The advent of large language models (LLMs) such as ChatGPT has attracted considerable attention in various domains due to their remarkable performance and versatility. As the use of these models continues to grow, the importance of effective prompt engineering has come to the fore. Prompt optimization emerges as a crucial challenge, as it has a direct impact on model performance and the extraction of relevant information. Recently, evolutionary algorithms (EAs) have shown promise in addressing this issue, paving the way for novel optimization strategies. In this work, we propose a evolutionary multi-objective (EMO) approach specifically tailored for prompt optimization called EMO-Prompts, using sentiment analysis as a case study. We use sentiment analysis capabilities as our experimental targets. Our results demonstrate that EMO-Prompts effectively generates prompts capable of guiding the LLM to produce texts embodying two conflicting emotions simultaneously.
A hallmark of intelligence is the ability to exhibit a wide range of effective behaviors. Inspired by this principle, Quality-Diversity algorithms, such as MAP-Elites, are evolutionary methods designed to generate a set of diverse and high-fitness solutions. However, as a genetic algorithm, MAP-Elites relies on random mutations, which can become inefficient in high-dimensional search spaces, thus limiting its scalability to more complex domains, such as learning to control agents directly from high-dimensional inputs. To address this limitation, advanced methods like PGA-MAP-Elites and DCG-MAP-Elites have been developed, which combine actor-critic techniques from Reinforcement Learning with MAP-Elites, significantly enhancing the performance and efficiency of Quality-Diversity algorithms in complex, high-dimensional tasks. While these methods have successfully leveraged the trained critic to guide more effective mutations, the potential of the trained actor remains underutilized in improving both the quality and diversity of the evolved population. In this work, we introduce DCRL-MAP-Elites, an extension of DCG-MAP-Elites that utilizes the descriptor-conditioned actor as a generative model to produce diverse solutions, which are then injected into the offspring batch at each generation. Additionally, we present an empirical analysis of the fitness and descriptor reproducibility of the solutions discovered by each algorithm. Finally, we present a second empirical analysis shedding light on the synergies between the different variations operators and explaining the performance improvement from PGA-MAP-Elites to DCRL-MAP-Elites.
In recent years, the emergence of the first quantum computers at a time when AI is undergoing a fruitful era has led many AI researchers to be tempted into adapting their algorithms to run on a quantum computer. However, in many cases the initial enthusiasm has ended in frustration, since the features and principles underlying quantum computing are very different from traditional computers. In this paper, we present a discussion of the difficulties arising when designing a quantum version of an evolutionary algorithm based on Darwin's evolutionary mechanism, the so-called genetic algorithms. The paper includes the code in both Python and QISKIT of the quantum version of one of these evolutionary algorithms allowing the reader to experience the setbacks arising when translating a classical algorithm to its quantum version. The algorithm studied in this paper, termed RQGA (Reduced Quantum Genetic Algorithm), has been chosen as an example that clearly shows these difficulties, which are common to other AI algorithms.
Multimodal optimization is often encountered in engineering problems, especially when different and alternative solutions are sought. Evolutionary algorithms can efficiently tackle multimodal optimization thanks to their features such as the concept of population, exploration/exploitation, and being suitable for parallel computation. This paper investigates whether a less-known optimizer, the Big Bang-Big Crunch (BBBC) algorithm, is suitable for multimodal optimization. We extended BBBC and propose k-BBBC, a clustering-based multi-modal optimizer. Additionally, we introduce two post-processing methods to (i) identify the local optima in a set of retrieved solutions (i.e., a population), and (ii) quantify the number of correctly retrieved optima against the expected ones (i.e., success rate). Our results show that k-BBBC performs well even with problems having a large number of optima (tested on $379$ optima) and high dimensionality (tested on $32$ decision variables), but it becomes computationally too expensive for problems with many local optima (i.e., in the CEC'2013 benchmark set). Compared to other multimodal optimization methods, it outperforms them in terms of accuracy (in both search and objective space) and success rate (number of correctly retrieved optima) when tested on basic multimodal functions, especially when elitism is applied; however, it requires knowing the number of optima of a problem, which makes its performance decrease when tested on niching competition test CEC'2013. Lastly, we validated our proposed post-processing methods by comparing their success rate to the actual one: results suggest that these methods can be used to evaluate the performance of a multimodal optimization algorithm by correctly identifying optima and providing an indication of success -- without the need to know where the optima are located in the search space.
