A multi-objective evolutionary approach for the nonlinear scale-free level problem

Abstract

Procedural Content Generation in games aims to produce replayable levels that might adapt to the player or designer preferences. One of the most popular approaches adopted for search-based level generation is the use of Evolutionary Algorithms. This paper addresses the context of dungeon generation and divide the problem in two steps: the first consists of generating the physical level, while the second is to create the puzzle. Although there are several approaches in the related literature for generating levels and puzzles, few are successful at generating unpredictable or diverse levels. The objective of this work is to propose a Multi-objective Evolutionary approach for generating the level and creating the puzzle providing a wide range of unpredictable and diverse solutions with different level dimensions. To achieve this goal, the level is modeled as scale-free topology with a nonlinear resolution. This model avoids the generation of linear, repetitive and grid-like levels, giving the algorithm additional freedom to explore the search space for diverse solutions. Four classical well-known evolutionary algorithms (SPEA2, PAES, NSGA-II and MOCell) were applied to both sub-problems. To analyze the results, we consider a set of quality indicators covering both convergence and diversity. Our results indicated that, the proposed multi-objective formulation was able to provide a wide range of satisfactory and diverse solutions with different level dimensions, independently of the algorithm used. Thus, the main contribution of this work is that level designers can choose between different solutions, based on solution properties and/or designer priorities.