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The multi-guide particle swarm optimisation (MGPSO) algorithm, originally developed for static multi-objective optimisation problems (SMOPs), has been recently adapted for dynamic multi-objective optimisation problems (DMOPs). The MGPSO is a multi-swarm approach where each subswarm optimises one of the objectives. It uses a bounded, crowding distance archive implementation that is managed at each environment change. This paper further adapts the MGPSO for DMOPs by proposing alternative quantum particle swarm optimisation (QPSO) strategies to allow efficient tracking of the changing Pareto-optimal set (POS) and Pareto-optimal front (POF). Specifically, the self-adaptive QPSO and the parent-centric crossover (PCX) QPSO are explored with varying quantum proportions of particles. A total of twenty-nine benchmark functions and six performance measures were implemented to evaluate the performance of the QPSO approaches. The experiments were run against five environment types with varying temporal and spatial severities. The best QPSO strategy was then compared with other state-of-the-art dynamic multi-objective optimisation algorithms (DMOAs). An extensive empirical analysis shows that MGPSO with 10% proportion of self-adaptive quantum particles achieves very competitive and oftentimes better results when compared with other DMOAs.

Selecting appropriate control parameters for the particle swarm optimization algorithm can be extremely time consuming and expensive, yet it is necessary in order to achieve optimal performance on a problem. Despite its significance, the issue of control parameter selection remains an open problem. This work leverages techniques from the field of fitness landscape analysis to characterize a large suite of benchmark problems. Extensive experimentation is performed to identify strong control parameters for each problem, and machine learning techniques are used to predict strong control parameters from the characterization of a problem. The results demonstrate that good generalization is possible with minimal training data. This suggests that the cost of parameter selection can be significantly reduced.

When designing effective parameter tuning and/or self-adaptive mechanisms for meta-heuristic optimizers, any insights about the configuration process and its associated landscape are of great benefit. Recently, the parameter configuration landscape (PCL) was proposed as a mechanism to formally study and characterize the landscape induced by the control parameter values of meta-heuristic search techniques. As an extension, the use of geomorphon landform types to further characterize and visualize the PCL was recently proposed. This study adopts the geomorphon classification scheme and applies it to particle swarm optimization (PSO). The methodology is applied on 20 minimization benchmark problems with various problem dimensions and swarm sizes, thereby providing deep insights into the PCL associated with PSO.

It is well known that appropriately configuring the control parameters for computational intelligence algorithms is a challenging problem. Thus, analysis of the configuration space can provide critical insights towards designing more effective parameter tuning strategies. Recently, the concept of parameter configuration landscapes was proposed by drawing parallels between the parameter configuration space and traditional fitness landscapes, thereby facilitating the use of fitness landscape analysis in the parameter configuration domain. This paper extends the idea of the parameter configuration landscape and proposes the use of geomorphons, a physical landform classification scheme, to visualize and characterize the parameter configuration landscape. Additionally, a measure of ruggedness is proposed to quantity the difficulty associated with tuning the control parameters for an algorithm. The proposed methodology is applied to the parameter configuration landscape of the differential evolution (DE) algorithm on 20 benchmark problems in 10, 30, and 50 dimensions.

The NichePSO algorithm was the first particle swarm optimization algorithm to utilize parallel swarms as an approach to solve multimodal optimization problems. Despite its strong results over many years of research, the NichePSO algorithm has always suffered from a major fundamental issue: The NichePSO algorithm uses multiple smaller subswarms that each search independent sections of the search area, searching for the different optima across the problem landscape. However, each run often ends with a single large subswarm absorbing every other subswarm that has been created, losing track of many of the optima found. This paper analyzes the NichePSO algorithm in detail, and shows evidence that this problem is caused by the subswarm merging strategy being used. Alternative merging approaches are proposed and it is shown that they do not suffer from the same issue as the traditional algorithm.

