The generation of motion behaviors plays a pivotal role in constructing effective simulated scenarios for testing autonomous driving systems (ADSs). The controllability (i.e., the ability to synthesize specific motion patterns) and multimodality (i.e., the capacity to represent multiple motion intentions) of generated motion behaviors are essential for the purposeful and comprehensive evaluation of ADS. Although recent studies have made progress in either multimodal or controllable motion behavior generation, it remains a major challenge to simultaneously generate multimodal motion behaviors in a controllable manner. In this work, we propose a unified framework, CoMoGen, to generate multimodal motion behaviors in a controllable manner under open-loop evaluation assumption. The proposed framework consists of three core components: i) a learning-based vehicle placer, responsible for positioning generated vehicles in non-conflicting initial locations; ii) a robust model-based trajectory candidate generator, capable of synthesizing controllable and multimodal trajectory candidates. iii) a learning-based trajectory selector, developed to evaluate and select multimodal trajectories for the placed vehicles. Experiments on the INTERACTION dataset demonstrate strong controllability and multimodality of CoMoGen. Further experiments on three additional real-world datasets, that are unseen during training, as well as on diverse synthesized high-definition maps, validate the remarkable generalization capability of CoMoGen.

Meta-Black-Box Optimization (MetaBBO) garners attention due to its success in automating the configuration and generation of black-box optimizers, significantly reducing the human effort required for optimizer design and discovering optimizers with higher performance than classic human-designed optimizers. However, existing MetaBBO methods conduct one-off training under the assumption that a stationary problem distribution with extensive and representative training problem samples is pre-available. This assumption is often impractical in real-world scenarios, where diverse problems following shifting distribution continually arise. Consequently, there is a pressing need for methods that can continuously learn from new problems encountered on-the-fly and progressively enhance their capabilities. In this work, we explore a novel paradigm of lifelong learning in MetaBBO and introduce LiBOG, a novel approach designed to learn from sequentially encountered problems and generate high-performance optimizers for Black-Box Optimization (BBO). LiBOG consolidates knowledge both across tasks and within tasks to mitigate catastrophic forgetting. Extensive experiments demonstrate LiBOG's effectiveness in learning to generate high-performance optimizers in a lifelong learning manner, addressing catastrophic forgetting while maintaining plasticity to learn new tasks.

This paper comprehensively reviews the metrics for measuring the diversity of game scenarios, spotlighting the innovative use of procedural content generation and other fields as cornerstones for enriching player experiences through diverse game scenarios. By traversing a wide array of disciplines, from affective modeling and multiagent systems to psychological studies, our research underscores the importance of diverse game scenarios in gameplay and education. Through a taxonomy of diversity metrics and evaluation methods, we aim to bridge the current gaps in literature and practice, offering insights into effective strategies for measuring and integrating diversity in game scenarios. Our analysis highlights the necessity for a unified taxonomy to aid developers and researchers in crafting more engaging and varied game worlds. This survey not only charts a path for future research in diverse game scenarios but also serves as a handbook for industry practitioners seeking to leverage diversity as a key component of game design and development.

The computational modeling of player experience is key to the generation of personalized game content. The notion offun, as one of the most peculiar and core aspects of game experience, has often been modeled and quantified for the purpose of content generation with varying success. Recently, measures of a player'sfunhave been ad-hoc designed to model moderate levels of in-game divergence in platformer games, inspired by Koster'stheory of fun. Such measures have shaped the reward functions of game content generative methods following theexperience-driven procedural content generation via reinforcement learning(EDRL) paradigm inSuper Mario BrosIn this article, we present a comprehensive user study involving over 90 participants with a dual purpose: to evaluate the ad-hocfunmetrics introduced in the literature and test the effectiveness of the EDRL framework to generate personalizedfunSuper Mario Brosexperiences in an online fashion. Our key findings suggest that moderate degrees of game level and gameplay divergence are highly consistent with the perceived notion offunof our participants, cross-verifying the ad-hoc designedfunmetrics. On the other hand, it appears that EDRL generators manage to match the preferred (i.e.,fun) game experiences of each persona, only in part and for some players. Our findings suggest that the use of multifaceted in-game data, such as events and actions, will likely enable the modeling of more nuanced gameplay behaviors. In addition, the verification of player persona modeling and the enhancement of player engagement through dynamic experience modelling are suggested as potential future directions.

Traveling salesman problem (TSP) is a combinatorial optimization problem, serving as basis for many real-world applications (e.g., transportation planning, circuit board design, and DNA sequencing). In TSP, it is common to encounter some dynamic events, for example, traffic jam, and roadworks in transportation planning. To deal with such dynamic TSP (DTSP) scenarios, numerous techniques have been designed over decades. In this article, we take a different perspective to study DTSP. Instead of focusing only on algorithm design for DTSP, we investigate how dynamic events in DTSP affect its fitness landscape (e.g., the location of local optimal solutions and the ruggedness level of search space). We consider three dynamic events, including node addition, node deletion and weight changes, and analyze how they affect the TSP with respect to the overall landscape structure and solution optimality. Experimental results show that the weight change event has great effect on the problem’s fitness landscape, introducing more local optima and reducing the basin of attraction for the global optimum. This may suggest that search algorithms need to have stronger exploration capability when handling weight change dynamic events. Furthermore, our experimental studies also demonstrate that the dynamic solution adaptation strategy on the original global optimum is effective for tracking the new optimum after dynamic changes.

