Searching for good and diverse game levels

Abstract: In procedural content generation, one is often interested in generating a large number of artifacts that are not only of high quality but also diverse, in terms of gameplay, visual impression or some other criterion. We investigate several search-based approaches to creating good and diverse game content, in particular approaches based on evolution strategies with or without diversity preservation mechanisms, novelty search and random search. The content domain is game levels, more precisely map sketches for strategy games, which are meant to be used as suggestions in the Sentient Sketchbook design tool. Several diversity metrics are possible for this type of content: we investigate tile-based, objective-based and visual impression distance. We find that evolution with diversity preservation mechanisms can produce both good and diverse content, but only when using appropriate distance measures. Reversely, we can draw conclusions about the suitability of these distance measures for the domain from the comparison of diversity preserving versus blind restart evolutionary algorithms.peer-reviewe

A spatially-structured PCG method for content diversity in a Physics-based simulation game

This paper presents a spatially-structured evolutionary algorithm (EA) to procedurally generate game maps of di ferent levels of di ficulty to be solved, in Gravityvolve!, a physics-based simulation videogame that we have implemented and which is inspired by the n- body problem, a classical problem in the fi eld of physics and mathematics. The proposal consists of a steady-state EA whose population is partitioned into three groups according to the di ficulty of the generated content (hard, medium or easy) which can be easily adapted to handle the automatic creation of content of diverse nature in other games. In addition, we present three fitness functions, based on multiple criteria (i.e:, intersections, gravitational acceleration and simulations), that were used experimentally to conduct the search process for creating a database of maps with di ferent di ficulty in Gravityvolve!.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

A Computational Study of Genetic Crossover Operators for Multi-Objective Vehicle Routing Problem with Soft Time Windows

The article describes an investigation of the effectiveness of genetic algorithms for multi-objective combinatorial optimization (MOCO) by presenting an application for the vehicle routing problem with soft time windows. The work is motivated by the question, if and how the problem structure influences the effectiveness of different configurations of the genetic algorithm. Computational results are presented for different classes of vehicle routing problems, varying in their coverage with time windows, time window size, distribution and number of customers. The results are compared with a simple, but effective local search approach for multi-objective combinatorial optimization problems

Visualization of Global Trade-Offs in Aerodynamic Problems by ARMOGAs

Trade-offs is one of important elements for engineering design problems characterized by multiple conflicting design objectives to be simultaneously improved. In many design problems such as aerodynamic design, due to computational reasons, only a limited number of evaluations can be allowed for industrial use. Efficient MOEAs, Adaptive Range Multi-Objective Genetic Algorithms (ARMOGAs), to identify trade-offs using a small number of function evaluations have been developed. In this study, ARMOGAs are applied to aerodynamic designs problems to identify trade-offs efficiently. In addition to identify trade-offs, trade-off analysis is also important to obtain useful knowledge about the design problem. To analyze the high-dimensional data of aerodynamic optimization problem, Self-Organizing Maps are applied to understand the trade-offs

Multi-Objective Global Pattern Search: Effective numerical optimisation in structural dynamics

With this work, a novel derivative-free multi-objective optimisation approach for solving engineering problems is presented. State-of-the-art algorithms usually require numerical experimentation in order to tune the algorithm’s multiple parameters to a specific optimisation problem. This issue is effectively tackled by the presented deterministic method which has only a single parameter. The most popular multi-objective optimisation algorithms are based on pseudo-random numbers and need several parameters to adjust the associated probability distributions. Deterministic methods can overcome this issue but have not attracted much research interest in the past decades and are thus seldom applied in practice. The proposed multi-objective algorithm is an extension of the previously introduced deterministic single-objective Global Pattern Search algorithm. It achieves a thorough recovery of the Pareto frontier by tracking a predefined number of non-dominated samples during the optimisation run. To assess the numerical efficiency of the proposed method, it is compared to the well-established NSGA2 algorithm. Convergence is demonstrated and the numerical performance of the proposed optimiser is discussed on the basis of several analytic test functions. Finally, the optimiser is applied to two structural dynamics problems: transfer function estimation and finite element model updating. The introduced algorithm performs well on test functions and robustly converges on the considered practical engineering problems. Hence, this deterministic algorithm can be a viable and beneficial alternative to random-number-based approaches in multi-objective engineering optimisation

