Visualising Basins of Attraction for the Cross-Entropy and the Squared Error Neural Network Loss Functions

Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method to visualise basins of attraction together with the associated stationary points via gradient-based random sampling. The proposed technique is used to perform an empirical study of the loss surfaces generated by two different error metrics: quadratic loss and entropic loss. The empirical observations confirm the theoretical hypothesis regarding the nature of neural network attraction basins. Entropic loss is shown to exhibit stronger gradients and fewer stationary points than quadratic loss, indicating that entropic loss has a more searchable landscape. Quadratic loss is shown to be more resilient to overfitting than entropic loss. Both losses are shown to exhibit local minima, but the number of local minima is shown to decrease with an increase in dimensionality. Thus, the proposed visualisation technique successfully captures the local minima properties exhibited by the neural network loss surfaces, and can be used for the purpose of fitness landscape analysis of neural networks.Comment: Preprint submitted to the Neural Networks journa

Cyber Security Maturity Model Capability at The Airports

Cybersecurity is an important facilitator for essential aviation safety. The adoption rate for levels of cyber-security protocols at commercial airports is the focus of this research. Scope of this research is limited to cybersecurity maturity model capability norms covering fourteen domains. The paper presents primary data collected from several airport authorities. This survey-based study will be useful in identifying areas for improving operational procedures and developing strong cybersecurity governance at airports. This will allow airports to understand risks and respond proactively by adopting cybersecurity best practices and resilience measures. This study includes domestic, international, privately owned airports, airstrips, or aerodromes. This research found that level one of cyber-security maturity model is the most followed while proactive and advance levels i.e., level 4 and 5 are least adhered to. Most airports appear to have some resources allocated to cyber protection and resilience

Cybersecurity Maturity Model Capability in Aviation and Railway Industry

Cybersecurity is pivotal for the established aviation and railway industries. This study will examine the compliance of various levels of cybersecurity practices according to Cybersecurity Maturity Model Capability. This study will conduct a survey for aviation and railways. The data collected will be compared to identify which of the two industries is more compliant with the cybersecurity operational procedures. It will also enable the two industries to better evaluate and proactively acknowledge the threats by implementing cybersecurity best practices, governance and resilience processes

Decision-Maker’s Preference-Driven Dynamic Multi-Objective Optimization

Dynamic multi-objective optimization problems (DMOPs) are optimization problems where elements of the problems, such as the objective functions and/or constraints, change with time. These problems are characterized by two or more objective functions, where at least two objective functions are in conflict with one another. When solving real-world problems, the incorporation of human decision-makers (DMs)’ preferences or expert knowledge into the optimization process and thereby restricting the search to a specific region of the Pareto-optimal Front (POF) may result in more preferred or suitable solutions. This study proposes approaches that enable DMs to influence the search process with their preferences by reformulating the optimization problems as constrained problems. The subsequent constrained problems are solved using various constraint handling approaches, such as the penalization of infeasible solutions and the restriction of the search to the feasible region of the search space. The proposed constraint handling approaches are compared by incorporating the approaches into a differential evolution (DE) algorithm and measuring the algorithm’s performance using both standard performance measures for dynamic multi-objective optimization (DMOO), as well as newly proposed measures for constrained DMOPs. The new measures indicate how well an algorithm was able to find solutions in the objective space that best reflect the DM’s preferences and the Pareto-optimality goal of dynamic multi-objective optimization algorithms (DMOAs). The results indicate that the constraint handling approaches are effective in finding Pareto-optimal solutions that satisfy the preference constraints of a DM

Fitness landscape analysis of weight-elimination neural networks

Neural network architectures can be regularised by adding a penalty term to the objective function, thus minimising network complexity in addition to the error. However, adding a term to the objective function inevitably changes the surface of the objective function. This study investigates the landscape changes induced by the weight elimination penalty function under various parameter settings. Fitness landscape metrics are used to quantify and visualise the induced landscape changes, as well as to propose sensible ranges for the regularisation parameters. Fitness landscape metrics are shown to be a viable tool for neural network objective function landscape analysis and visualisation.The National Research Foundation (NRF) of South Africa (Grant Number 46712).https://link.springer.com/journal/110632019-08-01hj2018Consumer Scienc

Performance measures for dynamic multi-objective optimisation algorithms

When algorithms solve dynamic multi-objective optimisation problems (DMOOPs), performance measures are required to quantify the performance of the algorithm and to compare one algorithm’s performance against that of other algorithms. However, for dynamic multiobjective optimisation (DMOO) there are no standard performance measures. This article provides an overview of the performance measures that have been used so far. In addition, issues with performance measures that are currently being used in the DMOO literature are highlighted.http://www.elsevier.com/locate/inshb201