Multiobjective evolutionary learning (MOEL) has demonstrated its advantages of training fairer machine learning models considering a predefined set of conflicting objectives, including accuracy and different fairness measures. Recent works propose to construct a representative subset of fairness measures as optimization objectives of MOEL throughout model training. However, the determination of a representative measure set relies on the dataset, prior knowledge, and requires substantial computational costs. What is more, those representative measures may differ across different model training processes. Instead of using a static predefined set determined before model training, this article proposes to dynamically and adaptively determine a representative measure set online during the model training. The dynamically determined representative set is then used as optimizing objectives of the MOEL framework and can vary with time. Extensive experimental results on 12 well-known benchmark datasets demonstrate that our proposed framework achieves outstanding performance compared to the state-of-the-art approaches for mitigating unfairness in terms of accuracy as well as 25 fairness measures although only a few of them were dynamically selected and used as optimization objectives. The results indicate the importance of setting optimization objectives dynamically during training.

Dynamic material handling (DMH) involves the assignment of dynamically arriving material transporting tasks to suitable vehicles in real time for minimizing makespan and tardiness. In real-world scenarios, historical task records are usually available, which enables the training of a decision policy on multiple instances consisting of historical records. Recently, reinforcement learning (RL) has been applied to solve DMH. Due to the occurrence of dynamic events such as new tasks, adaptability is highly required. Solving DMH is challenging since constraints, including task delay, should be satisfied. A feedback is received only when all tasks are served, which leads to sparse reward. Besides, making the best use of limited computational resources and historical records for training a robust policy is crucial. The time allocated to different problem instances would highly impact the learning process. To tackle those challenges, this article proposes a novel adaptive constrained evolutionary RL (ACERL) approach, which maintains a population of actors for diverse exploration. ACERL accesses each actor for tackling sparse rewards and constraint violation to restrict the behavior of the policy. Moreover, ACERL adaptively selects the most beneficial training instances for improving the policy. Extensive experiments on eight training and eight unseen test instances demonstrate the outstanding performance of ACERL compared with several state-of-the-art algorithms. Policies trained by ACERL can schedule the vehicles while fully satisfying the constraints. Additional experiments on 40 unseen noised instances show the robust performance of ACERL. Cross validation further presents the overall effectiveness of ACREL. Besides, a rigorous ablation study highlights the coordination and benefits of each ingredient of ACERL.

Recently, procedural content generation has exhibited considerable advancements in the domain of 2D game level generation such as Super Mario Bros. and Sokoban through large language models (LLMs). To further validate the capabilities of LLMs, this paper explores how LLMs contribute to the generation of 3D buildings in a sandbox game, Minecraft. We propose a Text to Building in Minecraft (T2BM) model, which involves refining prompts, decoding interlayer representation and repairing. Facade, indoor scene and functional blocks like doors are supported in the generation. Experiments are conducted to evaluate the completeness and satisfaction of buildings generated via LLMs. It shows that LLMs hold significant potential for 3D building generation. Given appropriate prompts, LLMs can generate correct buildings in Minecraft with complete structures and incorporate specific building blocks such as windows and beds, meeting the specified requirements of human users.

Recently, the emergence of large language models (LLMs) has unlocked new opportunities for procedural content generation. However, recent attempts mainly focus on level generation for specific games with defined game rules such as Super Mario Bros. and Zelda. This paper investigates the game generation via LLMs. Based on video game description language, this paper proposes an LLM-based framework to generate game rules and levels simultaneously. Experiments demonstrate how the framework works with prompts considering different combinations of context. Our findings extend the current applications of LLMs and offer new insights for generating new games in the area of procedural content generation.

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.

Recently, evolutionary reinforcement learning has obtained much attention in various domains. Maintaining a population of actors, evolutionary reinforcement learning utilises the collected experiences to improve the behaviour policy through efficient exploration. However, the poor scalability of genetic operators limits the efficiency of optimising high-dimensional neural networks. To address this issue, this paper proposes a novel cooperative coevolutionary reinforcement learning (CoERL) algorithm. Inspired by cooperative coevolution, CoERL periodically and adaptively decomposes the policy optimisation problem into multiple subproblems and evolves a population of neural networks for each of the subproblems. Instead of using genetic operators, CoERL directly searches for partial gradients to update the policy. Updating policy with partial gradients maintains consistency between the behaviour spaces of parents and offspring across generations. The experiences collected by the population are then used to improve the entire policy, which enhances the sampling efficiency. Experiments on six benchmark locomotion tasks demonstrate that CoERL outperforms seven state-of-the-art algorithms and baselines. Ablation study verifies the unique contribution of CoERL’s core ingredients.

