The aim of this paper is to identify Genetic Algorithms (GAs) which perform well over a range of continuous and smooth multimodal real-variable functions. In our study, we focus on testing GAs combining three classes of genetic operators: selection, crossover and replacement. The approach followed is time-constrained and thus our stopping criterion is a fixed number of generations. Results show...

Procedural content generation (PCG) is the programmatic generation of game content using a random or pseudo-random process that results in an unpredictable range of possible gameplay spaces. This methodology brings many advantages to game developers, such as reduced memory consumption. This works presents a procedural balanced map generator for a real-time strategy game: Planet Wars. This gener...

We consider the classical statistical learning/regression problem, when the value of a real random variable Y is to be predicted based on the observation of another random variableX . Given a class of functions F and a sample of independent copies of (X,Y ), one needs to choose a function f̂ from F such that f̂(X) approximates Y as well as possible, in the mean-squared sense. We introduce a new p...

The probability of winning a game, a set, and a match in tennis are computed, based on each player’s probability of winning a point on serve, which we assume are independent identically distributed (iid) random variables. Both two out of three and three out of five set matches are considered, allowing a 13-point tiebreaker in each set, if necessary. As a by-product of these formulas, we give an...

If T is an n-vertex tournament with a given number of 3-cycles, what can be said about the number of its 4-cycles? The most interesting range of this problem is where T is assumed to have c ⋅ n cyclic triples for some c > 0 and we seek to minimize the number of 4-cycles. We conjecture that the (asymptotic) minimizing T is a random blow-up of a constant-sized transitive tournament. Using the met...

From early days in computing, making computers play games like chess and Othello with a high level of skill has been a challenging and, lately, rewarding task. As computing power becomes increasingly more powerful, more and more complex learning techniques are employed to allow computers to learn different tasks. Games, however, remain a challenging and exciting domain for testing new technique...

We study the power of a tournament organizer in manipulating the outcome of a single elimination tournament by fixing the initial seeding. It is not known whether the organizer can efficiently fix the outcome of the tournament even if the match outcomes are known in advance. We generalize a result from prior work by giving a new condition such that the organizer can efficiently find a tournamen...

Tournament outcome uncertainty depends on: the design of the tournament; and the relative strengths of the competitors – the competitive balance. A tournament design comprises the arrangement of the individual matches, which we call the tournament structure, the seeding policy and the progression rules. In this paper, we investigate the effect of seeding policy for various tournament structures...

We study the tournament fixing problem (TFP), which asks whether a tournament organizer can rig a single-elimination (SE) tournament such that their favorite player wins, simply by adjusting the initial seeding. Prior results give two perspectives of TFP: on the one hand, deciding whether an arbitrary player can win any SE tournament is known to be NP-complete; on the other hand, there are a nu...