Mardé Helbig

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 othe r algorithms. However, for dynamic multi-objective 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.

Archive management for dynamic multi-objective optimisation problems using vector evaluated particle swarm optimisation

Many optimisation problems have more than one objective that are in conflict with one another and that change over time, called dynamic multi-objective problems. To solve these problems an algorithm must be able to track the changing Pareto Optimal Front (POF) over time and find a diverse set of solutions. This requires detecting that a change has occurred in the environment and then responding to the change. Responding to the change also requires to update the archive of non-dominated solutions that represents the found POF. This paper discusses various ways to manage the archive solutions when a change occurs in the environment. Furthermore, two new benchmark functions are presented where the POF is discontinuous. The dynamic Vector Evaluation Particle Swarm Optimisation (DVEPSO) algorithm is tested against a variety of benchmark function types and its performance is compared against three state-of-the-art DMOO algorithms.

Benchmarks for dynamic multi-objective optimisation algorithms

Algorithms that solve Dynamic Multi-Objective Optimisation Problems (DMOOPs) should be tested on benchmark functions to determine whether the algorithm can overcome specific difficulties that can occur in real-world problems. However, for Dynamic Multi-Objective Optimisation (DMOO), no standard benchmark functions are used. A number of DMOOPs have been proposed in recent years. However, no comprehensive overview of DMOOPs exist in the literature. Therefore, choosing which benchmark functions to use is not a trivial task. This article seeks to address this gap in the DMOO literature by providing a comprehensive overview of proposed DMOOPs, and proposing characteristics that an ideal DMOO benchmark function suite should exhibit. In addition, DMOOPs are proposed for each characteristic. Shortcomings of current DMOOPs that do not address certain characteristics of an ideal benchmark suite are highlighted. These identified shortcomings are addressed by proposing new DMOO benchmark functions with complicated Pareto-Optimal Sets (POSs), and approaches to develop DMOOPs with either an isolated or deceptive Pareto-Optimal Front (POF). In addition, DMOO application areas and real-world DMOOPs are discussed.

Analysing the performance of dynamic multi-objective optimisation algorithms

Dynamic multi-objective optimisation problems (DMOOPs) have more than one objective, with at least one objective changing over time. Since at least two of the objectives are normally in conflict with one another, a single solution does not exist and the goal of the algorithm is to track a set of tradeoff solutions over time. Analysing the performance of a dynamic multi-objective optimisation algorithm (DMOA) is not a trivial task. For each environment (before a change occurs) the DMOA has to find a set of solutions that are both diverse and as close as possible to the optimal trade-off solution set. In addition, the DMOA has to track the changing set of trade-off solutions over time. Approaches used to analyse the performance of dynamic single-objective optimisation algorithms (DSOAs) and DMOAs do not provide any information about the ability of the algorithms to track the changing optimum. Therefore, this paper introduces a new approach to analyse the performance of DMOAs and applies this approach to the results obtained by five DMOAs. In addition, it compares the new analysis approach to another approach that does not take the tracking ability of the DMOAs into account. The results indicate that the new analysis approach provide additional information, measuring the ability of the algorithm to find good performance measure values while tracking the changing optima.

Benchmarks for dynamic multi-objective optimisation

When algorithms solve dynamic multi-objective optimisation problems (DMOOPs), benchmark functions should be used to determine whether the algorithm can overcome specific difficulties that can occur in real-world problems. However, for dynamic multi-objective optimisation (DMOO) there are no standard benchmark functions that are used. This article proposes characteristics of an ideal set of DMOO benchmark functions, as well as suggested DMOOPs for each characteristic. The limitations of current DMOOPs and studies of dynamic multi-objective optimisation algorithms (DMOAs) are highlighted. In addition, new DMOO benchmark functions with complicated Pareto-optimal sets (POSs) and approaches to develop DMOOPs with either an isolated or deceptive Pareto-optimal front (POF) are introduced to address identified limitations of current DMOOPs.

Population-based metaheuristics for continuous boundary-constrained dynamic multi-objective optimisation problems

Abstract Most real-world optimisation problems are dynamic in nature with more than one objective, where at least two of these objectives are in conflict with one another. This kind of problems is referred to as dynamic multi-objective optimisation problems (DMOOPs). Most research in multi-objective optimisation (MOO) have focussed on static MOO (SMOO) and dynamic single-objective optimisation. However, in recent years, algorithms were proposed to solve dynamic MOO (DMOO). This paper provides an overview of the algorithms that were proposed in the literature to solve DMOOPs. In addition, challenges, practical aspects and possible future research directions of DMOO are discussed.

Issues with performance measures for dynamic multi-objective optimisation

In recent years a number of algorithms were proposed to solve dynamic multi-objective optimisation problems. However, a major problem in the field of dynamic multi-objective optimisation is a lack of standard performance measures to quantify the quality of solutions found by an algorithm. In addition, the selection of performance measures may lead to misleading results. This paper highlights issues that may cause misleading results when comparing dynamic multi-objective optimisation algorithms with performance measures that are currently used in the field.

Using Headless Chicken Crossover for Local Guide Selection When Solving Dynamic Multi-objective Optimization

One of the major issues that should be addressed when solving dynamic problems, is a loss of diversity. In addition, when solving multi-objective optimisation problems, one of the goals is to find a diverse set of solutions. Therefore, a key component of a dynamic multi-objective optimisation algorithm (DMOA) is an approach to increase diversity of either the dynamic multi-objective optimisation algorithm DMOA’s individuals or the guides that guide the search of the DMOA. This study investigates whether using the headless chicken macromutation operator for local guide selection improves the performance of the dynamic vector evaluated particle swarm optimisation (DVEPSO) algorithm. Results indicate that the operator does improve the accuracy of the set of solutions that is found by DVEPSO. However, fewer solutions are found.

Search space boundaries in neural network error landscape analysis

Fitness landscape analysis encompasses a selection of techniques designed to estimate the properties of a search landscape associated with an optimisation problem. Applied to neural network training, fitness landscape analysis can be used to establish the link between the shape of the objective function and various neural network design and architecture properties. However, most fitness landscape analysis metrics rely on search space sampling. Since neural network search space is unbounded, it is unclear what subset of the search space should be sampled to obtain representative measurements. This study analyses fitness landscape properties of neural networks under various search space boundaries, and proposes meaningful search space bounds for neural network fitness landscape analysis.

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.