In many practical applications, usually, similar optimisation problems or scenarios repeatedly appear. Learning from previous problem-solving experiences can help adjust algorithm components of meta-heuristics, e.g., adaptively selecting promising search operators, to achieve better optimisation performance. However, those experiences obtained from previously solved problems, namely offline experiences, may sometimes provide misleading perceptions when solving a new problem, if the characteristics of previous problems and the new one are relatively different. Learning from online experiences obtained during the ongoing problem-solving process is more instructive but highly restricted by limited computational resources. This paper focuses on the effective combination of offline and online experiences. A novel hybrid framework that learns to dynamically and adaptively select promising search operators is proposed. Two adaptive operator selection modules with complementary paradigms cooperate in the framework to learn from offline and online experiences and make decisions. An adaptive decision policy is maintained to balance the use of those two modules in an online manner. Extensive experiments on 170 widely studied real-value benchmark optimisation problems and a benchmark set with 34 instances for combinatorial optimisation show that the proposed hybrid framework outperforms the state-of-the-art methods. Ablation study verifies the effectiveness of each component of the framework.

Deep reinforcement learning has recently been successfully applied to online procedural content generation in which a policy determines promising game-level segments. However, existing methods can hardly discover diverse level patterns, while the lack of diversity makes the gameplay boring. This paper proposes an ensemble reinforcement learning approach that uses multiple negatively correlated sub-policies to generate different alternative level segments, and stochastically selects one of them following a selector model. A novel policy regularisation technique is integrated into the approach to diversify the generated alternatives. In addition, we develop theorems to provide general methodologies for optimising policy regularisation in a Markov decision process. The proposed approach is compared with several state-of-the-art policy ensemble methods and classic methods on a well-known level generation benchmark, with two different reward functions expressing game-design goals from different perspectives. Results show that our approach boosts level diversity notably with competitive performance in terms of the reward. Furthermore, by varying the regularisation coefficient, the trained generators form a well-spread Pareto front, allowing explicit trade-offs between diversity and rewards of generated levels.

In this paper, we revisit endless online level generation with the recently proposed experience-driven procedural content generation via reinforcement learning (EDRL) framework. Inspired by an observation that EDRL tends to generate recurrent patterns, we formulate a notion ofstate space closurewhich makes any stochastic state appeared possibly in an infinite-horizon online generation process can be found within a finite-horizon. Through theoretical analysis, we find that even though state space closure arises a concern about diversity, it generalises EDRL trained with a finite-horizon to the infinite-horizon scenario without deterioration of content quality. Moreover, we verify the quality and the diversity of contents generated by EDRL via empirical studies, on the widely usedSuper Mario Bros.benchmark. Experimental results reveal that the diversity of levels generated by EDRL is limited due to the state space closure, whereas their quality does not deteriorate in a horizon which is longer than the one specified in the training. Concluding our outcomes and analysis, future work on endless online level generation via reinforcement learning should address the issue of diversity while assuring the occurrence of state space closure and quality.

The demand for indoor synthesis has increased significantly in recent years because of the emergence of computational design. This work designs and develops MyRoom, a Unity plugin that can import layout datasets for indoor synthesis and procedurally generate and interactively design indoor scenes. MyRoom enables users to easily edit and visualize non-intuitive layout description data, making it easier to generate and manipulate indoor scenes in Unity. MyRoom provides a user-friendly interface and powerful tools for designing and optimizing indoor layouts, including an automatic layout generator, making it ideal for game developers, interior designers, and researchers in the digital world-building industry. With MyRoom, users can streamline the process of creating high-quality indoor scenes in games and achieve their design goals efficiently.

Procedurally generating cities in Minecraft provides players more diverse scenarios and could help understand and improve the design of cities in other digital worlds and the real world. This paper presents a city generator that was submitted as an entry to the 2023 Edition of Minecraft Settlement Generation Competition for Minecraft. The generation procedure is composed of six main steps, namely vegetation clearing, terrain reshaping, building layout generation, route planning, streetlight placement, and wall construction. Three algorithms, including a heuristic-based algorithm, an evolving layout algorithm, and a random one are applied to generate the building layout, thus determining where to place different redstone style buildings, and tested by generating cities on random maps in limited time. Experimental results show that the heuristic-based algorithm is capable of finding an acceptable building layout faster for flat maps, while the evolving layout algorithm performs better in evolving layout for rugged maps. A user study is conducted to compare our generator with outstanding entries of the competition’s 2022 edition using the competition’s evaluation criteria and shows that our generator performs well in the adaptation and functionality criteria.

For solving combinatorial optimisation problems with metaheuristics, different search operators are applied for sampling new solutions in the neighbourhood of a given solution. It is important to understand the relationship between operators for various purposes, e.g., adaptively deciding when to use which operator to find optimal solutions efficiently. However, it is difficult to theoretically analyse this relationship, especially in the complex solution space of combinatorial optimisation problems. In this paper, we propose to empirically analyse the relationship between operators in terms of the correlation between their local optima and develop a measure for quantifying their relationship. The comprehensive analyses on a wide range of capacitated vehicle routing problem benchmark instances show that there is a consistent pattern in the correlation between commonly used operators. Based on this newly proposed local optima correlation metric, we propose a novel approach for adaptively selecting among the operators during the search process. The core intention is to improve search efficiency by preventing wasting computational resources on exploring neighbourhoods where the local optima have already been reached. Experiments on randomly generated instances and commonly used benchmark datasets are conducted. Results show that the proposed approach outperforms commonly used adaptive operator selection methods.

