Automated Metaheuristic Algorithm Design with Autoregressive Learning

TL;DR

ALDes reframes automated metaheuristic design as autoregressive sequence generation using a transformer backbone, enabling variable-length, structurally diverse algorithm designs. It introduces a novel sequence representation (components, hyperparameters, pointers, conditions) and a problem-embedding module to condition designs on target landscapes, with EWC supporting continual learning. Empirical results on 23 pseudo-Boolean benchmarks and two real-world tasks show ALDes-generated algorithms outperform 24 of 25 human baselines and exhibit varied structures (VNS, ILS, GA-like) tailored to problem contexts. The work demonstrates the practicality of automated, continual metaheuristic design and points to future directions in scaling up to larger pre-trained designers for open-ended problem solving.

Abstract

Automated design of metaheuristic algorithms offers an attractive avenue to reduce human effort and gain enhanced performance beyond human intuition. Current automated methods design algorithms within a fixed structure and operate from scratch. This poses a clear gap towards fully discovering potentials over the metaheuristic family and fertilizing from prior design experience. To bridge the gap, this paper proposes an autoregressive learning-based designer for automated design of metaheuristic algorithms. Our designer formulates metaheuristic algorithm design as a sequence generation task, and harnesses an autoregressive generative network to handle the task. This offers two advances. First, through autoregressive inference, the designer generates algorithms with diverse lengths and structures, enabling to fully discover potentials over the metaheuristic family. Second, prior design knowledge learned and accumulated in neurons of the designer can be retrieved for designing algorithms for future problems, paving the way to continual design of algorithms for open-ended problem-solving. Extensive experiments on numeral benchmarks and real-world problems reveal that the proposed designer generates algorithms that outperform all human-created baselines on 24 out of 25 test problems. The generated algorithms display various structures and behaviors, reasonably fitting for different problem-solving contexts. Code will be released after paper publication.

Figures (5)

• Figure 1: Three instantiations of the sequence representation. The (a) Tabu search has two components, local_search and tabu_list. The local_search (with hyperparameter o defines the neighborhood region) executes once (count condition 1), then the flow forward to update the tabu_list (hyperparameter 5 refers the list's length) once (count condition 1), after that the flow forward to the next algorithm round. Likewise, in (b), the local_search iterates until reaching a local optimal (event condition local_optimal). In (c), 0.1,20 (0.15,30) are the crossover (mutation) probability and distribution, respectively.
• Figure 2: Workflow of the proposed ALDes.
• Figure 3: ALDes's training performance versus episodes. Averaged over 5 trails.
• Figure 4: Average performance over all runs of five generated algorithms on the test instance of each problem. The five algorithms are inferred from ALDes's five training trials with different seeds. In each subfigure, the $i$th row reports the test results after training on the first $i$ problems. For example, the $(3,2)$th cell of subfigure (a) shows the performance of algorithms for F2 ($148.07$), in which algorithms are inferred from the ALDes that has been trained on F1, F2, and F3.
• Figure 5: ALDes's training performance versus episodes. Averaged over 5 trails. The one-off curves report the results of training from scratch. The continual curves report the results of training under the continual task settings. The insets resize the continual curves to show the convergent tendency.