Singular Continuation: Generating Piece-wise Linear Approximations to Pareto Sets via Global Analysis

We propose a strategy for approximating Pareto optimal sets based on the global analysis framework proposed by Smale (Dynamical systems, New York, 1973, pp. 531-544). The method highlights and exploits the underlying manifold structure of the Pareto sets, approximating Pareto optima by means of simplicial complexes. The method distinguishes the hierarchy between singular set, Pareto critical set and stable Pareto critical set, and can handle the problem of superposition of local Pareto fronts, occurring in the general nonconvex case. Furthermore, a quadratic convergence result in a suitable set-wise sense is proven and tested in a number of numerical examples.Comment: 29 pages, 12 figure

Design space exploration of RF-circuit blocks

ii iii Acknowledgments This thesis was written in the framework of an internship at NXP Semiconductors. It describes the results of a six months master project. I was supervised by Prof. Dr. W.H.A. Schilders of NXP Semiconductors and the Technical University Eindhoven and furthermore, by Dr. ir. J. A. Croon of NXP Semiconductors. Herewith, I want to express my deep gratitude to Prof. Schilders, who has guided me during the project and for proofreading of the thesis. Furthermore, I want to thank Dr. Croon sincerely for the helpful discussions, for the detailed corrections of the thesis and furthermore for the interesting introduction to semiconductor device modeling. Additionally, I want to thank Univ.-Prof. Dipl.-Ing. Dr. H. Gfrerer of the Johannes Kepler University Linz for reviewing this work and for his useful suggestions during the project. iv vContent

An Adaptive Scheme to Generate the Pareto Front Based on the Epsilon-Constraint Method

We discuss methods for generating or approximating the Pareto set of multiobjective optimization problems by solving a sequence of constrained single-objective problems. The necessity of determining the constraint value a priori is shown to be a serious drawback of the original epsilon-constraint method. We therefore propose a new, adaptive scheme to generate appropriate constraint values during the run. A simple example problem is presented, where the running time (measured by the number of constrained single-objective sub-problems to be solved) of the original epsilon-constraint method is exponential in the problem size (number of decision variables), although the size of the Pareto set grows only linearly. We prove that --- independent of the problem or the problem size --- the time complexity of the new scheme is O(k^{m-1}), where k is the number of Pareto-optimal solutions to be found and m the number of objectives. Simulation results for the example problem as well as for different instances of the multiobjective knapsack problem demonstrate the behavior of the method, and links to reference implementations are provided

Procedural Content Generation for Real-Time Strategy Games

Videogames are one of the most important and profitable sectors in the industry of entertainment. Nowadays, the creation of a videogame is often a large-scale endeavor and bears many similarities with, e.g., movie production. On the central tasks in the development of a videogame is content generation, namely the definition of maps, terrains, non-player characters (NPCs) and other graphical, musical and AI-related components of the game. Such generation is costly due to its complexity, the great amount of work required and the need of specialized manpower. Hence the relevance of optimizing the process and alleviating costs. In this sense, procedural content generation (PCG) comes in handy as a means of reducing costs by using algorithmic techniques to automatically generate some game contents. PCG also provides advantages in terms of player experience since the contents generated are typically not fixed but can vary in different playing sessions, and can even adapt to the player herself. For this purpose, the underlying algorithmic technique used for PCG must be also flexible and adaptable. This is the case of computational intelligence in general and evolutionary algorithms in particular. In this work we shall provide an overview of the use of evolutionary intelligence for PCG, with special emphasis on its use within the context of real-time strategy games. We shall show how these techniques can address both playability and aesthetics, as well as improving the game AI