Evolutionary algorithms have been used to evolve a population of actors to generate diverse experiences for training reinforcement learning agents, which helps to tackle the temporal credit assignment problem and improves the exploration efficiency. However, when adapting this approach to address constrained problems, balancing the trade-off between the reward and constraint violation is hard. In this paper, we propose a novel evolutionary constrained reinforcement learning (ECRL) algorithm, which adaptively balances the reward and constraint violation with stochastic ranking, and at the same time, restricts the policy's behaviour by maintaining a set of Lagrange relaxation coefficients with a constraint buffer. Extensive experiments on robotic control benchmarks show that our ECRL achieves outstanding performance compared to state-of-the-art algorithms. Ablation analysis shows the benefits of introducing stochastic ranking and constraint buffer.

As one of the core parts of flexible manufacturing systems, material handling involves storage and transportation of materials between workstations with automated vehicles. The improvement in material handling can impulse the overall efficiency of the manufacturing system. However, the occurrence of dynamic events during the optimisation of task arrangements poses a challenge that requires adaptability and effectiveness. In this paper, we aim at the scheduling of automated guided vehicles for dynamic material handling. Motivated by some real-world scenarios, unknown new tasks and unexpected vehicle breakdowns are regarded as dynamic events in our problem. We formulate the problem as a constrained Markov decision process which takes into account tardiness and available vehicles as cumulative and instantaneous constraints, respectively. An adaptive constrained reinforcement learning algorithm that combines Lagrangian relaxation and invalid action masking, named RCPOM, is proposed to address the problem with two hybrid constraints. Moreover, a gym-like dynamic material handling simulator, named DMH-GYM, is developed and equipped with diverse problem instances, which can be used as benchmarks for dynamic material handling. Experimental results on the problem instances demonstrate the outstanding performance of our proposed approach compared with eight state-of-the-art constrained and non-constrained reinforcement learning algorithms, and widely used dispatching rules for material handling.

Reinforcement learning algorithms have performed well in playing challenging board and video games. More and more studies focus on improving the generalisation ability of reinforcement learning algorithms. The GVGAI Learning Competition aims to develop agents capable of learning to play different game levels that were unseen during training. This paper summarises the five years' GVGAI Learning Competition editions. At each edition, three new games were designed. The training and test levels were designed separately in the first three editions. Since 2020, three test levels of each game were generated by perturbing or combining two training levels. Then, we present a novel reinforcement learning technique with dual-observation for general video game playing, assuming that it is more likely to observe similar local information in different levels rather than global information. Instead of directly inputting a single, raw pixel-based screenshot of the current game screen, our proposed general technique takes the encoded, transformed global and local observations of the game screen as two simultaneous inputs, aiming at learning local information for playing new levels. Our proposed technique is implemented with three state-of-the-art reinforcement learning algorithms and tested on the game set of the 2020 GVGAI Learning Competition. Ablation studies show the outstanding performance of using encoded, transformed dual observations as input.

The eight papers in this special section focus on applications of evolutionary computation to games to demonstrate several ways in which evolution can push boundaries and explore new areas of what is possible in the realm of games research, with a focus on game-playing, automatic agent parameter tuning, automatic game testing, and procedural content generation.

In the literature of mitigating unfairness in machine learning, many fairness measures are designed to evaluate predictions of learning models and also utilised to guide the training of fair models. It has been theoretically and empirically shown that there exist conflicts and inconsistencies among accuracy and multiple fairness measures. Optimising one or several fairness measures may sacrifice or deteriorate other measures. Two key questions should be considered, how to simultaneously optimise accuracy and multiple fairness measures, and how to optimise all the considered fairness measures more effectively. In this paper, we view the mitigating unfairness problem as a multi-objective learning problem considering the conflicts among fairness measures. A multi-objective evolutionary learning framework is used to simultaneously optimise several metrics (including accuracy and multiple fairness measures) of machine learning models. Then, ensembles are constructed based on the learning models in order to automatically balance different metrics. Empirical results on eight well-known datasets demonstrate that compared with the state-of-the-art approaches for mitigating unfairness, our proposed algorithm can provide decision-makers with better tradeoffs among accuracy and multiple fairness metrics. Furthermore, the high-quality models generated by the framework can be used to construct an ensemble to automatically achieve a better tradeoff among all the considered fairness metrics than other ensemble methods.

Game consists of multiple types of content, while the harmony of different content types play an essential role in game design. However, most works on procedural content generation consider only one type of content at a time. In this paper, we propose and formulate online level generation from music, in a way of matching a level feature to a music feature in real-time, while adapting to players’ play speed. A generic framework named online player-adaptive procedural content generation via reinforcement learning, OPARL for short, is built upon the experience-driven reinforcement learning and controllable reinforcement learning, to enable online level generation from music. Furthermore, a novel control policy based on local search and k-nearest neighbours is proposed and integrated into OPARL to control the level generator considering the play data collected online. Results of simulation-based experiments show that our implementation of OPARL is competent to generate playable levels with difficulty degree matched to the “energy” dynamic of music for different artificial players in an online fashion.