The purpose of this paper is to compare the abilities and deficiencies of various swarm based algorithms for training artificial neural networks. This paper uses seven algorithms, seven regression problems, sixteen classification problems, and four bounded activation functions to compare algorithms in regards to loss, accuracy, hidden unit saturation, and overfitting. It was found that particle swarm optimization is the top algorithm for regression problems based on loss, firefly algorithm was the top algorithm for classification problems when examining accuracy and loss. The ant colony optimization and artificial bee colony algorithms caused the least amount of hidden unit saturation, with the bacterial foraging optimization algorithm producing the least amount of overfitting.

Many optimization algorithms suffer under the curse of dimensionality - a problem that describes a decrease in performance as the number of problem variables increases. Particle swarm optimization (PSO) is no exception to this performance degradation. Cooperative methods have since been introduced for PSO in order to increase its effectiveness for high dimensional problems by following a divide and conquer approach to large dimensional problems. Performance still suffers for such cooperative PSO (CPSO) variants, mostly due to the dependencies among variables. This paper demonstrates the performance of two new variants of CPSO, namely decomposition and merging cooperative swarm optimization, referred to as DCPSO and MCPSO respectively. The goal of these variants is to improve performance for large scale problems with variable dependencies. Empirical results show that DCPSO and MCPSO were able to perform better than standard CPSO-Sk, CPSOHk and a random grouping variant, CCPSO, for specific problem classes. While empirical results show that the best strategy between merging and decomposition is very much problem dependent, the MCPSO generally converged earlier than the DCPSO.

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.

Complex networks are becoming an integral tool for our understanding of an enormous variety of natural and artificial systems. A number of human-designed network generation procedures have been proposed that reasonably model specific real-life phenomena in structure and dynamics. Consequently, breakthroughs in genetics, medicine, epidemiology, neuroscience, telecommunications, and the social sciences have recently resulted. A graph model is an algorithm capable of constructing arbitrarily sized networks, whose end structure will exhibit certain statistical and structural properties. The process of deriving an accurate graph model is very time intensive and challenging and may only yield highly accurate models for very specific phenomena. An automated approach based on genetic programming was recently proposed by the authors. However, this initial system suffered from a number of drawbacks, including an under-emphasis on creating hub vertices, the requirement of user intervention to determine objective weights, and the arbitrary approach toward selecting the most representative model from a population of candidate models. In this paper, we propose solutions to these problems and show experimentally that the new system represents a significant improvement and is very capable of reproducing existing common graph models from even a single small initial network.

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.

The quantum particle swarm optimization (QPSO) algorithm is a variant of the traditional particle swarm optimization (PSO) algorithm aimed at solving dynamic optimization problems. Some particles in the QPSO algorithm are selected as “quantum” particles and the positions of these particles are sampled, using some probability distribution, within a radius (i.e., a hypersphere) around the global best position while the remainder of particles follow standard PSO behaviour. The exploration and exploitation of the QPSO algorithm is heavily influenced by the probability distribution used as well as the size of the quantum radius. However, the best probability distribution and radius size are both problem and environment dependent. This work proposes using a parent centric crossover (PCX) operator to generate the positions of quantum particles, thereby removing the need for radius and probability distribution parameters completely. Two variants are proposed and results indicate that both variants are superior to QPSO, especially in environments exhibiting high temporal severity.

The quantum particle swarm optimization (QPSO) algorithm was developed to address the limitations of the traditional particle swarm optimization (PSO) algorithm in dynamic environments. Some particles in the QPSO algorithm are chosen as "quantum" particles, and the positions of these are sampled uniformly within a radius (i.e., A hyper sphere) centred around the global best particle. The remainder of particles follow standard PSO behaviour. This paper proposes sampling various alternative probability distributions to update the positions of quantum particles. Ten probability distributions are examined on dynamic environments with varying dimensionalities, temporal change severities, and spatial change severities, with both single-peak and five-peak environments considered. Results indicated that the most effective distribution to use is dependent upon the type of dynamism present. In general, it was observed that a small quantum radius was preferable to a large radius, indicating that exploitation is more beneficial than exploration with regards to QPSO performance. Finally, despite having been commonly used in various QPSO applications, the performance of the uniform distribution was found to be sub-par.

