Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Constrained optimization of high-dimensional numerical problems plays an important role in many scientific and industrial applications. Function evaluations in many industrial applications are severely limited and no analytical information about objective function and constraint functions is available. For such expensive black-box optimization tasks, the constraint optimization algorithm COBRA was proposed, making use of RBF surrogate modeling for both the objective and the constraint functions. COBRA has shown remarkable success in solving reliably complex benchmark problems in less than 500 function evaluations. Unfortunately, COBRA requires careful adjustment of parameters in order to do so. In this work we present a new self-adjusting algorithm SACOBRA, which is based on COBRA and capable to achieve high-quality results with very few function evaluations and no parameter tuning. It is shown with the help of performance profiles on a set of benchmark problems (G-problems, MOPTA08) that SACOBRA consistently outperforms any COBRA algorithm with fixed parameter setting. We analyze the importance of the several new elements in SACOBRA and find that each element of SACOBRA plays a role to boost up the overall optimization performance. We discuss the reasons behind and get in this way a better understanding of high-quality RBF surrogate modeling

Enhancements to constrained novelty search : two-population novelty search for generating game content

Novelty search is a recent algorithm geared to explore search spaces without regard to objectives; minimal criteria novelty search is a variant of this algorithm for constrained search spaces. For large search spaces with multiple constraints, however, it is hard to find a set of feasible individuals that is both large and diverse. In this paper, we present two new methods of novelty search for constrained spaces, Feasible-Infeasible Novelty Search and Feasible-Infeasible Dual Novelty Search. Both algorithms keep separate populations of feasible and infeasible individuals, inspired by the FI-2pop genetic algorithm. These algorithms are applied to the problem of creating diverse and feasible game levels, representative of a large class of important problems in procedural content generation for games. Results show that the new algorithms under certain conditions can produce larger and more diverse sets of feasible strategy game maps than existing algorithms. However, the best algorithm is contingent on the particularities of the search space and the genetic operators used. It is also shown that the proposed enhancement of offspring boosting increases performance in all cases.The research is supported, in part, by the FP7 ICT project SIREN (project no: 258453) and by the FP7 ICT project C2Learn (project no: 318480).peer-reviewe

Constrained novelty search : a study on game content generation

Novelty search is a recent algorithm geared toward exploring search spaces without regard to objectives. When the presence of constraints divides a search space into feasible space and infeasible space, interesting implications arise regarding how novelty search explores such spaces. This paper elaborates on the problem of constrained novelty search and proposes two novelty search algorithms which search within both the feasible and the infeasible space. Inspired by the FI-2pop genetic algorithm, both algorithms maintain and evolve two separate populations, one with feasible and one with infeasible individuals, while each population can use its own selection method. The proposed algorithms are applied to the problem of generating diverse but playable game levels, which is representative of the larger problem of procedural game content generation. Results show that the two-population constrained novelty search methods can create, under certain conditions, larger and more diverse sets of feasible game levels than current methods of novelty search, whether constrained or unconstrained. However, the best algorithm is contingent on the particularities of the search space and the genetic operators used. Additionally, the proposed enhancement of offspring boosting is shown to enhance performance in all cases of two-population novelty search.peer-reviewe

Solving the G-problems in less than 500 iterations: Improved efficient constrained optimization by surrogate modeling and adaptive parameter control

Algorithms and the Foundations of Software technolog