Gina M. B. Oliveira

The best currently known class of dynamically equivalent cellular automata rules for density classification

Abstract The possibility of performing computations with cellular automata (CAs) opens up new conceptual issues in emergent computation. Driven by this motivation, a recurring problem in this context is the automatic search for good one-dimensional, binary CA rules that can perform well in the density classification task (DCT), that is, the ability to discover which cell state outnumbers the other state. In the past, the most successful attempts to reach this target have relied on evolutionary searches in the space of possible rules. Along this line, a multiobjective, heuristic evolutionary approach, implemented as a distributed cooperative system, is presented here, which yielded outstanding results, including a rule that led to the characterisation of a class of four equivalent rules, all of them with the best performance currently available in the literature for the DCT.

Some Investigations About Synchronization and Density Classification Tasks in One-dimensional and Two-dimensional Cellular Automata Rule Spaces

The study of computational aspects of cellular automata (CA) is a recurrent theme being that the investigation of specific tasks to be solved by CA rules a common and widely-known approach. We investigated two of the most-studied computational tasks: synchronization (ST) and density classification (DCT). Different specifications of CA rule space were analyzed for both tasks: one-dimensional rules with radius 1 and 2, and two-dimensional rules with von Neumann and Moore neighborhoods. We also analyzed different lattice sizes when trying to execute these tasks. Several evolutionary experiments were performed to characterize ST and DCT on these different scenarios. Some interesting results have been occurred from these experiments as the adequacy of the tasks to be solved in two-dimensional spaces instead of 1D even using rules with the same length and the dependency to the parity of the lattice size related to good rules for DCT in 1D and 2D spaces.

Multicast flow routing: Evaluation of heuristics and multiobjective evolutionary algorithms

In this work, a multiobjective genetic algorithm-based model for multicast flow routing with QoS and Traffic Engineering requirements is discussed. Two heuristics for subtree reconnection are investigated, applicable in crossover and mutation operators. Experiments with three multiobjective evolutionary algorithms (NSGA-II, SPEA and SPEA2) and the proposed heuristics are carried on, whose results indicate that SPEA2 overcame SPEA and NSGA-II, besides providing the best combination with one the heuristics, obtaining the best average results. This work also shows that the proposed heuristics guarantee the consistency of the proposed model, since they fix a previous heuristic that can potentially generate invalid solutions.

A multi-objective evolutionary algorithm with ε-dominance to calculate multicast routes with QoS requirements

Multicasting routing is an effective way to communicate among multiple hosts in computer networks. Usually multiple quality of service (QoS) guarantees are required in most of multicast applications. Several researchers have investigated genetic algorithms-based models for multicast route computation with QoS requirements. The evolutionary models proposed here use multi-objective approaches in a Pareto sense to solve this problem and to deal with the inheriting multiple metrics involved in QoS proposal. Basically, we construct three QoS-constrained multicasting routing algorithms; the first one was based on NSGA, the second one was based on NSGA-II and the third is an adaptation of NSGA-II incorporating the concept of ε-dominance. These algorithms were applied to find multicast routes over two network topologies. Three different pairs of objectives were evaluated; the first objective used in each pair is related to the total cost of a multicast route and the second metric is related to delay. The first evaluated delay metric computes the total delay involved in the tree solution; the second one computes the mean delay accumulated from the source to each destination node; the third one is the maximum delay accumulated from the source to a destination node. Our results indicated that the NSGA-II environment incorporating the concept of ε-dominance - named ε-NSGA-II multicasting routing - returned the best performance.

An Improved Cellular Automata-Based Model for Robot Path-Planning

Cellular automata (CA) are able to represent high complex phenomena and can be naturally simulated by digital processors due to its intrinsic discrete nature. CA have been recently considered for path planning in autonomous robotics. In this work we started by adapting a model proposed by Ioannidis et al. to deal with scenarios with a single robot, turning it in a more decentralized approach. However, by simulating this model we noticed a problem that prevents the robot to continue on its path and avoid obstacles. A new version of the model was then proposed to solve it. This new model uses CA transition rules with Moore neighborhood and four possible states per cell. Simulations and experiments involving real e-puck robots were performed to evaluate the model. The results show a real improvement in the robot performance.

Multiobjective Evolutionary Algorithms and a Combined Heuristic for Route Reconnection Applied to Multicast Flow Routing

Multicast transmission corresponds to send data to several destinations often involving requirements of Quality of Service (QoS) and Traffic Engineering (TE). This work investigates new evolutionary models to tackle Multicast Flow Routing in a Pareto multiobjective perspective. Two multiobjective evolutionary algorithms (SPEA and SPEA2) were applied as the underlying search of such models. QoS and TE requirements are also considered in the route calculus by optimizing four objectives - maximum link utilization, total cost, maximum end-to-end delay and hops count - attending a link capacity constraint. Besides, three heuristics for subtrees reconnection to be used on crossover and mutation operators are investigated. The first heuristic uses a shortest path algorithm to improve the convergence; the second one employs a random search to reconnect subtrees into a valid route and the third one mixes the other two combining the good skills of each one. The resultant evolutionary environments were evaluated using four multiobjective metrics: two for convergence and two for diversity. SPEA2 reached better results than SPEA on the vast majority cases. The design of crossover and mutation operators that provide more diversity lead to very good improvements on both multiobjective goals - convergence and diversity - being that the heuristic which combines random and shortest path reconnections and returned the best results.