Many real-world optimization problems contain multiple goals to be optimized concurrently. Vector-evaluated particle swarm optimization is a particle swarm optimization variant which employs multiple swarms to solve multi-objective optimization problems. Each swarm optimizes a single objective and information regarding current best positions is passed among swarms using a knowledge transfer strategy. This paper investigates the application of a local search technique to the vector-evaluated particle swarm optimization algorithm. A hill climbing algorithm is applied to non-dominated solutions, dominated solutions, swarm personal best positions and swarm global best positions. Performance of each local search strategy is compared with the standard vector-evaluated particle swarm optimization algorithm using various knowledge transfer strategies. The results indicate that three out of the four local search techniques significantly improved performance of the vector-evaluated particle swarm optimization algorithm for problems possessing two objectives. No significant performance improvement was found for three-objective problems.

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.

The vector evaluated particle swarm optimization (VEPSO) algorithm is a multi-swarm variation of the traditional particle swarm optimization (PSO) used to solve static multi-objective optimization problems (MOOPs). Recently, the dynamic VEPSO (DVEPSO) algorithm was proposed as an extension to VEPSO enabling the algorithm to handle dynamic MOOPs (DMOOPs). While DVEPSO has been successful at handling DMOOPs, the change detection mechanism relied on observing changes in objective space. An alternative strategy is proposed by using charged PSO (CPSO) sub-swarms with decision space change detection to address the outdated memory issue observed in vanilla PSO. This dynamic PSO variant allows for (implicit) decision space tracking not seen in DVEPSO while implicitly handling the diversity issue seen in dynamic environments. The proposed charged VEPSO is compared to DVEPSO on a wide variety of dynamic environment types. Results indicated that, in general, the proposed charged VEPSO outperformed the existing DVEPSO. Further, charged VEPSO exhibited better front-tracking abilities, while DVEPSO was superior with regards to locating the Pareto front.

Most optimization algorithms are designed to solve static, unchanging problems. However, many real-world problems exhibit dynamic behavior. Particle swarm optimization (PSO) is a successful metaheuristic methodology which has been adapted for locating and tracking optima in dynamic environments. Recently, a powerful new class of PSO strategies using cooperative principles was shown to improve PSO performance in static environments. While there exist many PSO algorithms designed for dynamic optimization problems, only one cooperative PSO strategy has been introduced for this purpose, and it has only been studied under one type of dynamism. This study proposes a new cooperative PSO strategy designed for dynamic environments. The newly proposed algorithm is shown to achieve significantly lower error rates when compared to well-known algorithms across problems with varying dimensionalities, temporal change severities, and spatial change severities.

Hub location problem is a NP-hard problem that frequently arises in the design of transportation and distribution systems, postal delivery networks, and airline passenger flow. We propose a simple but effective genetic algorithm (GA) for the uncapacitated single allocation hub location problem (USAHLP). Our main contribution is two new simple chromosome encoding schemes based on indirect representation and two crossover operators. We performed an empirical study to evaluate the effectiveness of the proposed GA using well-known benchmark problems from the Civil Aeronautics Board (CAB) and Australian Post (AP) data sets. The GA found all best-known solutions for the 80 CAB problems and introduced new solutions for the larger problem instances for AP data. The proposed GA can easily be extended to other variants of location problems arising in network design planning in transportation and distributed systems.

Ring-based network design problems have many important applications, especially in the fields of logistics and telecommunications. This paper focuses on the recently proposed two-connected network with bounded rings problem. We investigate the search difficulty of both the Euclidean edge and unit edge length ring size bounds flavors of this problem by performing an information-theoretic fitness landscape analysis for several instances of the problem. Our results further confirm the hypothesis that the unit edge length version of the problem is indeed more difficult. The investigation also further reveals that smaller sized ring bounds lead to harder problems for Euclidean edge lengths. However, for unit edge lengths we did not establish such a relationship