Recent years, there has been growing interests in experience-driven procedural level generation. Various metrics have been formulated to model player experience and help generate personalised levels. In this work, we question whether experience metrics can adapt to agents with different personas. We start by reviewing existing metrics for evaluating game levels. Then, focusing on platformer games, we design a framework integrating various agents and evaluation metrics. Experimental studies on Super Mario Bros. indicate that using the same evaluation metrics but agents with different personas can generate levels for particular persona. It implies that, for simple games, using a game-playing agent of specific player archetype as a level tester is probably all we need to generate levels of diverse behaviour engagement.

The recently introduced EDRL framework approaches the experience-driven (ED) procedural generation of game content via a reinforcement learning (RL) perspective. EDRL has so far shown its effectiveness in generating novel platformer game levels endlessly in an online fashion. This paper extends the framework by integrating multiple facets of game creativity in the ED generation process. In particular, we employ EDRL on the creative facets of game level and gameplay design in Super Mario Bros. Inspired by Koster’s theory of fun, we formulate fun as moderate degrees of level or gameplay divergence and equip the algorithm with such reward functions. Moreover, we enable faster and more efficient game content generation through an episodic generative soft actor-critic algorithm. The resulting multifaceted EDRL is not only capable of generating fun levels efficiently, but it is also robust with respect to dissimilar playing styles and initial game level conditions.

Memetic algorithm (MA) is widely applied to optimize routing problems as it provides one way to combine local search with global search. However, the local search in MA needs to be carefully designed according to the problem’s characteristics. In this article, we consider a real-world large-scale waste collection problem with multiple depots, multiple disposal facilities, multiple trips, and working time constraints. Vehicles with a limited capacity and working time can start from different depots, collect waste at different sites, and make multiple trips to different disposal facilities to empty the waste and return to its origin. While the existing work considered problems with multiple trips and time constraints, none have tackled problems with multiple depots, multiple disposal facilities, multiple trips, as well as working time constraints. The change from “single-depot” to “multidepot” not only reflects better the situation in real life but also leads to a qualitative different and more complex problem. In this article, we first model this complex problem mathematically. Then, a novel region-focused MA is proposed to tackle this new challenge. Compared to classic MA, this region-focused one is enhanced by two major components: 1) a new heuristic-assisted solution initialization algorithm and 2) a region-focused local search with novel heuristics. Comprehensive computational studies show that our proposed approaches significantly outperform several state-of-the-arts on our real problem of thousands of tasks. The new local search procedure and solution initialization method significantly improve the search ability in combination with global search ability of MA.

We introduce a procedural content generation (PCG) framework at the intersections of experience-driven PCG and PCG via reinforcement learning, named ED(PCG)RL, EDRL in short. EDRL is able to teach RL designers to generate endless playable levels in an online manner while respecting particular experiences for the player as designed in the form of reward functions. The framework is tested initially in the Super Mario Bros game. In particular, the RL designers of Super Mario Bros generate and concatenate level segments while considering the diversity among the segments. The correctness of the generation is ensured by a neural net-assisted evolutionary level repairer and the playability of the whole level is determined through AI-based testing. Our agents in this EDRL implementation learn to maximise a quantification of Koster's principle of fun by moderating the degree of diversity across level segments. Moreover, we test their ability to design fun levels that are diverse over time and playable. Our proposed framework is capable of generating endless, playable Super Mario Bros levels with varying degrees of fun, deviation from earlier segments, and playability. EDRL can be generalised to any game that is built as a segment-based sequential process and features a built-in compressed representation of its game content.

The time-series GAN and periodic spatial GAN show different yet competitive performance in terms of the evaluation metrics adopted, their deviation from human-designed danmakus, and the diversity of generated danmakus. The preliminary experimental studies presented here showcase that potential of time-series GANs for sequential content generation in games.

Applying latent variable evolution to game level design has become more and more popular as little human expert knowledge is required. However, defective levels with illegal patterns may be generated due to the violation of constraints for level design. A traditional way of repairing the defective levels is programming specific rule-based repairers to patch the flaw. However, programming these constraints is sometimes complex and not straightforward. An autonomous level repairer which is capable of learning the constraints is needed. In this paper, we propose a novel approach, CNet, to learn the probability distribution of tiles giving its surrounding tiles on a set of real levels, and then detect the illegal tiles in generated new levels. Then, an evolutionary repairer is designed to search for optimal replacement schemes equipped with a novel search space being constructed with the help of CNet and a novel heuristic function. The proposed approaches are proved to be effective in our case study of repairing GAN-generated and artificially destroyed levels of Super Mario Bros. game. Our CNet-assisted evolutionary repairer can also be easily applied to other games of which the levels can be represented by a matrix of objects or tiles.

Choosing automatically the right algorithm using problem descriptors is a classical component of combinatorial optimization. It is also a good tool for making evolutionary algorithms fast, robust and versatile. We present Shiwa, an algorithm good at both discrete and continuous, noisy and noise-free, sequential and parallel, black-box optimization. Our algorithm is experimentally compared to competitors on YABBOB, a BBOB comparable testbed, and on some variants of it, and then validated on several real world testbeds.