In this paper, we scale evolutionary algorithms to high-dimensional optimization problems that deceptively possess a low effective dimensionality (certain dimensions do not significantly affect the objective function). To this end, an instantiation of the multiform optimization paradigm is presented, where multiple low-dimensional counterparts of a target high-dimensional task are generated via random embeddings. Since the exact relationship between the auxiliary (low-dimensional) tasks and the target is a priori unknown, a multiform evolutionary algorithm is developed for unifying all formulations into a single multi-task setting. The resultant joint optimization enables the target task to efficiently reuse solutions evolved across various low-dimensional searches via cross-form genetic transfers, hence speeding up overall convergence characteristics. To validate the overall efficacy of our proposed algorithmic framework, comprehensive experimental studies are carried out on well-known continuous benchmark functions as well as a set of practical problems in the hyper-parameter tuning of machine learning models and deep learning models in classification tasks and Predator-Prey games, respectively.
We present a tool for exploring the design space of shaders using an interactive evolutionary algorithm integrated with the Unity editor, a well-known commercial tool for video game development. Our framework leverages the underlying graph-based representation of recent shader editors and interactive evolution to allow designers to explore several visual options starting from an existing shader. Our framework encodes the graph representation of a current shader as a chromosome used to seed the evolution of a shader population. It applies graph-based recombination and mutation with a set of heuristics to create feasible shaders. The framework is an extension of the Unity editor; thus, designers with little knowledge of evolutionary computation (and shader programming) can interact with the underlying evolutionary engine using the same visual interface used for working on game scenes.
Computational cost in metaheuristics such as Evolutionary Algorithms (EAs) is often a major concern, particularly with their ability to scale. In data-based training, traditional EAs typically use a significant portion, if not all, of the dataset for model training and fitness evaluation in each generation. This makes EAs suffer from high computational costs incurred during the fitness evaluation of the population, particularly when working with large datasets. To mitigate this issue, we propose a Machine Learning (ML)-driven Distance-based Selection (DBS) algorithm that reduces the fitness evaluation time by optimizing test cases. We test our algorithm by applying it to 24 benchmark problems from Symbolic Regression (SR) and digital circuit domains and then using Grammatical Evolution (GE) to train models using the reduced dataset. We use GE to test DBS on SR and produce a system flexible enough to test it on digital circuit problems further. The quality of the solutions is tested and compared against the conventional training method to measure the coverage of training data selected using DBS, i.e., how well the subset matches the statistical properties of the entire dataset. Moreover, the effect of optimized training data on run time and the effective size of the evolved solutions is analyzed. Experimental and statistical evaluations of the results show our method empowered GE to yield superior or comparable solutions to the baseline (using the full datasets) with smaller sizes and demonstrates computational efficiency in terms of speed.
In mineral processing plants, grinding is a crucial step, accounting for approximately 50 percent of the total mineral processing costs. Semi-autogenous grinding mills are extensively employed in the grinding circuit of mineral processing plants. Maximizing SAG mill throughput is of significant importance considering its profound financial outcomes. However, the optimum process parameter setting aimed at achieving maximum mill throughput remains an uninvestigated domain in prior research. This study introduces a hybrid intelligent framework leveraging expert knowledge, machine learning techniques, and evolutionary algorithms to address this research need. In this study, we utilize an extensive industrial dataset comprising 36743 records and select relevant features based on the insights of industry experts. Following the removal of erroneous data, a comprehensive evaluation of 17 diverse machine learning models is undertaken to identify the most accurate predictive model. To improve the model performance, feature selection and outlier detection are executed. The resultant optimal model, trained with refined features, serves as the objective function within three distinct evolutionary algorithms. These algorithms are employed to identify parameter configurations that maximize SAG mill throughput while adhering to the working limits of input parameters as constraints. Notably, our analysis revealed that CatBoost, as an ensemble model, stands out as the most accurate predictor. Furthermore, differential evolution emerges as the preferred optimization algorithm, exhibiting superior performance in both achieving the highest mill throughput predictions and ensuring robustness in predictions, surpassing alternative methods.
