Generative Evolutionary Strategy For Black-Box Optimizations

TL;DR

This work addresses black-box optimization in high-dimensional spaces, where traditional methods struggle with non-convexity, stochasticity, and multi-objective demands. It introduces Generative Evolutionary Optimization (GEO), a hybrid that tightly couples Evolutionary Strategy (ES) with Generative Surrogate Neural networks (GSN) to maintain $O(N)$ time complexity while stabilizing surrogate training and enabling multi-objective optimization. The core contributions include a training-instability mitigation strategy that concentrates data near the first Pareto front via non-dominated sorting and separate critics per objective, plus a detailed operation protocol for iterative mutation, evaluation, and selection. Empirical results on high-dimensional non-convex benchmarks demonstrate that GEO scales to thousands of dimensions and often outperforms baselines like ES and L-GSO, suggesting significant practical value for scalable, robust black-box optimization and potential applications in reinforcement learning and beyond.

Abstract

Many scientific and technological problems are related to optimization. Among them, black-box optimization in high-dimensional space is particularly challenging. Recent neural network-based black-box optimization studies have shown noteworthy achievements. However, their capability in high-dimensional search space is still limited. This study proposes a black-box optimization method based on the evolution strategy (ES) and the generative neural network (GNN) model. We designed the algorithm so that the ES and the GNN model work cooperatively. This hybrid model enables reliable training of surrogate networks; it optimizes multi-objective, high-dimensional, and stochastic black-box functions. Our method outperforms baseline optimization methods in this experiment, including ES, and Bayesian optimization.

Figures (10)

• Figure 1: a) Structural differences between GAN and GSN. b) A schematic figure illustrating the training instability of GSN. The suboptimal point does not converge towards the near-optimal region, but rather diverges in the opposite direction. c) The vicious cycle between the generator and critic, which is the origin of divergence.
• Figure 2: a) The overall algorithm of GEO. b) ES contributes to GSN by ensuring a stable training region, while GSN aids ES in carrying out efficient mutations. This creates a virtuous cycle where both algorithms complement each other's weaknesses.
• Figure 3: a) Comparison of GEO with baseline algorithms such as BO (Bayesian Optimization), GA (Genetic Algorithm), CMA-ES, and GEO with a single-layer generator. b) Comparison with LSM, a modified version of L-GSO.
• Figure 4: a) Optimization results after 100,000 function calls in two-objective function with 8192 dimensions. To investigate the influence of the initial condition, we conducted experiments differentiating between Latin Hyper Cube (LHC) initialization and point initialization (I) that is the same as the GEO neural network initial state. The results show that the influence of the initial states is insignificant. b) Optimization results in a stochastic environment with random noise added to the ZDT function, after 100,000 function calls in 8192 dimensions.
• Figure 5: Changes in the optimization results of each algorithm as the dimension increases, using the ZDT3 test function after 100,000 function calls.