Molecular discovery, when formulated as an optimization problem, presents significant computational challenges because optimization objectives can be non-differentiable. Evolutionary Algorithms (EAs), often used to optimize black-box objectives in molecular discovery, traverse chemical space by performing random mutations and crossovers, leading to a large number of expensive objective evaluations. In this work, we ameliorate this shortcoming by incorporating chemistry-aware Large Language Models (LLMs) into EAs. Namely, we redesign crossover and mutation operations in EAs using LLMs trained on large corpora of chemical information. We perform extensive empirical studies on both commercial and open-source models on multiple tasks involving property optimization, molecular rediscovery, and structure-based drug design, demonstrating that the joint usage of LLMs with EAs yields superior performance over all baseline models across single- and multi-objective settings. We demonstrate that our algorithm improves both the quality of the final solution and convergence speed, thereby reducing the number of required objective evaluations. Our code is available at http://github.com/zoom-wang112358/MOLLEO
Evolutionary algorithms (EAs) have emerged as a predominant approach for addressing multi-objective optimization problems. However, the theoretical foundation of multi-objective EAs (MOEAs), particularly the fundamental aspects like running time analysis, remains largely underexplored. Existing theoretical studies mainly focus on basic MOEAs, with little attention given to practical MOEAs. In this paper, we present a running time analysis of strength Pareto evolutionary algorithm 2 (SPEA2) for the first time. Specifically, we prove that the expected running time of SPEA2 for solving three commonly used multi-objective problems, i.e., $m$OneMinMax, $m$LeadingOnesTrailingZeroes, and $m$-OneJumpZeroJump, is $O(\mu n\cdot \min\{m\log n, n\})$, $O(\mu n^2)$, and $O(\mu n^k \cdot \min\{mn, 3^{m/2}\})$, respectively. Here $m$ denotes the number of objectives, and the population size $\mu$ is required to be at least $(2n/m+1)^{m/2}$, $(2n/m+1)^{m-1}$ and $(2n/m-2k+3)^{m/2}$, respectively. The proofs are accomplished through general theorems which are also applicable for analyzing the expected running time of other MOEAs on these problems, and thus can be helpful for future theoretical analysis of MOEAs.
The problem-solving performance of many evolutionary algorithms, including genetic programming systems used for program synthesis, depends on the values of hyperparameters including mutation rates. The mutation method used to produce some of the best results to date on software synthesis benchmark problems, Uniform Mutation by Addition and Deletion (UMAD), adds new genes into a genome at a predetermined rate and then deletes genes at a rate that balances the addition rate, producing no size change on average. While UMAD with a predetermined addition rate outperforms many other mutation and crossover schemes, we do not expect a single rate to be optimal across all problems or all generations within one run of an evolutionary system. However, many current adaptive mutation schemes such as self-adaptive mutation rates suffer from pathologies like the vanishing mutation rate problem, in which the mutation rate quickly decays to zero. We propose an adaptive bandit-based scheme that addresses this problem and essentially removes the need to specify a mutation rate. Although the proposed scheme itself introduces hyperparameters, we either set these to good values or ensemble them in a reasonable range. Results on software synthesis and symbolic regression problems validate the effectiveness of our approach.
Evolutionary multitasking (EMT) is an emerging approach for solving multitask optimization problems (MTOPs) and has garnered considerable research interest. The implicit EMT is a significant research branch that utilizes evolution operators to enable knowledge transfer (KT) between tasks. However, current approaches in implicit EMT face challenges in adaptability, due to the use of a limited number of evolution operators and insufficient utilization of evolutionary states for performing KT. This results in suboptimal exploitation of implicit KT's potential to tackle a variety of MTOPs. To overcome these limitations, we propose a novel Learning to Transfer (L2T) framework to automatically discover efficient KT policies for the MTOPs at hand. Our framework conceptualizes the KT process as a learning agent's sequence of strategic decisions within the EMT process. We propose an action formulation for deciding when and how to transfer, a state representation with informative features of evolution states, a reward formulation concerning convergence and transfer efficiency gain, and the environment for the agent to interact with MTOPs. We employ an actor-critic network structure for the agent and learn it via proximal policy optimization. This learned agent can be integrated with various evolutionary algorithms, enhancing their ability to address a range of new MTOPs. Comprehensive empirical studies on both synthetic and real-world MTOPs, encompassing diverse inter-task relationships, function classes, and task distributions are conducted to validate the proposed L2T framework. The results show a marked improvement in the adaptability and performance of implicit EMT when solving a wide spectrum of unseen MTOPs.