In the article, within the framework of the Boolean Satisfiability problem (SAT), the problem of estimating the hardness of specific Boolean formulas w.r.t. a specific complete SAT solving algorithm is considered. Based on the well-known Strong Backdoor Set (SBS) concept, we introduce the notion of decomposition hardness (d-hardness). If $B$ is an arbitrary subset of the set of variables occurring in a SAT formula $C$, and $A$ is an arbitrary complete SAT solver , then the d-hardness expresses an estimate of the hardness of $C$ w.r.t. $A$ and $B$. We show that the d-hardness of $C$ w.r.t. a particular $B$ can be expressed in terms of the expected value of a special random variable associated with $A$, $B$, and $C$. For its computational evaluation, algorithms based on the Monte Carlo method can be used. The problem of finding $B$ with the minimum value of d-hardness is formulated as an optimization problem for a pseudo-Boolean function whose values are calculated as a result of a probabilistic experiment. To minimize this function, we use evolutionary algorithms. In the experimental part, we demonstrate the applicability of the concept of d-hardness and the methods of its estimation to solving hard unsatisfiable SAT instances.
The landscapes of real-world optimization problems can vary strongly depending on the application. In engineering design optimization, objective functions and constraints are often derived from governing equations, resulting in moderate multimodality. However, benchmark problems with such moderate multimodality are typically confined to low-dimensional cases, making it challenging to conduct meaningful comparisons. To address this, we present a benchmark test suite focused on the design of human-powered aircraft for single and multi-objective optimization. This test suite incorporates governing equations from aerodynamics and material mechanics, providing a realistic testing environment. It includes 60 problems across three difficulty levels, with a wing segmentation parameter to scale complexity and dimensionality. Both constrained and unconstrained versions are provided, with penalty methods applied to the unconstrained version. The test suite is computationally inexpensive while retaining key characteristics of engineering problems. Numerical experiments indicate the presence of moderate multimodality, and multi-objective problems exhibit diverse Pareto front shapes.
Evolutionary multitasking (EMT) has emerged as a popular topic of evolutionary computation over the past decade. It aims to concurrently address multiple optimization tasks within limited computing resources, leveraging inter-task knowledge transfer techniques. Despite the abundance of multitask evolutionary algorithms (MTEAs) proposed for multitask optimization (MTO), there remains a comprehensive software platform to help researchers evaluate MTEA performance on benchmark MTO problems as well as explore real-world applications. To bridge this gap, we introduce the first open-source optimization platform, named MTO-Platform (MToP), for EMT. MToP incorporates over 50 MTEAs, more than 200 MTO problem cases with real-world applications, and {over 20 performance metrics}. Moreover, to facilitate comparative analyses between MTEAs and traditional evolutionary algorithms, we adapted over 50 popular single-task evolutionary algorithms to address MTO problems. MToP boasts a user-friendly graphical interface, facilitating results analysis, data export, and schematics visualization. More importantly, MToP is designed with extensibility in mind, allowing users to develop new algorithms and tackle emerging problem domains. The source code of MToP is available at https://github.com/intLyc/MTO-Platform.
Multi-objective optimization problems (MOPs) necessitate the simultaneous optimization of multiple objectives. Numerous studies have demonstrated that evolutionary computation is a promising paradigm for solving complex MOPs, which involve optimization problems with large-scale decision variables, many objectives, and expensive evaluation functions. However, existing multi-objective evolutionary algorithms (MOEAs) encounter significant challenges in generating high-quality populations when solving diverse complex MOPs. Specifically, the distinct requirements and constraints of the population result in the inefficiency or even incompetence of MOEAs in addressing various complex MOPs. Therefore, this paper proposes the concept of pre-evolving for MOEAs to generate high-quality populations for diverse complex MOPs. Drawing inspiration from the classical transformer architecture, we devise dimension embedding and objective encoding techniques to configure the pre-evolved model (PEM). The PEM is pre-evolved on a substantial number of existing MOPs. Subsequently, when fine-evolving on new complex MOPs, the PEM transforms the population into the next generation to approximate the Pareto-optimal front. Furthermore, it utilizes evaluations on new solutions to iteratively update the PEM for subsequent generations, thereby efficiently solving various complex MOPs. Experimental results demonstrate that the PEM outperforms state-of-the-art MOEAs on a range of complex MOPs.
