Experience-Based Evolutionary Algorithms for Expensive Optimization

TL;DR

It is argued that hard optimization problems could be tackled efficiently by making better use of experiences gained in related problems, and an experience-based surrogate-assisted evolutionary algorithm (SAEA) framework is proposed to enhance the optimization efficiency of expensive problems.

Abstract

Optimization algorithms are very different from human optimizers. A human being would gain more experiences through problem-solving, which helps her/him in solving a new unseen problem. Yet an optimization algorithm never gains any experiences by solving more problems. In recent years, efforts have been made towards endowing optimization algorithms with some abilities of experience learning, which is regarded as experience-based optimization. In this paper, we argue that hard optimization problems could be tackled efficiently by making better use of experiences gained in related problems. We demonstrate our ideas in the context of expensive optimization, where we aim to find a near-optimal solution to an expensive optimization problem with as few fitness evaluations as possible. To achieve this, we propose an experience-based surrogate-assisted evolutionary algorithm (SAEA) framework to enhance the optimization efficiency of expensive problems, where experiences are gained across related expensive tasks via a novel meta-learning method. These experiences serve as the task-independent parameters of a deep kernel learning surrogate, then the solutions sampled from the target task are used to adapt task-specific parameters for the surrogate. With the help of experience learning, competitive regression-based surrogates can be initialized using only 1$d$ solutions from the target task ($d$ is the dimension of the decision space). Our experimental results on expensive multi-objective and constrained optimization problems demonstrate that experiences gained from related tasks are beneficial for the saving of evaluation budgets on the target problem.

Figures (3)

• Figure 1: Diagram of our experience-based SAEA framework. The grey block includes all modules that are related to the evolutionary optimization of target task $T_*$. The MDKL surrogate modeling method used in the framework consists of a meta-learning procedure and an adaptation procedure. The meta-learning procedure learns experiences (task-independent parameters $\bm{\gamma^e}$) from related tasks $T_i$. Based on the learned experiences, the adaptation procedure adapts MDKL task-specific parameters to approximate target task $T_*$. Note that existing SAEAs train and update their surrogates on $S_*$ only, thus their workflows do not contain a meta-learning procedure and they can not gain experiences from related tasks.
• Figure 2: Diagram of our deep kernel implementation. The continuous lines depict the training process, the dotted lines depict the inference process. $Q_*$ denotes query samples to be evaluated on our surrogates. The neural network ensures the expressive power of our deep kernel. Common features of related tasks are represented by neural network parameters $\textbf{w}, \textbf{b}$ and base kernel parameters $\bm{\theta}^e, \textbf{p}^e$, which are the learned experiences. Task-specific increments $\Delta \bm{\theta}^*$ and $\Delta \textbf{p}^*$ distinguishes a given task $T_*$ from other tasks.
• Figure 3: Results of 30 runs on the engine calibration problem, all BSFC values are normalized. The evaluation budget is set to 60, including 40, 6 samples used to initialize surrogates for cons_EGO and its experience-based variant, respectively. Figs. (a) and (c) show how BSFC and the number of feasible solutions vary with the number of evaluations, respectively. The star markers highlight the results achieved when 20 evaluations are used in the optimization process. Figs. (b) and (d) illustrate the statistical results of BSFC and the number of feasible solutions when the evaluation budget has run out. Mean values are shown on the top, the results in brackets are achieved at the star markers of Figs. (a) and (c).