Generative Adversarial Networks (GANs) are an emerging form of indirect encoding. The GAN is trained to induce a latent space on training data, and a real-valued evolutionary algorithm can search that latent space. Such Latent Variable Evolution (LVE) has recently been applied to game levels. However, it is hard for objective scores to capture level features that are appealing to players. Therefore, this paper introduces a tool for interactive LVE of tile-based levels for games. The tool also allows for direct exploration of the latent dimensions, and allows users to play discovered levels. The tool works for a variety of GAN models trained for both Super Mario Bros. and The Legend of Zelda, and is easily generalizable to other games. A user study shows that both the evolution and latent space exploration features are appreciated, with a slight preference for direct exploration, but combining these features allows users to discover even better levels. User feedback also indicates how this system could eventually grow into a commercial design tool, with the addition of a few enhancements.

The reliable facility location problem (RFLP) is an important research topic of operational research and plays a vital role in the decision-making and management of modern supply chain and logistics. Through solving RFLP, the decision-maker can obtain reliable location decisions under the risk of facilities’ disruptions or failures. In this paper, we propose a novel model for the RFLP. Instead of assuming allocating a fixed number of facilities to each customer as in the existing works, we set the number of allocated facilities as an independent variable in our proposed model, which makes our model more close to the scenarios in real life but more difficult to be solved by traditional methods. To handle it, we propose EAMLS, a hybrid evolutionary algorithm, which combines a memorable local search (MLS) method and an evolutionary algorithm (EA). Additionally, a novel metric called l3-value is proposed to assist the analysis of the algorithm’s convergence speed and exam the process of evolution. The experimental results show the effectiveness and superior performance of our EAMLS, compared to a CPLEX solver and a Genetic Algorithm (GA), on large-scale problems.

Many enhancements for Monte Carlo tree search (MCTS) have been applied successfully in general game playing (GGP). MCTS and its enhancements are controlled by multiple parameters that require extensive and time-consuming offline optimization. Moreover, as the played games are unknown in advance, offline optimization cannot tune parameters specifically for single games. This paper proposes a self-adaptive MCTS strategy (SA-MCTS) that integrates within the search a method to automatically tune search-control parameters online per game. It presents five different allocation strategies that decide how to allocate available samples to evaluate parameter values. Experiments with 1 s play-clock on multiplayer games show that for all the allocation strategies the performance of SA-MCTS that tunes two parameters is at least equal to or better than the performance of MCTS tuned offline and not optimized per-game. The allocation strategy that performs the best is N-Tuple Bandit Evolutionary Algorithm (NTBEA). This strategy also achieves a good performance when tuning four parameters. SA-MCTS can be considered as a successful strategy for domains that require parameter tuning for every single problem, and it is also a valid alternative for domains where offline parameter tuning is costly or infeasible.

Very expensive problems are very common in practical system that one fitness evaluation costs several hours or even days. Surrogate assisted evolutionary algorithms (SAEAs) have been widely used to solve this crucial problem in the past decades. However, most studied SAEAs focus on solving problems with a budget of at least ten times of the dimension of problems which is unacceptable in many very expensive real-world problems. In this paper, we employ Voronoi diagram to boost the performance of SAEAs and propose a novel framework named Voronoi-based efficient surrogate assisted evolutionary algorithm (VESAEA) for very expensive problems, in which the optimization budget, in terms of fitness evaluations, is only 5 times of the problem's dimension. In the proposed framework, the Voronoi diagram divides the whole search space into several subspace and then the local search is operated in some potentially better subspace. Additionally, in order to trade off the exploration and exploitation, the framework involves a global search stage developed by combining leave-one-out cross-validation and radial basis function surrogate model. A performance selector is designed to switch the search dynamically and automatically between the global and local search stages. The empirical results on a variety of benchmark problems demonstrate that the proposed framework significantly outperforms several state-of-art algorithms with extremely limited fitness evaluations. Besides, the efficacy of Voronoi-diagram is furtherly analyzed, and the results show its potential to optimize very expensive problems.

Game-based benchmarks have been playing an essential role in the development of Artificial Intelligence (AI) techniques. Providing diverse challenges is crucial to push research toward innovation and understanding in modern techniques. Rinascimento provides a parameterised partially-observable multiplayer card-based board game, these parameters can easily modify the rules, objectives and items in the game. We describe the framework in all its features and the game-playing challenge providing baseline game-playing AIs and analysis of their skills. We reserve to agents' hyper-parameter tuning a central role in the experiments highlighting how it can heavily influence the performance. The base-line agents contain several additional contribution to Statistical Forward Planning algorithms.

Surrogate-assisted evolutionary algorithms (SAEAs) are powerful optimisation tools for computationally expensive problems (CEPs). However, a randomly selected algorithm may fail in solving unknown problems due to no free lunch theorems, and it will cause more computational resource if we re-run the algorithm or try other algorithms to get a much solution, which is more serious in CEPs. In this paper, we consider an algorithm portfolio for SAEAs to reduce the risk of choosing an inappropriate algorithm for CEPs. We propose two portfolio frameworks for very expensive problems in which the maximal number of fitness evaluations is only 5 times of the problem's dimension. One framework named Par-IBSAEA runs all algorithm candidates in parallel and a more sophisticated framework named UCB-IBSAEA employs the Upper Confidence Bound (UCB) policy from reinforcement learning to help select the most appropriate algorithm at each iteration. An effective reward definition is proposed for the UCB policy. We consider three state-of-the-art individual-based SAEAs on different problems and compare them to the portfolios built from their instances on several benchmark problems given limited computation budgets. Our experimental studies demonstrate that our proposed portfolio frameworks significantly outperform any single algorithm on the set of benchmark problems.

