Amine M. Boumaza

On the evolution of artificial Tetris players

In the paper, we focus the use of evolutionary algorithms to learn strategies to play the game of Tetris. We describe the problem and discuss the nature of the search space. We present experiments to illustrate the learning process of our artificial player, and provide a new procedure to speed up the learning time. The results we present compare with the best known artificial player, and show how our evolutionary algorithm is able to rediscover player strategies previously published. Finally we provide some ideas to improve the performance of artificial Tetris players.

Stochastic search for global neighbors selection in collaborative filtering

Neighborhood based collaborative filtering is a popular approach in recommendation systems. In this paper we propose to apply evolutionary computation to reduce the size of the model used for the recommendation. We formulate the problem of constructing the set of neighbors as an optimization problem that we tackle by stochastic local search. The results we present show that our approach produces a set of global neighbors made up of less than 16% of the entire set of users, thus decreases the size of the model by 84%. Furthermore, this reduction leads to a slight increase of the accuracy of a state of the art clustering based approach, without impacting the coverage.

From neighbors to global neighbors in collaborative filtering: an evolutionary optimization approach

The accuracy of recommendations of collaborative filtering based recommender systems mainly depends on which users (the neighbors) are exploited to estimate a users ratings. We propose a new approach of neighbor selection, which adopts a global point of view. This approach defines a unique set of possible neighbors, shared by all users, referred to as Global Neighbors (GN). We view the problem of defining GN as a combinatorial optimization problem and propose to use an evolutionary algorithm to tackle this search. Our aim is to find a relatively small GN as the size of the resulting model, as well as the complexity of the computation of recommendations highly depend on the size of GN. We present experiments and results on a standard benchmark data-set from the recommender system community that support our choice of the evolutionary approach and show that it leads to a high accuracy of recommendations and a high coverage, while dramatically reducing the size of the model (by 84%). We also show that the evolutionary approach produces results able to generate accurate recommendations to unseen users, while easily allowing the insertion of new users in the system with little overhead.

Learning environment dynamics from self-adaptation: a preliminary investigation

We present an experimental study that shows a relationship between the dynamics of the environment and the adaptation of strategy parameters. Experiments conducted on two adaptive evolutionary strategies SA-ES and CMA-ES on the dynamic sphere function, show that the nature of the movements of the functions optimum are reflected in the evolution of the mutation steps. Three types of movements are presented: constant, linear and quadratic velocity, in all, the evolution of mutation steps during adaptation reflect distinctly the nature of the movements. Furthermore with CMA-ES, the direction of movement of the optimum can be extracted.

A multilevel tabu search with backtracking for exploring weak schur numbers

In the field of Ramsey theory, the weak Schur numberWS(k) is the largest integer n for which their exists a partition into k subsets of the integers [1,n] such that there is no x<y<z all in the same subset with x+y=z. Although studied since 1941, only the weak Schur numbers WS(1) through WS(4) are precisely known, for k≥5 the WS(k) are only bracketed within rather loose bounds. We tackle this problem with a tabu search scheme, enhanced by a multilevel and backtracking mechanism. While heuristic approaches cannot definitely settle the value of weak Schur numbers, they can improve the lower bounds by finding suitable partitions, which in turn can provide ideas on the structure of the problem. In particular we exhibit a suitable 6-partition of [1,574] obtained by tabu search, improving on the current best lower bound for WS(6).

Meta-heuristic search and square erickson matrices

A Ramsey theory problem, that can be seen as a 2 dimensional extension of the Van der Waerden theorem, was posed by Martin J. Erickson in his book [1]: “find the minimum n such that if the lattice points of [n] × [n] are two-colored, there exist four points of one color lying on the vertices of a square with sides parallel to the axes”. This was solved recently by Bacher and Eliahou in 2009 [2], who showed that n = 15. In this paper we tackle a derived version of this problem, searching for the minimum n that forces the existence of a monochromatic 3] × [3] subgrid of [n] × [n] of the form {i, i + t, i + 2t} × {j, j + t, j + 2t} for any 2-coloring of [n] × [n]. We use meta-heuristics on this open problem to find instances of 2-colorations without monochromatic [3] × [3] subgrid of the above form, setting a lower bound on n. In particular we found such a binary square grid of size 662, implying that n > 662.

Maintaining Diversity in Robot Swarms with Distributed Embodied Evolution

In this paper, we investigate how behavioral diversity can be maintained in evolving robot swarms by using distributed Embodied Evolution. In these approaches, each robot in the swarm runs a separate evolutionary algorithm, and populations on each robot are built through local communication when robots meet; therefore, genome survival results not only from fitness-based selection but also from spatial spread. To better understand how diversity is maintained in distributed EE, we propose a postanalysis diversity measure, that we take from two perspectives, global diversity (over the swarm), and local diversity (on each robot), on two swarm robotic tasks (navigation and item collection), with different intensities of selection pressure, and compare the results of distributed EE to a centralized case. We conclude that distributed evolution intrinsically maintains a larger behavioral diversity when compared to centralized evolution, which allows for the search algorithm to reach higher performances, especially in the more challenging collection task.

Designing artificial tetris players with evolution strategies and racing

This article describes how racing procedures in evolution strategies can help reduce the number of evaluations. This idea is illustrated on learning Tetris players which can be addressed as a stochastic optimization problem. Different experiments show the benefits of the racing procedures in evolution strategies which can significantly reduce the number of evaluations.

Reducing the learning time of tetris in evolution strategies

Designing artificial players for the game of Tetris is a challenging problem that many authors addressed using different methods. Very performing implementations using evolution strategies have also been proposed. However one drawback of using evolution strategies for this problem can be the cost of evaluations due to the stochastic nature of the fitness function. This paper describes the use of racing algorithms to reduce the amount of evaluations of the fitness function in order to reduce the learning time. Different experiments illustrate the benefits and the limitation of racing in evolution strategies for this problem. Among the benefits is designing artificial players at the level of the top ranked players at a third of the cost.

Convergence and rate of convergence of a foraging ant model

We present an ant model that solves a discrete foraging problem. We describe simulations and provide a complete convergence analysis: we show that the ant population computes the solution of some optimal control problem and converges in some well defined sense. We discuss the rate of convergence with respect to the number of ants: we give experimental and theoretical arguments that suggest that this convergence rate can be superlinear with respect to the number of agents. Furthermore, we explain how this model can be extended in order to solve optimal control problems in general and argue that such an approach can be applied to any problem that involves the computation of the fixed point of a contraction mapping. This allows to design a large class of formally well understood ant like algorithms for problem solving.