A benchmark generator for dynamic multi-objective optimization problems

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Many real-world optimization problems appear to not only have multiple objectives that conflict each other but also change over time. They are dynamic multi-objective optimization problems (DMOPs) and the corresponding field is called dynamic multi-objective optimization (DMO), which has gained growing attention in recent years. However, one main issue in the field of DMO is that there is no standard test suite to determine whether an algorithm is capable of solving them. This paper presents a new benchmark generator for DMOPs that can generate several complicated characteristics, including mixed Pareto-optimal front (convexity-concavity), strong dependencies between variables, and a mixed type of change, which are rarely tested in the literature. Experiments are conducted to compare the performance of five state-of-the-art DMO algorithms on several typical test functions derived from the proposed generator, which gives a better understanding of the strengths and weaknesses of these tested algorithms for DMOPs

Evolutionary Dynamic Multi-Objective Optimisation : A survey

Peer reviewedPostprin

On the evolutionary optimisation of many conflicting objectives

This inquiry explores the effectiveness of a class of modern evolutionary algorithms, represented by Non-dominated Sorting Genetic Algorithm (NSGA) components, for solving optimisation tasks with many conflicting objectives. Optimiser behaviour is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal trade-off surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behaviour are offered via the concepts of dominance resistance and active diversity promotion

A Scalable Test Suite for Continuous Dynamic Multiobjective Optimization

Dynamic multiobjective optimization (DMO) has gained increasing attention in recent years. Test problems are of great importance in order to facilitate the development of advanced algorithms that can handle dynamic environments well. However, many of the existing dynamic multiobjective test problems have not been rigorously constructed and analyzed, which may induce some unexpected bias when they are used for algorithmic analysis. In this paper, some of these biases are identified after a review of widely used test problems. These include poor scalability of objectives and, more importantly, problematic overemphasis of static properties rather than dynamics making it difficult to draw accurate conclusion about the strengths and weaknesses of the algorithms studied. A diverse set of dynamics and features are then highlighted that a good test suite should have. We further develop a scalable continuous test suite, which includes a number of dynamics or features that have been rarely considered in literature but frequently occur in real life. It is demonstrated with empirical studies that the proposed test suite are more challenging to the DMO algorithms found in the literature. The test suite can also test algorithms in ways that existing test suites cannot

Vector Autoregressive Evolution for Dynamic Multi-Objective Optimisation

Dynamic multi-objective optimisation (DMO) handles optimisation problems with multiple (often conflicting) objectives in varying environments. Such problems pose various challenges to evolutionary algorithms, which have popularly been used to solve complex optimisation problems, due to their dynamic nature and resource restrictions in changing environments. This paper proposes vector autoregressive evolution (VARE) consisting of vector autoregression (VAR) and environment-aware hypermutation to address environmental changes in DMO. VARE builds a VAR model that considers mutual relationship between decision variables to effectively predict the moving solutions in dynamic environments. Additionally, VARE introduces EAH to address the blindness of existing hypermutation strategies in increasing population diversity in dynamic scenarios where predictive approaches are unsuitable. A seamless integration of VAR and EAH in an environment-adaptive manner makes VARE effective to handle a wide range of dynamic environments and competitive with several popular DMO algorithms, as demonstrated in extensive experimental studies. Specially, the proposed algorithm is computationally 50 times faster than two widely-used algorithms (i.e., TrDMOEA and MOEA/D-SVR) while producing significantly better results

An Open Framework for Constructing Continuous Optimization Problems

Many artificial benchmark problems have been proposed for different kinds of continuous optimization, e.g., global optimization, multi-modal optimization, multi-objective optimization, dynamic optimization, and constrained optimization. However, there is no unified framework for constructing these types of problems and possible properties of many problems are not fully tunable. This will cause difficulties for researchers to analyze strengths and weaknesses of an algorithm. To address these issues, this paper proposes a simple and intuitive framework, which is able to construct different kinds of problems for continuous optimization. The framework utilizes the k-d tree to partition the search space and sets a certain number of simple functions in each subspace. The framework is implemented into global/multimodal optimization, dynamic single objective optimization, multiobjective optimization, and dynamic multi-objective optimization, respectively. Properties of the proposed framework are discussed and verified with traditional evolutionary algorithms