Constrained submodular optimization problems play a key role in the area of combinatorial optimization as they capture many NP-hard optimization problems. So far, Pareto optimization approaches using multi-objective formulations have been shown to be successful to tackle these problems while single-objective formulations lead to difficulties for algorithms such as the $(1+1)$-EA due to the presence of local optima. We introduce for the first time single-objective algorithms that are provably successful for different classes of constrained submodular maximization problems. Our algorithms are variants of the $(1+\lambda)$-EA and $(1+1)$-EA and increase the feasible region of the search space incrementally in order to deal with the considered submodular problems.
The rise of powerful large language models (LLMs) has spurred a new trend in building LLM-based autonomous agents for solving complex tasks, especially multi-agent systems. Despite the remarkable progress, we notice that existing works are heavily dependent on human-designed frameworks, which greatly limits the functional scope and scalability of agent systems. How to automatically extend the specialized agent to multi-agent systems to improve task-solving capability still remains a significant challenge. In this paper, we introduce EvoAgent, a generic method to automatically extend expert agents to multi-agent systems via the evolutionary algorithm, thereby improving the effectiveness of LLM-based agents in solving tasks. Specifically, we consider the existing agent frameworks as the initial individual and then apply a series of evolutionary operators (e.g., mutation, crossover, selection, etc.) to generate multiple agents with diverse agent settings. EvoAgent can be generalized to any LLM-based agent framework, and can automatically extend the existing agent framework to multi-agent systems without any extra human designs. Experimental results across various tasks have shown that EvoAgent can automatically generate multiple expert agents and significantly enhance the task-solving capabilities of LLM-based agents.
Fine-tuning pre-trained language models, particularly large language models, demands extensive computing resources and can result in varying performance outcomes across different domains and datasets. This paper examines the approach of integrating multiple models from diverse training scenarios into a unified model. This unified model excels across various data domains and exhibits the ability to generalize well on out-of-domain data. We propose a knowledge fusion method named Evolver, inspired by evolutionary algorithms, which does not need further training or additional training data. Specifically, our method involves aggregating the weights of different language models into a population and subsequently generating offspring models through mutation and crossover operations. These offspring models are then evaluated against their parents, allowing for the preservation of those models that show enhanced performance on development datasets. Importantly, our model evolving strategy can be seamlessly integrated with existing model merging frameworks, offering a versatile tool for model enhancement. Experimental results on mainstream language models (i.e., encoder-only, decoder-only, encoder-decoder) reveal that Evolver outperforms previous state-of-the-art models by large margins. The code is publicly available at {https://github.com/duguodong7/model-evolution}.
