Nelis Franken

Combining particle swarm optimisation with angle modulation to solve binary problems

The optimisation process of a particular problem generally has many influencing factors including the parameter choices, problem constraints as well as the complexity of the optimisation algorithm and optimisation problem among others. The dimensionality of a problem influences the computational complexity in converging to a valid solution. With problems defined in larger and more abstract dimensions, complexity becomes a problem as the solutions presented by the algorithm are more likely to be sub-optimal. An interesting and unique manner to reduce the complexity of binary problems is developed in this paper: angle modulation is applied to generate a bit string to solve binary problems, using particle swarm optimisation (PSO) to evolve the function coefficients of a trigonometric model. Instead of evolving a high dimensional bit vector, angle modulation reduces the problem to a four-dimensional problem defined in continuous space. Experimental results show that the angle modulation method is faster than the standard binary PSO, and that accuracy is improved for most benchmark functions used

Particle swarm optimization approaches to coevolve strategies for the iterated prisoner's dilemma

This paper presents and investigates the application of coevolutionary training techniques based on particle swarm optimization (PSO) to evolve playing strategies for the nonzero sum problem of the iterated prisoners dilemma (IPD). Three different coevolutionary PSO techniques are used, differing in the way that IPD strategies are presented: A neural network (NN) approach in which the NN is used to predict the next action, a binary PSO approach in which the particle represents a complete playing strategy, and finally, a novel approach that exploits the symmetrical structure of man-made strategies. The last technique uses a PSO algorithm as a function approximator to evolve a function that characterizes the dynamics of the IPD. These different PSO approaches are compared experimentally with one another, and with popular man-made strategies. The performance of these approaches is evaluated in both clean and noisy environments. Results indicate that NNs cooperate well, but may develop weak strategies that can cause catastrophic collapses. The binary PSO technique does not have the same deficiency, instead resulting in an overall state of equilibrium in which some strategies are allowed to exploit the population, but never dominate. The symmetry approach is not as successful as the binary PSO approach in maintaining cooperation in both noisy and noiseless environments-exhibiting selfish behavior against the benchmark strategies and depriving them of receiving almost any payoff. Overall, the PSO techniques are successful at generating a variety of strategies for use in the IPD, duplicating and improving on existing evolutionary IPD population observations.

Binary Differential Evolution

The ability of differential evolution (DE) to perform well in continuous-valued search spaces is well documented. The arithmetic reproduction operator used by differential evolution is simple, however, the manner in which the operator is defined, makes it practically impossible to effectively apply the standard DE to other problem spaces. An interesting and unique mapping method is examined which will enable the DE algorithm to operate within binary space. Using angle modulation, a bit string can be generated using a trigonometric generating function. The DE is used to evolve the coefficients to the trigonometric function, thereby allowing a mapping from continuous-space to binary-space. Instead of evolving the higher-dimensional binary solution directly, angle modulation is used together with DE to reduce the complexity of the problem into a 4-dimensional continuous-valued problem. Experimental results indicate the effectiveness of the technique and the viability for the DE to operate in binary space.

Comparing PSO structures to learn the game of checkers from zero knowledge

This paper investigates the effectiveness of various particle swarm optimiser structures to learn how to play the game of checkers. Co-evolutionary techniques are used to train the game playing agents. Performance is compared against a player making moves at random. Initial experimental results indicate definite advantages in using certain information sharing structures and swarm size configurations to successfully learn the game of checkers.

Visual exploration of algorithm parameter space

In this article we apply information visualization techniques to the domain of swarm intelligence. We describe an intuitive approach that enables researchers and designers of stochastic optimization algorithms to efficiently determine trends and identify optimal regions in an algorithms parameter search space. The parameter space is evenly sampled using low-discrepancy sequences, and visualized using parallel coordinates. Various techniques are applied to iteratively highlight areas that influence the optimization algorithms performance on a particular problem. By analyzing experimental data with this technique, we were able to gain important insight into the complexity of the target problem domain. For example, we were able to confirm some underlying theoretical assumptions of an important class of population-based stochastic algorithms. Most importantly, the technique improves the efficiency of finding good parameter settings by orders of magnitude.

PSO approaches to coevolve IPD strategies

This paper investigates two different approaches using particle swarm optimisation (PSO) to evolve strategies for iterated prisoners dilemma (IPD). Strategies evolved by the lesser known binary PSO algorithm are compared to strategies evolved by neural networks that were trained using PSO. Evolved strategies are compared against well-known game theory strategies, with positive results. The presence of noise during IPD interactions are also investigated, and evolved strategies are compared against the same well-known game theory strategies in a noisy environment.

Investigating binary PSO parameter influence on the knights cover problem

The underlying relationship between various PSO parameters is experimentally examined by applying the binary PSO (BinPSO) algorithm to solve the knights cover problem. An exhaustive analysis of the cognitive and social acceleration constants is performed, as well as an investigation into the influence of an increased maximum velocity on overall performance. An intuitive visualisation method eases the analysis of experimental results, and certain assumptions about the direct mapping of continuous PSO to BinPSO parameter values are corrected. The effects of increasing the complexity of the problem are also directly studied and recommendations made to improve performance under larger board sizes

Nonlinear mapping using particle swarm optimisation

Large datasets consisting of high-dimensional vectors commonly describe complex objects. Having these vectors exist in a smaller dimension where the topological characteristics of the original space are preserved, allows clusters or patterns inherent in the data to be identified. This paper investigates the capability of various particle swarm optimisation (PSO) structures to effectively map a high-dimensional dataset to a lower-dimensional set. Four different local nonlinear mapping methods are investigated. Results obtained from the experiments give a clear indication of which nonlinear method to use when certain conditions hold