Kyle Robert Harrison

Inertia weight control strategies for particle swarm optimization: Too much momentum, not enough analysis

Particle swarm optimization (PSO) is a population-based, stochastic optimization technique inspired by the social dynamics of birds. The PSO algorithm is rather sensitive to the control parameters, and thus, there has been a significant amount of research effort devoted to the dynamic adaptation of these parameters. The focus of the adaptive approaches has largely revolved around adapting the inertia weight as it exhibits the clearest relationship with the exploration/exploitation balance of the PSO algorithm. However, despite the significant amount of research efforts, many inertia weight control strategies have not been thoroughly examined analytically nor empirically. Thus, there are a plethora of choices when selecting an inertia weight control strategy, but no study has been comprehensive enough to definitively guide the selection. This paper addresses these issues by first providing an overview of 18 inertia weight control strategies. Secondly, conditions required for the strategies to exhibit convergent behaviour are derived. Finally, the inertia weight control strategies are empirically examined on a suite of 60 benchmark problems. Results of the empirical investigation show that none of the examined strategies, with the exception of a randomly selected inertia weight, even perform on par with a constant inertia weight.

Knowledge Transfer Strategies for Vector Evaluated Particle Swarm Optimization

Vector evaluated particle swarm optimization (VEPSO) is a multi-swarm variant of the traditional particle swarm optimization (PSO) algorithm applied to multi-objective problems (MOPs). Each sub-objective is allocated a single sub-swarm and knowledge transfer strategies (KTSs) are used to pass information between swarms. The original VEPSO used a ring KTS, and while VEPSO has shown to be successful in solving MOPs, other algorithms have been shown to produce better results. One reason for VEPSO to perform worse than other algorithms may be due to the inefficiency of the KTS used in the original VEPSO. This paper investigates new KTSs for VEPSO in order to improve its performance. The results indicated that a hybrid strategy using parent-centric crossover (PCX) on global best solutions generally lead to a higher hypervolume while using PCX on archive solutions generally lead to a better distributed set of solutions.

The sad state of self-adaptive particle swarm optimizers

The performance of the Particle Swarm Optimization (PSO) algorithm can be greatly improved if the parameters are appropriately tuned. However, tuning the control parameters for PSO algorithms has traditionally been a time-consuming, empirical process. Furthermore, ideal parameters may be time-dependent. To address the issue of parameter tuning, self-adaptive PSO (SAPSO) algorithms adapt the PSO control parameters over time. While many such SAPSO techniques have been proposed, their behaviour is not well understood as no in-depth critical analysis of their adaptation mechanisms has been performed. This study examines the convergence behaviour of eight SAPSO algorithms both analytically and empirically. Evidence clearly indicates that the field of self-adaptive PSO algorithms is in a sad state, given that many techniques either demonstrate divergent behaviour coupled with excessive invalid particles, and thus infeasible solutions, or have prohibitively low particle step sizes caused by rapid convergence.

A scalability study of multi-objective particle swarm optimizers

Particle swarm optimization (PSO) is a well-known optimization technique originally proposed for solving single-objective, continuous optimization problems. However, PSO has been extended in various ways to handle multi-objective optimization problems (MOPs). The scalability of multi-objective PSO algorithms as the number of sub-objectives increases has not been well examined; most observations are for two to four objectives. It has been observed that the performance of multiobjective optimizers for a low number of sub-objectives can not be generalized to problems with higher numbers of sub-objectives. With this in mind, this paper presents a scalability study of three well-known multi-objective PSOs, namely vector evaluated PSO (VEPSO), optimized multi-objective PSO (oMOPSO), and speed-constrained multi-objective PSO (SMPSO) with up to eight sub-objectives. The study indicates that as the number of sub-objectives increases, SMPSO scaled the best, oMOPSO scaled the worst, while VEPSOs performance was dependent on the knowledge transfer strategy (KTS) employed, with parent centric recombination (PCX) based approaches scaling consistently better.

A meta-analysis of centrality measures for comparing and generating complex network models

Abstract Complex networks are often characterized by their statistical and topological network properties such as degree distribution, average path length, and clustering coefficient. However, many more characteristics can also be considered such as graph similarity, centrality, or flow properties. These properties have been utilized as feedback for algorithms whose goal is to ascertain plausible network models (also called generators) for a given network. However, a good set of network measures to employ that can be said to sufficiently capture network structure is not yet known. In this paper we provide an investigation into this question through a meta-analysis that quantifies the ability of a subset of measures to appropriately compare model (dis)similarity. The results are utilized as fitness measures for improving a recently proposed genetic programming (GP) framework that is capable of ascertaining a plausible network model from a single network observation. It is shown that the candidate model evaluation criteria of the GP system to automatically infer existing (man-made) network models, in addition to real-world networks, is improved.

