Knowledge transfer in dynamic multi-objective optimization

Ruan, Gan (2024). Knowledge transfer in dynamic multi-objective optimization. University of Birmingham. Ph.D.

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Abstract

Dynamic multi-objective optimization problems (DMOPs) are optimization problems possessing multiple conflicting objectives varying with time. This type of problems widely exists in the real world, such as planning, resource allocation and scheduling problems. Knowledge transfer, a methodology inspired by the machine learning community, has been recently used for solving DMOPs, since it can transfer useful information from solving one problem instance to solve another related problem instance, potentially speeding up the optimization process for the new instance. This thesis contributes to the study of knowledge transfer in dynamic multi-objective optimization as follows:
1. Intuitively, it is doubtful that knowledge transfer approaches would always be beneficial for improving optimization when solving DMOPs with changing position and/or shape of Pareto sets (PSs) and/or Pareto fronts (PFs), since transferring knowledge from an unrelated problem would be harmful to the optimization of the target problem. Therefore, an investigation is made to determine in which cases transfer works and fails. We find that knowledge transfer indeed does not always work and show that it fails on problems with fixed PS and when environmental changes are small. Moreover, we show that using a linear kernel function to transfer results in better quality of transferred solutions than using a Gaussian one.
2. Given that knowledge transfer contributes to improving optimization quality but introduces an overhead in the optimization process, a series of computational studies are carried out to comprehensively understand the efficiency and effectiveness of knowledge transfer when solving DMOPs with changing position and/or shape of PFs/PSs. Specifically, we computationally find that the 'inner' optimization method introduced by transfer learning is very time-consuming. We also find that spending the time optimizing instead of transferring knowledge would lead to better results, which defeats the purpose of knowledge transfer. Then, we propose to use two alternatives to replace the existing `inner' optimization method and find that the transfer algorithm with one alternative achieves better transfer efficiency and solutions quality.
3. Different from most other DMOPs where dynamic changes lead to changing position and/or shape of PSs and/or PFs, DMOPs with a changing number of objectives usually result in expansion or contraction of the PF or PS manifold when the number of objectives increases or reduces, respectively. Therefore, to improve the optimization process when there is a change in the number of objectives, it is intuitive to determine the expansion and contraction directions. These directions could then be used to generate transferred solutions for the new environment and further expand or contract the PSs. Therefore, we firstly propose a heuristic way to determine PS expansion and contraction directions. Then, a novel knowledge transfer algorithm is proposed via PS expansion and contraction based on the found directions for solving DMOPs with a changing number of objectives. The algorithm is able to achieve transferred solutions with good diversity after changes, improving optimization especially in fast changing environments.
4. Moreover, it may also be possible to learn the expansion and contraction directions, so that determining them does not rely entirely on heuristics, potentially leading to more effective transfer of knowledge. Therefore, a novel learning method for determining the expansion and contraction directions is proposed based on principal component analysis, further expanding and contracting the PSs. Specifically, principal component analysis is firstly conducted on the PS of the previous environment to get the candidates of the expansion and contraction directions. Then, the most promising directions for the expansion and contraction are selected according to dominance relationship between existing solutions and those generated along the candidate directions. This approach is able to improve solution quality, not only right after changes but also after optimization of different generations.

Type of Work:

Thesis (Doctorates > Ph.D.)

Award Type:

Doctorates > Ph.D.

Supervisor(s):