A Coevolutionary Approach to Cellular Automata-Based Task Scheduling

Cellular Automata (CA) have been proposed for task scheduling in multiprocessor architectures. CA-based models aim to be fast and decentralized schedulers. Previous models employ an off-line learning stage in which an evolutionary method is used to discover cellular automata rules able to solve an instance of a task scheduling. A central point of CA-based scheduling is the reuse of transition rules learned for one specific program graph in the schedule of new instances. However, our investigation about previous models showed that evolved rules do not actually have such generalization ability. A new approach is presented here named multigraph coevolutionary learning, in which a population of program graphs is evolved simultaneously with rules population leading to more generalized transition rules. Results obtained have shown the evolution of rules with better generalization abilitywhen they are compared with those obtained using previous approaches.

Synchronous cellular automata-based scheduler initialized by heuristic and modeled by a pseudo-linear neighborhood

Cellular automata (CA) are able to produce a global behavior from local interactions between their units. They have been applied to the task scheduling problem in multiprocessor systems in a very distinguished way. As this problem is NP-Complete, heuristics and meta-heuristics are usually employed. However, these techniques must always start the scheduling process from scratch for each new parallel application given as input. On the other hand, the main advantage to use CA for scheduling is the discovery of rules while solving one application and their subsequent reuse in other instances. Recently studies related to CA-based scheduling have shown relevant approaches as the use of synchronous updating in CA evolution and good results in multiprocessor systems with two processors. However, some aspects, such as the low performance of CA-based schedulers in architectures with more than two processors and during the reuse of the discovered rules, need to be investigated. This paper presents two new models to improve CA-based scheduling to deal with such aspects. The first proposal refers to the employment of a construction heuristic to initialize CA evolution and the second one is a new neighborhood model able to capture the dependence and relations strength among the tasks in a very simple way. It was named pseudo-linear neighborhood. An extensive experimental evaluation was performed using graphs of parallel programs found in the literature and new ones randomly generated. Experimental analysis showed the combined application of both techniques makes the search for CA transition rules during learning stage more robust and leads to a significant gain when considering the reuse of them on real-world conditions.

Analyzing the effects of neighborhood crossover in multiobjective multicast flow routing problem

Multicast transmission corresponds to send data to several destinations, often involving requirements of Quality of Service (QoS) and Traffic Engineering (TE). These multiple requirements lead to the need of optimizing a set of conflicting objectives subject to constraints. We investigate algorithms to perform the calculus of multicast routes while minimizing five objectives - mean link utilization, maximum link utilization, total cost, maximum end-to-end delay and hops count - attending a link capacity constraint. New multiobjective evolutionary models to tackle multicast routing are discussed here based on SPEA2 and NSGA-II. The key investigation performed here is about the incorporation of Neighborhood Crossover (NC) as the mating selection of parent pairs. Two variations of NC with different shuffling strategies are discussed here. The incorporation of both NC methods to the routing environments leaded to significant improvements mainly on convergence, while maintaining a compromise on diversity. Our results indicate that the evolutionary model based on SPEA2 using a shuffle procedure, in which after sorting the population according to a focused objective, an individual can cross over with a neighbor around a small range (10%), had returned the better results. A comparison of the results obtained by the aforementioned evolutionary model with the traditional Dijkstras (Shortest Path Tree) and Takahashi-Matsuyama algorithms shows that the our proposal is a very competitive multicast routing model.

Using dynamic behavior prediction to guide an evolutionary search for designing two-dimensional cellular automata

The investigations carried out about the relationships between the generic dynamic behavior of cellular automata (CA) and their computational abilities have established a very active research area. Evolutionary methods have been used to look for CA with predefined computational abilities; one in particular that has been widely studied is the ability to solve the density classification task (DCT). The majority of these studies are focused on the one-dimensional CA. It has recently been shown that the use of a heuristic guided by parameters that estimate the dynamic behavior of 1D CA can improve the evolutionary search for DCT. The present work shows the application of three parameters previously published in the one-dimensional context generalized to the two-dimensional space: sensitivity, neighborhood dominance and activity propagation were used to evolve CA able to perform the two-dimensional version of the density classification task. The results obtained show that the parameters can effectively help a genetic algorithm in searching for 2D CA. A new rule was found which performed better than others previously published for the 2D DCT.