Key challenges and future directions of dynamic multi-objective optimisation

Abstract

Many real-world problems have more than one objective and are dynamic in nature, where either an objective function or constraint can vary over time. These problems are referred to as dynamic multi-objective optimisation problems (DMOOPs). A key challenge for dynamic multi-objective optimisation (DMOO) research is efficiently evaluating and analysing the performance of DMOO algorithms (DMOAs). This includes benchmarks, performance measures and the approach used to analyse the obtained results. Most research in recent years focussed on either dynamic single-objective or static multi-objective optimisation. In the field of DMOO, research focussed on unconstrained DMOOPs. A few papers have recently proposed constrained DMOOPs. Therefore, a key sub-challenge in DMOO is to have a standard benchmark suite that contains both unconstrained and constrained DMOOPs with various characteristics. In addition, the constraints used in the benchmarks should be guided by constraints that occur in real-world problems. Most approaches used to analyse the performance of DMOAs do not take into account how well a DMOA tracks the changing optimal solutions over time, i.e. how well it performs in each of the various environments. Furthermore, there are still certain DMOOPs that the proposed algorithms struggle to solve. Therefore, more research is required with regards to the development of algorithms that can solve DMOOPs efficiently. Another important aspect of DMOO is the decision making process that can either occur offline or interactively. This paper discusses these key challenges and progress that has been made to address these challenges. Furthermore, actions to deal with the outstanding issues are also proposed.