Large Language Models (LLMs) have achieved significant progress across various fields and have exhibited strong potential in evolutionary computation, such as generating new solutions and automating algorithm design. Surrogate-assisted selection is a core step in evolutionary algorithms to solve expensive optimization problems by reducing the number of real evaluations. Traditionally, this has relied on conventional machine learning methods, leveraging historical evaluated evaluations to predict the performance of new solutions. In this work, we propose a novel surrogate model based purely on LLM inference capabilities, eliminating the need for training. Specifically, we formulate model-assisted selection as a classification and regression problem, utilizing LLMs to directly evaluate the quality of new solutions based on historical data. This involves predicting whether a solution is good or bad, or approximating its value. This approach is then integrated into evolutionary algorithms, termed LLM-assisted EA (LAEA). Detailed experiments compared the visualization results of 2D data from 9 mainstream LLMs, as well as their performance on optimization problems. The experimental results demonstrate that LLMs have significant potential as surrogate models in evolutionary computation, achieving performance comparable to traditional surrogate models only using inference. This work offers new insights into the application of LLMs in evolutionary computation. Code is available at: https://github.com/hhyqhh/LAEA.git
This paper presents an interactive platform to interpret multi-objective evolutionary algorithms. Sokoban level generation is selected as a showcase for its widespread use in procedural content generation. By balancing the emptiness and spatial diversity of Sokoban levels, we illustrate the improved two-archive algorithm, Two_Arch2, a well-known multi-objective evolutionary algorithm. Our web-based platform integrates Two_Arch2 into an interface that visually and interactively demonstrates the evolutionary process in real-time. Designed to bridge theoretical optimisation strategies with practical game generation applications, the interface is also accessible to both researchers and beginners to multi-objective evolutionary algorithms or procedural content generation on a website. Through dynamic visualisations and interactive gameplay demonstrations, this web-based platform also has potential as an educational tool.
Representations for black-box optimisation methods (such as evolutionary algorithms) are traditionally constructed using a delicate manual process. This is in contrast to the representation that maps DNAs to phenotypes in biological organisms, which is at the hear of biological complexity and evolvability. Additionally, the core of this process is fundamentally the same across nearly all forms of life, reflecting their shared evolutionary origin. Generative models have shown promise in being learnable representations for black-box optimisation but they are not per se designed to be easily searchable. Here we present a system that can meta-learn such representation by directly optimising for a representation's ability to generate quality-diversity. In more detail, we show our meta-learning approach can find one Neural Cellular Automata, in which cells can attend to different parts of a "DNA" string genome during development, enabling it to grow different solvable 2D maze structures. We show that the evolved genotype-to-phenotype mappings become more and more evolvable, not only resulting in a faster search but also increasing the quality and diversity of grown artefacts.
Multi-objective optimization problems (MOPs) are ubiquitous in real-world applications, presenting a complex challenge of balancing multiple conflicting objectives. Traditional evolutionary algorithms (EAs), though effective, often rely on domain-specific expertise and iterative fine-tuning, hindering adaptability to unseen MOPs. In recent years, the advent of Large Language Models (LLMs) has revolutionized software engineering by enabling the autonomous generation and refinement of programs. Leveraging this breakthrough, we propose a new LLM-based framework that autonomously designs EA operators for solving MOPs. The proposed framework includes a robust testing module to refine the generated EA operator through error-driven dialogue with LLMs, a dynamic selection strategy along with informative prompting-based crossover and mutation to fit textual optimization pipeline. Our approach facilitates the design of EA operators without the extensive demands for expert intervention, thereby speeding up the innovation of EA operators. Empirical studies across various MOP categories validate the robustness and superior performance of our proposed framework.
Network intrusion detection is one of the most important issues in the field of cyber security, and various machine learning techniques have been applied to build intrusion detection systems. However, since the number of features to describe the network connections is often large, where some features are redundant or noisy, feature selection is necessary in such scenarios, which can both improve the efficiency and accuracy. Recently, some researchers focus on using multi-objective evolutionary algorithms (MOEAs) to select features. But usually, they only consider the number of features and classification accuracy as the objectives, resulting in unsatisfactory performance on a critical metric, detection rate. This will lead to the missing of many real attacks and bring huge losses to the network system. In this paper, we propose DR-MOFS to model the feature selection problem in network intrusion detection as a three-objective optimization problem, where the number of features, accuracy and detection rate are optimized simultaneously, and use MOEAs to solve it. Experiments on two popular network intrusion detection datasets NSL-KDD and UNSW-NB15 show that in most cases the proposed method can outperform previous methods, i.e., lead to fewer features, higher accuracy and detection rate.