An Experimental Evaluation of Multi-objective Evolutionary Algorithms for Detecting Critical Nodes in Complex Networks

Identifying critical nodes in complex networks has become an important task across a variety of application domains. In this paper we propose a multi-objective version of the critical node detection problem, which aims to minimize pairwise connectivity in a graph by removing a subset of \(K\) nodes. Interestingly, while it has been recognized that this problem is inherently multi-objective since it was formulated, until now only single-objective algorithms have been proposed. After explicitly stating the new multi-objective problem variant, we then give a brief comparison of six common multi-objective evolutionary algorithms using sixteen common benchmark problem instances. A comparison of the results attained by viewing the algorithm as a single versus multi-objective problem is also conducted. We find that of the examined algorithms, NSGAII generally produces the most desirable approximation fronts. We also demonstrate that while related, the best multi-objective solutions do not translate into the best single-objective solutions.

Demonstrating the power of object-oriented genetic programming via the inference of graph models for complex networks

Traditionally, GP used a single tree-based representation which does not lend itself well to state-based programs or multiple behaviours. To alleviate this drawback, object-oriented GP (OOGP) introduced a means of evolving programs with multiple behaviours which could be easily extended to state-based programs. However, the production of programs which allowed embedded knowledge and produced readable code was still not easily addressed using the OOGP methodology. Exemplified through the evolution of graph models for complex networks, this paper demonstrates the benefits of a new approach to OOGP inspired by abstract classes and linear GP. Furthermore, the new approach to OOGP, named LinkableGP, facilitates the embedding of expert knowledge while also maintaining the benefits of OOGP.

Incorporating expert knowledge in object-oriented genetic programming

Genetic programming (GP) has proven to be successful at generating programs which solve a wide variety of problems. Object-oriented GP (OOGP) extends traditional GP by allowing the simultaneous evolution of multiple program trees, and thus multiple functions. OOGP has been shown to be capable of evolving more complex structures than traditional GP. However, OOGP does not facilitate the incorporation of expert knowledge within the resulting evolved type. This paper proposes an alternative OOGP methodology which does incorporate expert knowledge by the use of a user-supplied partially-implemented type definition, i.e. an abstract class.

Optimal parameter regions for particle swarm optimization algorithms

Particle swarm optimization (PSO) is a stochastic search algorithm based on the social dynamics of a flock of birds. The performance of the PSO algorithm is known to be sensitive to the values assigned to its control parameters. While many studies have provided reasonable ranges in which to initialize the parameters based on their long-term behaviours, such previous studies fail to quantify the empirical performance of parameter configurations across a wide variety of benchmark problems. This paper specifically address this issue by examining the performance of a set of 1012 parameter configurations of the PSO algorithm over a set of 22 benchmark problems using both the global-best and local-best topologies. Results indicate that, in general, parameter configurations which are within close proximity to the boundaries of the best-known theoretically-defined convergent region lead to better performance than configurations which are further away. Moreover, results indicate that neighbourhood topology plays a far more significant role than modality and separability when determining the regions in parameter space which perform well.

Investigating Fitness Measures for the Automatic Construction of Graph Models

Graph models are often constructed as a tool to better understand the growth dynamics of complex networks. Traditionally, graph models have been constructed through a very time consuming and difficult manual process. Recently, there have been various methods proposed to alleviate the manual efforts required when constructing these models, using statistical and evolutionary strategies. A major difficulty associated with automated approaches lies in the evaluation of candidate models. To address this difficulty, this paper examines a number of well-known network properties using a proposed meta-analysis procedure. The meta-analysis demonstrated how these network measures interacted when used together as classifiers to determine network, and thus model, (dis)similarity. The analytical results formed the basis of a fitness evaluation scheme used in a genetic programming (GP) system to automatically construct graph models for complex networks. The GP-based automatic inference system was used to reproduce two well-known graph models, the results of which indicated that the evolved models exemplified striking similarity when compared to their respective targets on a number of structural network properties.