The twelve papers in this special section focus on game competition frameworks for the research and education markets. Presents highlights of some high-quality research and remarkable educational applications using the game competition frameworks.

General video game playing aims at designing an agent that is capable of playing multiple video games with no human intervention. In 2014, the General Video Game Artificial Intelligence (GVGAI) competition framework was created and released with the purpose of providing researchers a common open-source and easy-to-use platform for testing their artificial intelligence (AI) methods with potentially infinity of games created using the video game description language (VGDL). The framework has been expanded into several tracks during the last few years to meet the demands of different research directions. The agents are required either to play multiple unknown games with or without access to game simulations, or to design new game levels or rules. This survey paper presents the VGDL, the GVGAI framework, existing tracks, and reviews the wide use of GVGAI framework in research, education, and competitions five years after its birth. A future plan of framework improvements is also described.

This paper describes the N-Tuple Bandit Evolutionary Algorithm (NTBEA), an optimisation algorithm developed for noisy and expensive discrete (combinatorial) optimisation problems. The algorithm is applied to two game-based hyperparameter optimisation problems. The N-Tuple system directly models the statistics, approximating the fitness and number of evaluations of each modelled combination of parameters. The model is simple, efficient and informative. Results show that the NTBEA significantly outperforms grid search and an estimation of distribution algorithm.

Generative Adversarial Networks (GANs) are a machine learning approach capable of generating novel example outputs across a space of provided training examples. Procedural Content Generation (PCG) of levels for video games could benefit from such models, especially for games where there is a pre-existing corpus of levels to emulate. This paper trains a GAN to generate levels for Super Mario Bros using a level from the Video Game Level Corpus. The approach successfully generates a variety of levels similar to one in the original corpus, but is further improved by application of the Covariance Matrix Adaptation Evolution Strategy (CMA-ES). Specifically, various fitness functions are used to discover levels within the latent space of the GAN that maximize desired properties. Simple static properties are optimized, such as a given distribution of tile types. Additionally, the champion A* agent from the 2009 Mario AI competition is used to assess whether a level is playable, and how many jumping actions are required to beat it. These fitness functions allow for the discovery of levels that exist within the space of examples designed by experts, and also guide the search towards levels that fulfill one or more specified objectives.

This paper showcases the setting and results of the first Two-Player General Video Game AI Competition, which ran in 2016 at the IEEE World Congress on Computational Intelligence and the IEEE Conference on Computational Intelligence and Games. The challenges for the general game AI agents are expanded in this track from the single-player version, looking at direct player interaction in both competitive and cooperative environments of various types and degrees of difficulty. The focus is on the agents not only handling multiple problems, but also having to account for another intelligent entity in the game, who is expected to work toward their own goals (winning the game). This other player will possibly interact with first agent in a more engaging way than the environment or any nonplaying character may do. The top competition entries are analyzed in detail and the performance of all agents is compared across the four sets of games. The results validate the competition system in assessing generality, as well as showing Monte Carlo tree search continuing to dominate by winning the overall championship. However, this approach is closely followed by rolling horizon evolutionary algorithms, employed by the winner of the second leg of the contest.

Pac-Man and its equally popular successor Ms.Pac-Man are often attributed to being the frontrunners of the golden age of arcade video games. Their impact goes well beyond the commercial world of video games and both games have featured in numerous academic research projects over the last two decades. In fact, scientific interest is on the rise and many avenues of research have been pursued, including studies in robotics, biology, sociology, and psychology. The most active field of research is computational intelligence, not least because of popular academic gaming competitions that feature Ms. Pac-Man. This paper summarizes the peer-reviewed research that focuses on either game (or close variants thereof) with particular emphasis on the field of computational intelligence. The potential usefulness of games like Pac-Man for higher education is also discussed and the paper concludes with a discussion of prospects for future work.

Fuzzy relationships exist between students’ learning performance with various abilities and a test item. However, the challenges in implementing adaptive assessment agents are obtaining sufficient items, efficient and accurate computerized estimation, and a substantial feedback agent. Additionally, the agent must immediately estimate students’ ability item by item, which places a considerable burden on the server, especially for a group test. Hence, the implementation of an adaptive assessment agent is more difficult in practice. This paper proposes an agent with particle swarm optimization (PSO) based on a fuzzy markup language (FML) for students’ learning performance evaluation and educational applications, and the proposed agent is according to the response data from a conventional test and an item response theory (IRT)-based three-parameter logistic model. First, we apply a Gauss–Seidel based parameter estimation mechanism to estimate the items’ parameters according to the response data, and then to compare its results with those of an IRT-based Bayesian parameter estimation mechanism. In addition, we propose a static-IRT test assembly mechanism to assemble a form for the conventional test. The presented FML-based dynamic assessment mechanism infers the probability of making a correct response to the item for a student with various abilities. Moreover, this paper also proposes a novel PSO-based FML (PFML) learning mechanism for optimizing the parameters between items and students. Finally, we adopt aK-fold cross-validation mechanism to evaluate the performance of the proposed agent. Experimental results show that the novel PFML learning mechanism for the parameter estimation and learning optimization performs favorably. We believe the proposed PFML will be a reference for education research and pedagogy and an important colearning mechanism for future human–machine educational applications.