Gene expression programming is an evolutionary optimization algorithm with the potential to generate interpretable and easily implementable equations for regression problems. Despite knowledge gained from previous optimizations being potentially available, the initial candidate solutions are typically generated randomly at the beginning and often only include features or terms based on preliminary user assumptions. This random initial guess, which lacks constraints on the search space, typically results in higher computational costs in the search for an optimal solution. Meanwhile, transfer learning, a technique to reuse parts of trained models, has been successfully applied to neural networks. However, no generalized strategy for its use exists for symbolic regression in the context of evolutionary algorithms. In this work, we propose an approach for integrating transfer learning with gene expression programming applied to symbolic regression. The constructed framework integrates Natural Language Processing techniques to discern correlations and recurring patterns from equations explored during previous optimizations. This integration facilitates the transfer of acquired knowledge from similar tasks to new ones. Through empirical evaluation of the extended framework across a range of univariate problems from an open database and from the field of computational fluid dynamics, our results affirm that initial solutions derived via a transfer learning mechanism enhance the algorithm's convergence rate towards improved solutions.
This study explores the application of evolutionary generative algorithms in music production to preserve and enhance human creativity. By integrating human feedback into Differential Evolution algorithms, we produced six songs that were submitted to international record labels, all of which received contract offers. In addition to testing the commercial viability of these methods, this paper examines the long-term implications of content generation using traditional machine learning methods compared with evolutionary algorithms. Specifically, as current generative techniques continue to scale, the potential for computer-generated content to outpace human creation becomes likely. This trend poses a risk of exhausting the pool of human-created training data, potentially forcing generative machine learning models to increasingly depend on their random input functions for generating novel content. In contrast to a future of content generation guided by aimless random functions, our approach allows for individualized creative exploration, ensuring that computer-assisted content generation methods are human-centric and culturally relevant through time.
Evolutionary algorithms, rooted in Darwin's theorem, can be considered as a base for implementing deep/machine learning models. This approach can noticeably increase the accuracy in most cases as shown in this paper. This experiment aims to evaluate the performance of two evolutionary algorithms, an evolutionary neural network (ENN) and an evolutionary CNN-based algorithm with mutation and crossover (ECNNB), on the Fashion-MNIST, MNIST, and EMNIST_Digits datasets. The performance of the ENN algorithm is examined for 10, 50, and 100 generations, with 50 generations being used due to computational limitations. The results show that the accuracy of the model improves as the number of generations increases. However, the ECNNB model consistently outperforms the ENN model on all three datasets, with an average accuracy of 92.58% on Fashion-MNIST, 99.32% on MNIST, and 99.50% on EMNIST_Digits, compared to 88.54 %, 98.05 %, and 98.95 %, respectively, for the ENN model. The performance of both models is compared with other state-of-the-art models in the literature. These results highlight the significance of well-designed models in achieving high accuracy in machine learning tasks.
From the formation of snowflakes to the evolution of diverse life forms, emergence is ubiquitous in our universe. In the quest to understand how complexity can arise from simple rules, abstract computational models, such as cellular automata, have been developed to study self-organization. However, the discovery of self-organizing patterns in artificial systems is challenging and has largely relied on manual or semi-automatic search in the past. In this paper, we show that Quality-Diversity, a family of Evolutionary Algorithms, is an effective framework for the automatic discovery of diverse self-organizing patterns in complex systems. Quality-Diversity algorithms aim to evolve a large population of diverse individuals, each adapted to its ecological niche. Combined with Lenia, a family of continuous cellular automata, we demonstrate that our method is able to evolve a diverse population of lifelike self-organizing autonomous patterns. Our framework, called Leniabreeder, can leverage both manually defined diversity criteria to guide the search toward interesting areas, as well as unsupervised measures of diversity to broaden the scope of discoverable patterns. We demonstrate both qualitatively and quantitatively that Leniabreeder offers a powerful solution for discovering self-organizing patterns. The effectiveness of unsupervised Quality-Diversity methods combined with the rich landscape of Lenia exhibits a sustained generation of diversity and complexity characteristic of biological evolution. We provide empirical evidence that suggests unbounded diversity and argue that Leniabreeder is a step toward replicating open-ended evolution in silico.
