈37% fewer EA evaluations	Correct Classification Ratio (CCR), network complexity
Video game planning (Gaina et al., 2017)	RHEA-Vanilla	Win rates up to 100% (vs baseline 26%) for Chopper; mixture strategies dominate in low-budget regimes	Win rate (%), game score
Binary optimization (Wang et al., 29 Nov 2025)	Rand, OBL, SVM-SS, KAES	On 72 test instances, MPI outperformed Rand on 69, SVM-SS on 44 (with means higher in 71/72 and 55/72 cases, respectively)	Mean best value after 800 FEs

These results indicate that combining diverse or adaptively transferred experience can yield statistically significant increases in solution quality and convergence rate relative to standard or single-method initialization. Notably, MPI achieves robust transfer even to higher-dimensional, previously unseen binary classes, illustrating a high degree of generalization (Wang et al., 29 Nov 2025).

6. Guidelines, Limitations, and Extensions

Optimal configuration of MPI depends on the evolutionary domain, solution encoding, and function evaluation budget:

• Mixture weights: Determination rules can be empirical (win-rate analysis), domain-driven (problem determinism/stochasticity), or adaptively tuned during optimization.
• Source experience selection: For transfer-based MPI, correlation-based surrogate ranking coupled with decoder-only fine-tuning scales effectively to new instances while minimizing negative transfer.
• Diversity and coverage: Structural diversity is maximized when source experiences (or seed generators) explore orthogonal subspaces or model classes; random interpolation of transferred solutions further enhances explorability.

Known limitations include additional overhead (e.g., 3–4 minutes per run for surrogate fine-tuning in the VAE-based approach) and static injection (no dynamic refresh or mid-run transfer). Extension opportunities include accelerating transfer via few-shot meta-learning, injecting new experience-based individuals during evolution, and generalizing MPI to other classes of EAs, such as DE, PSO, or neuroevolutionary schemes beyond PUNNs and binary GAs (Tallón-Ballesteros et al., 9 Feb 2024, Wang et al., 29 Nov 2025).

7. Significance and Broader Implications

Mixture-of-Experience for Population Initialization represents a convergence of experience-driven optimization and population diversity engineering. Across multiple domains—neural architecture search, evolutionary planning, and binary combinatorial optimization—MPI consistently improves both the efficiency and efficacy of evolutionary search. A plausible implication is that, as repositories of prior optimization experience grow, generalized, data-rich MPI strategies could underpin scalable black-box optimization for heterogeneous, high-dimensional, and evaluation-limited problem families. This aligns with trends in meta-learning, attentive initialization, and lifelong optimization. The extent of effective transfer, selection, and adaptation in MPI frameworks is thus of central interest for future EA and metaheuristic research.

References:

(Tallón-Ballesteros et al., 9 Feb 2024, Gaina et al., 2017, Wang et al., 29 Nov 2025)