This paper describes a new evolutionary algorithm that is especially well suited to AI-Assisted Game Design. The approach adopted in this paper is to use observations of AI agents playing the game to estimate the game's quality. Some of best agents for this purpose are General Video Game AI agents, since they can be deployed directly on a new game without game-specific tuning; these agents tend to be based on stochastic algorithms which give robust but noisy results and tend to be expensive to run. This motivates the main contribution of the paper: the development of the novel N-Tuple Bandit Evolutionary Algorithm, where a model is used to estimate the fitness of unsampled points and a bandit approach is used to balance exploration and exploitation of the search space. Initial results on optimising a Space Battle game variant suggest that the algorithm offers far more robust results than the Random Mutation Hill Climber and a Biased Mutation variant, which are themselves known to offer competitive performance across a range of problems. Subjective observations are also given by human players on the nature of the evolved games, which indicate a preference towards games generated by the N-Tuple algorithm.

The Random Mutation Hill-Climbing algorithm is a direct search technique mostly used in discrete domains. It repeats the process of randomly selecting a neighbour of a best-so-far solution and accepts the neighbour if it is better than or equal to it. In this work, we propose to use a novel method to select the neighbour solution using a set of independent multi-armed bandit-style selection units which results in a bandit-based Random Mutation Hill-Climbing algorithm. The new algorithm significantly outperforms Random Mutation Hill-Climbing in both OneMax (in noise-free and noisy cases) and Royal Road problems (in the noise-free case). The algorithm shows particular promise for discrete optimisation problems where each fitness evaluation is expensive.

Most games have, or can be generalised to have, a number of parameters that may be varied in order to provide instances of games that lead to very different player experiences. The space of possible parameter settings can be seen as a search space, and we can therefore use a Random Mutation Hill Climbing algorithm or other search methods to find the parameter settings that induce the best games. One of the hardest parts of this approach is defining a suitable fitness function. In this paper we explore the possibility of using one of a growing set of General Video Game AI agents to perform automatic play-testing. This enables a very general approach to game evaluation based on estimating the skill-depth of a game. Agent-based play-testing is computationally expensive, so we compare two simple but efficient optimisation algorithms: the Random Mutation Hill-Climber and the Multi-Armed Bandit Random Mutation Hill-Climber. For the test game we use a space-battle game in order to provide a suitable balance between simulation speed and potential skill-depth. Results show that both algorithms are able to rapidly evolve game versions with significant skill-depth, but that choosing a suitable resampling number is essential in order to combat the effects of noise.

This paper is devoted to noisy optimization in case of a noise with standard deviation as large as variations of the fitness values, specifically when the variance does not decrease to zero around the optimum. We focus on comparing methods for choosing the number of resamplings. Experiments are performed on the differential evolution algorithm. By mathematical analysis, we design a new rule for choosing the number of resamplings for noisy optimization, as a function of the dimension, and validate its efficiency compared to existing heuristics.

Monte Carlo simulations are widely accepted as a tool for evaluating positions in games. It can be used inside tree search algorithms, simple Monte Carlo search, Nested Monte Carlo and the famous Monte Carlo Tree Search algorithm which is at the heart of the current revolution in computer games. If one has access to a perfect simulation policy, then there is no need for an estimation of the game value. In any other cases, an evaluation through Monte Carlo simulations is a possible approach. However, games simulations are, in practice, biased. Many papers are devoted to improve Monte Carlo simulation policies by reducing this bias. In this paper, we propose a complementary tool: instead of modifying the simulations, we modify the way they are averaged by adjusting weights. We apply our method to MCTS for Tsumego solving. In particular, we improve Gnugo-MCTS without any online computational overhead.

Owing to advanced technical progress in information and communication technology, computerized adaptive assessment becomes more and more important for the personalized learning achievement. According to the response data from the conventional test and three-parameter logistic (3PL) model of the item response theory (IRT), this paper combines IRT with fuzzy markup language (FML) for an adaptive assessment application. The novel FML-based IRT estimation mechanism includes a Gauss-Seidel (GS) parameter estimation mechanism, a fuzzy knowledge base and a fuzzy rule base, to estimate the item parameters for each item. Meanwhile, it is able to infer the possibility of correct response to each item for each involved student. Additionally, this paper also proposes a static-IRT test assembly mechanism to assemble a form for the conventional test. After that, this paper chooses 5-fold cross validation to validate the research performance. From the experimental results, it shows that the proposed approach performs better than the traditional Bayesian estimation one.

In this paper we compare Differential Evolution (DE), an evolutionary algorithm, to classical bandit algorithms over the non-stationary bandit problem. First we define a testcase where the variation of the distributions depends on the number of times an option is evaluated rather than over time. This definition allows the possibility to apply these algorithms over a wide range of problems such as black-box portfolio selection. Second we present our own variant of discounted Upper Confidence Bound (UCB) algorithm that outperforms the current state-of-the-art algorithms for the non-stationary bandit problem. Third, we introduce a variant of DE and show that, on a selection over a portfolio of solvers for the Cart-Pole problem, our version of DE outperforms the current best UCB algorithms.