In the real world, there exist a class of optimization problems that multiple (local) optimal solutions in the solution space correspond to a single point in the objective space. In this paper, we theoretically show that for such multimodal problems, a simple method that considers the diversity of solutions in the solution space can benefit the search in evolutionary algorithms (EAs). Specifically, we prove that the proposed method, working with crossover, can help enhance the exploration, leading to polynomial or even exponential acceleration on the expected running time. This result is derived by rigorous running time analysis in both single-objective and multi-objective scenarios, including $(\mu+1)$-GA solving the widely studied single-objective problem, Jump, and NSGA-II and SMS-EMOA (two well-established multi-objective EAs) solving the widely studied bi-objective problem, OneJumpZeroJump. Experiments are also conducted to validate the theoretical results. We hope that our results may encourage the exploration of diversity maintenance in the solution space for multi-objective optimization, where existing EAs usually only consider the diversity in the objective space and can easily be trapped in local optima.
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex multiscale or hierarchical strucutre. While MMF promises to yields a useful wavelet basis, finding the factorization itself is hard, and existing greedy methods tend to be brittle. In this paper, we propose a ``learnable'' version of MMF that carfully optimizes the factorization using metaheuristics, specifically evolutionary algorithms and directed evolution, along with Stiefel manifold optimization through backpropagating errors. We show that the resulting wavelet basis far outperforms prior MMF algorithms and gives comparable performance on standard learning tasks on graphs. Furthermore, we construct the wavelet neural networks (WNNs) learning graphs on the spectral domain with the wavelet basis produced by our MMF learning algorithm. Our wavelet networks are competitive against other state-of-the-art methods in molecular graphs classification and node classification on citation graphs. We release our implementation at https://github.com/HySonLab/LearnMMF
In the area of multi-objective evolutionary algorithms (MOEAs), there is a trend of using an archive to store non-dominated solutions generated during the search. This is because 1) MOEAs may easily end up with the final population containing inferior solutions that are dominated by other solutions discarded during the search process and 2) the population that has a commensurable size of the problem's Pareto front is often not practical. In this paper, we theoretically show, for the first time, that using an archive can guarantee speed-ups for MOEAs. Specifically, we prove that for two well-established MOEAs (NSGA-II and SMS-EMOA) on two commonly studied problems (OneMinMax and LeadingOnesTrailingZeroes), using an archive brings a polynomial acceleration on the expected running time. The reason is that with an archive, the size of the population can reduce to a small constant; there is no need for the population to keep all the Pareto optimal solutions found. This contrasts existing theoretical studies for MOEAs where a population with a commensurable size of the problem's Pareto front is needed. The findings in this paper not only provide a theoretical confirmation for an increasingly popular practice in the design of MOEAs, but can also be beneficial to the theory community towards studying more practical MOEAs.
The problem of finding the optimal placement of emergency exits in an indoor environment to facilitate the rapid and orderly evacuation of crowds is addressed in this work. A cellular-automaton model is used to simulate the behavior of pedestrians in such scenarios, taking into account factors such as the environment, the pedestrians themselves, and the interactions among them. A metric is proposed to determine how successful or satisfactory an evacuation was. Subsequently, two metaheuristic algorithms, namely an iterated greedy heuristic and an evolutionary algorithm (EA) are proposed to solve the optimization problem. A comparative analysis shows that the proposed EA is able to find effective solutions for different scenarios, and that an island-based version of it outperforms the other two algorithms in terms of solution quality.