Many practical problems involve multiple interdependent agents, each aiming to optimize its own objectives. Wargame strategy optimization, which requires optimizing strategies for at least two agents—attackers and defenders—presents unique challenges due to the interdependence of the agents’ strategies. This characteristic necessitates a co-evolutionary approach, where each agent’s strategy is continually adjusted in response to the other’s. The complexity increases when each agent pursues multiple conflicting objectives, resulting in Pareto-optimal strategy sets that require sequential decision-making (DM). To address these challenges, we introduce a novel multi-objective competitive co-evolutionary optimization (MoCCoEv) framework, specifically tailored for wargame strategy optimization. This framework integrates regularity-based search with an iterative and interactive DM approach, fostering a continuous interplay between co-evolving agents. Additionally, we introduce the concept of progressive shrinking, which interactively reduces the dimensions of the agents’ strategy parameters to mirror real-world decision-making by enforcing commitment to earlier moves and facilitating effective strategic choices. Our flexible and adaptable framework also supports alternative strategies, such as deception, and can be applied to other multi-agent optimization problems.

In many practical problem-solving tasks, instead of a single desired solution, often the goal is to find multiple alternate solutions (optimal or otherwise). In such tasks, most often, numerical methods are employed to find one solution at a time by making the desired solution the focus of the ensuing computational task. On the other hand, evolutionary multi-objective optimization (EMO) algorithms – population-based computational procedures – have demonstrated their ability to find multiple optimal solutions resulting from optimizing two or more conflicting objectives simultaneously. In this paper, we highlight the principles of an EMO procedure and discuss how it can be extended to find multiple alternate solutions for a number of different problem-solving tasks encountered in practice. This ‘multiobjectivization’ task requires researchers to choose at least two conflicting goals arising from the specific problem-solving task and apply a suitably modified version of an existing EMO algorithm to find multiple alternate solutions. These extensions broaden EMO research and its applications, and also enable a unified approach for solving various practical problem-solving tasks.

Wargame strategy optimization involves two competing agents—offense and defense—and requires extensive simulations of wargame tools, resulting in high computational costs for evaluating potential strategies. To reduce these costs, surrogate models are employed to approximate the objective functions, with their accuracy directly affecting the optimization process. This paper proposes a novel framework for progressive surrogate modeling to improve the quality of surrogate models while addressing the wargame strategy optimization problem. Our approach utilizes a Multi-objective Competitive Co-Evolutionary (MoCCoEv) algorithm, which iteratively refines the surrogate models. The process begins by using MoCCoEv algorithm to optimize wargame strategies generating new strategies. The new strategies are then replaced in the training data to update and improve the surrogate models. This cyclical process ensures that the models are continuously refined in the regions of interest, leading to more accurate predictions and enhanced optimization results.

The goal of a generic evolutionary multi- or many-objective algorithm is to explore a search space and find the trade-off optimal solutions for two or more conflicting objectives. In platform-based practical design optimization problems, it is not sufficient to just find a set of trade-off optimal solutions, certain regularity properties are expected in the entire fleet of trade-off solutions. For this purpose, we propose a scalable regularity-based optimization framework - RegEM(a)O - which automatically extracts polynomial regularity principles from the resulting Pareto-optimal front of multi- or many-objective problems. Thereafter, it attempts to search for a regular front of trade-off solutions following a similar form of polynomial regularity principles. Despite being slightly worse than the true Pareto-optimal solutions, regular solutions possess simple properties among them, making them easily interpretable, their inventory easily maintainable, and easily scalable. In this paper, we apply RegEM(a)O to a number of small and large-scale real-world engineering design problems to demonstrate its practical advantage.

Multi-objective optimization problems give rise to a set of Pareto-optimal solutions, each of which makes a trade-off among the objectives. When multiple Pareto-optimal solutions are to be implemented for different applications as platform-based solutions, a solution principle common to them is highly desired for easier understanding, implementation, and management purposes. In this paper, we propose a systematic search methodology that deviates from finding Pareto-optimal solutions, but finds a set of near Pareto-optimal solutions sharing common principles of a desired structure and still possessing a trade-off among objectives. After proposing the regular evolutionary multi-objective optimization (RegEMO) algorithm, we first demonstrate its working principle on a number of constrained and unconstrained multi-objective test problems. Thereafter, we demonstrate the practical significance of the proposed approach to a number of engineering design problems. Searching for a set of solutions with common principles of desire, rather than theoretical Pareto-optimal solutions without any common structure, is a practically meaningful task and this paper should encourage more such practice-oriented developments of EMO in the near future.

Automated machine learning (AutoML) greatly eases human efforts in architecture engineering. However, mainstream AutoML methods like neural architecture search (NAS) are customized for well-designed search spaces wherein promising architectures are densely distributed. In contrast, AutoML-Zero builds machine-learning algorithms using basic primitives and can explore novel architectures beyond human knowledge. AutoML-Zero shows the potential to deploy machine learning systems by not taking advantage of either feature engineering or architectural engineering. In its current form, it only optimizes a single objective like accuracy and has no mechanism to ensure that the constraints of real-world applications are satisfied. We propose a multi-objective variant of AutoML-Zero called MOAZ, that distributes solutions on a Pareto front by trading off accuracy against the computational complexity of the machine learning algorithm. In addition to generating different Pareto-optimal solutions, MOAZ can effectively explore the sparse search space to improve search efficiency. Experimental results on linear regression tasks show MOAZ reduces the median complexity by 87.4% compared to AutoML-Zero while accelerating the median target performance achievement speed by 82%. In addition, our preliminary results on non-linear regression tasks show the potential for further improvements in search accuracy and for reducing the need for human intervention in AutoML.

Autonomous robots deployed in the real world will need control policies that rapidly adapt to environmental changes. To this end, we propose AutoRobotics-Zero (ARZ), a method based on AutoML-Zero that discovers zero-shot adaptable policies from scratch. In contrast to neural network adaption policies, where only model parameters are optimized, ARZ can build control algorithms with the full expressive power of a linear register machine. We evolve modular policies that tune their model parameters and alter their inference algorithm on-the-fly to adapt to sudden environmental changes. We demonstrate our method on a realistic simulated quadruped robot, for which we evolve safe control policies that avoid falling when individual limbs suddenly break. This is a challenging task in which two popular neural network baselines fail. Finally, we conduct a detailed analysis of our method on a novel and challenging non-stationary control task dubbed Cataclysmic Cartpole. Results confirm our findings that ARZ is significantly more robust to sudden environmental changes and can build simple, interpretable control policies.