We present DARLEI, a framework that combines evolutionary algorithms with parallelized reinforcement learning for efficiently training and evolving populations of UNIMAL agents. Our approach utilizes Proximal Policy Optimization (PPO) for individual agent learning and pairs it with a tournament selection-based generational learning mechanism to foster morphological evolution. By building on Nvidia's Isaac Gym, DARLEI leverages GPU accelerated simulation to achieve over 20x speedup using just a single workstation, compared to previous work which required large distributed CPU clusters. We systematically characterize DARLEI's performance under various conditions, revealing factors impacting diversity of evolved morphologies. For example, by enabling inter-agent collisions within the simulator, we find that we can simulate some multi-agent interactions between the same morphology, and see how it influences individual agent capabilities and long-term evolutionary adaptation. While current results demonstrate limited diversity across generations, we hope to extend DARLEI in future work to include interactions between diverse morphologies in richer environments, and create a platform that allows for coevolving populations and investigating emergent behaviours in them. Our source code is also made publicly at https://saeejithnair.github.io/darlei.
Pointer Network (PtrNet) is a specific neural network for solving Combinatorial Optimization Problems (COPs). While PtrNets offer real-time feed-forward inference for complex COPs instances, its quality of the results tends to be less satisfactory. One possible reason is that such issue suffers from the lack of global search ability of the gradient descent, which is frequently employed in traditional PtrNet training methods including both supervised learning and reinforcement learning. To improve the performance of PtrNet, this paper delves deeply into the advantages of training PtrNet with Evolutionary Algorithms (EAs), which have been widely acknowledged for not easily getting trapped by local optima. Extensive empirical studies based on the Travelling Salesman Problem (TSP) have been conducted. Results demonstrate that PtrNet trained with EA can consistently perform much better inference results than eight state-of-the-art methods on various problem scales. Compared with gradient descent based PtrNet training methods, EA achieves up to 30.21\% improvement in quality of the solution with the same computational time. With this advantage, this paper is able to at the first time report the results of solving 1000-dimensional TSPs by training a PtrNet on the same dimensionality, which strongly suggests that scaling up the training instances is in need to improve the performance of PtrNet on solving higher-dimensional COPs.
Evolutionary algorithms face significant challenges when dealing with dynamic multi-objective optimization because Pareto optimal solutions and/or Pareto optimal fronts change. This paper proposes a unified paradigm, which combines the kernelized autoncoding evolutionary search and the centriod-based prediction (denoted by KAEP), for solving dynamic multi-objective optimization problems (DMOPs). Specifically, whenever a change is detected, KAEP reacts effectively to it by generating two subpopulations. The first subpoulation is generated by a simple centriod-based prediction strategy. For the second initial subpopulation, the kernel autoencoder is derived to predict the moving of the Pareto-optimal solutions based on the historical elite solutions. In this way, an initial population is predicted by the proposed combination strategies with good convergence and diversity, which can be effective for solving DMOPs. The performance of our proposed method is compared with five state-of-the-art algorithms on a number of complex benchmark problems. Empirical results fully demonstrate the superiority of our proposed method on most test instances.
Protein structure prediction (PSP) is predicting the three-dimensional of protein from its amino acid sequence only based on the information hidden in the protein sequence. One of the efficient tools to describe this information is protein energy functions. Despite the advancements in biology and computer science, PSP is still a challenging problem due to its large protein conformation space and inaccurate energy functions. In this study, PSP is treated as a many-objective optimization problem and four conflicting energy functions are used as different objectives to be optimized. A novel Pareto-dominance-archive and Coordinated-selection-strategy-based Many-objective-optimizer (PCM) is proposed to perform the conformation search. In it, convergence and diversity-based selection metrics are used to enable PCM to find near-native proteins with well-distributed energy values, while a Pareto-dominance-based archive is proposed to save more potential conformations that can guide the search to more promising conformation areas. The experimental results on thirty-four benchmark proteins demonstrate the significant superiority of PCM in comparison with other single, multiple, and many-objective evolutionary algorithms. Additionally, the inherent characteristics of iterative search of PCM can also give more insights into the dynamic progress of protein folding besides the final predicted static tertiary structure. All these confirm that PCM is a fast, easy-to-use, and fruitful solution generation method for PSP.
In a multi objective setting, a portfolio manager's highly consequential decisions can benefit from assessing alternative forecasting models of stock index movement. The present investigation proposes a new approach to identify a set of nondominated neural network models for further selection by the decision maker. A new coevolution approach is proposed to simultaneously select the features and topology of neural networks (collectively referred to as neural architecture), where the features are viewed from a topological perspective as input neurons. Further, the coevolution is posed as a multicriteria problem to evolve sparse and efficacious neural architectures. The well known dominance and decomposition based multiobjective evolutionary algorithms are augmented with a nongeometric crossover operator to diversify and balance the search for neural architectures across conflicting criteria. Moreover, the coevolution is augmented to accommodate the data based implications of distinct market behaviors prior to and during the ongoing COVID 19 pandemic. A detailed comparative evaluation is carried out with the conventional sequential approach of feature selection followed by neural topology design, as well as a scalarized coevolution approach. The results on the NASDAQ index in pre and peri COVID time windows convincingly demonstrate that the proposed coevolution approach can evolve a set of nondominated neural forecasting models with better generalization capabilities.
There are many combinatorial optimization problems whose solutions are best represented by permutations. The classic traveling salesperson seeks an optimal ordering over a set of cities. Scheduling problems often seek optimal orderings of tasks or activities. Although some evolutionary approaches to such problems utilize the bit strings of a genetic algorithm, it is more common to directly represent solutions with permutations. Evolving permutations directly requires specialized evolutionary operators. Over the years, many crossover and mutation operators have been developed for solving permutation problems with evolutionary algorithms. In this paper, we survey the breadth of evolutionary operators for permutations. We implemented all of these in Chips-n-Salsa, an open source Java library for evolutionary computation. Finally, we empirically analyze the crossover operators on artificial fitness landscapes isolating different permutation features.
Optimization problems find widespread use in both single-objective and multi-objective scenarios. In practical applications, users aspire for solutions that converge to the region of interest (ROI) along the Pareto front (PF). While the conventional approach involves approximating a fitness function or an objective function to reflect user preferences, this paper explores an alternative avenue. Specifically, we aim to discover a method that sidesteps the need for calculating the fitness function, relying solely on human feedback. Our proposed approach entails conducting direct preference learning facilitated by an active dueling bandit algorithm. The experimental phase is structured into three sessions. Firstly, we assess the performance of our active dueling bandit algorithm. Secondly, we implement our proposed method within the context of Multi-objective Evolutionary Algorithms (MOEAs). Finally, we deploy our method in a practical problem, specifically in protein structure prediction (PSP). This research presents a novel interactive preference-based MOEA framework that not only addresses the limitations of traditional techniques but also unveils new possibilities for optimization problems.
Bent Boolean functions are important objects in cryptography and coding theory, and there are several general approaches for constructing such functions. Metaheuristics proved to be a strong choice as they can provide many bent functions, even when the size of the Boolean function is large (e.g., more than 20 inputs). While bent Boolean functions represent only a small part of all Boolean functions, there are several subclasses of bent functions providing specific properties and challenges. One of the most interesting subclasses comprises (anti-)self-dual bent Boolean functions. This paper provides a detailed experimentation with evolutionary algorithms with the goal of evolving (anti-)self-dual bent Boolean functions. We experiment with two encodings and two fitness functions to directly evolve self-dual bent Boolean functions. Our experiments consider Boolean functions with sizes of up to 16 inputs, and we successfully construct self-dual bent functions for each dimension. Moreover, when comparing with the evolution of bent Boolean functions, we notice that the difficulty for evolutionary algorithms is rather similar. Finally, we also tried evolving secondary constructions for self-dual bent functions, but this direction provided no successful results.