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Transfer Learning based Dynamic Multiobjective Optimization Algorithms
Min Jiang, Zhongqiang Huang, Liming Qiu, Wenzhen Huang, Gary G. Yen
TL;DR
DMOPs require tracking changing Pareto-optimal fronts, while existing prediction methods often overlook non-IID data across environments. Tr-DMOEA integrates transfer learning with population-based evolutionary algorithms to reuse past Pareto knowledge, and experiments across three algorithms and twelve benchmark functions support its effectiveness and robustness. The paper notes that parameter tuning was not performed individually and that change detection is outside its scope.
Problem
DMOPs require tracking changing Pareto-optimal fronts, but traditional prediction methods often assume IID data despite distribution differences across environments.
Method
Tr-DMOEA uses transfer component analysis to reuse past Pareto-optimal knowledge and generate an initial population for a population-based evolutionary algorithm.
Results
Experiments with NSGA-II, MOPSO, and RM-MEDA on twelve benchmark functions found that transfer learning greatly improved solution quality and algorithm robustness in almost all results.
Takeaways & Limitations
The framework provides a reusable integration for population-based multiobjective algorithms and offers a potential avenue for efficient evolutionary algorithms for DMOPs.
Takeaways & Limitations
The experiments did not tune parameters individually for each algorithm and benchmark function, although the authors expected separate tuning could yield better results.
Abstract
from arXiv · showhide
One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is the optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing the "experiences" to construct a prediction model via statistical machine learning approaches. However most of the existing methods ignore the non-independent and identically distributed nature of data used to construct the prediction model. In this paper, we propose an algorithmic framework, called Tr-DMOEA, which integrates transfer learning and population-based evolutionary algorithm for solving the DMOPs. This approach takes the transfer learning method as a tool to help reuse the past experience for speeding up the evolutionary process, and at the same time, any population based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this, we incorporate the proposed approach into the development of three well-known algorithms, nondominated sorting genetic algorithm II (NSGA-II), multiobjective particle swarm optimization (MOPSO), and the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA), and then employ twelve benchmark functions to test these algorithms as well as compare with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed method through exploiting machine learning technology.
3 School of Electrical and Computer Engineering, Oklahoma State University, USA
The paper addresses dynamic multiobjective optimization, with transfer learning among its central themes.
- The paper concerns dynamic multi-objective optimization, domain adaptation, dimensionality reduction, transfer learning, and evolutionary algorithms.
1 Introduction
DMOPs require tracking Pareto-optimal solutions as objectives change, but prediction methods commonly rely on an unsuitable IID assumption. The paper proposes integrating transfer learning with evolutionary algorithms to reuse past experience and improve search efficiency.
- DMOP objectives vary over time or environments, creating a need to track changing Pareto-optimal fronts in applications such as dynamic portfolio optimization.
- Prediction-based methods reuse past solutions, but changing Pareto fronts can make training and predicted samples follow different distributions.
- Traditional machine-learning prediction models leave performance room when training and predicted samples violate the IID hypothesis.
- Tr-DMOEA integrates transfer learning with evolutionary algorithms to construct a prediction model from past Pareto-optimal solutions.
- The paper focuses on rapid re-optimization after a dynamic change has been detected, not on detecting or identifying the change itself.
- The proposed design preserves evolutionary-algorithm advantages while reusing past experience to improve search efficiency for DMOPs.
2 Preliminary Studies and Related Research
The paper reviews DMOP definitions and established strategies, then identifies distribution mismatch as a key weakness of prediction-based approaches. It motivates transfer learning as a way to reuse correlated historical Pareto information without assuming IID data.
- A DMOP minimizes multiple time-dependent objectives over a bounded decision space, with dynamic Pareto-optimal sets and fronts defined at each time.
- An ideal dynamic multiobjective algorithm should track the changing Pareto-optimal front closely while maintaining solution diversity.
- Existing DMOP algorithms include diversity, memory, multi-population, and prediction-based methods.
- Diversity methods introduce random or mutated individuals after changes to help populations recover variation.
- Memory methods reuse stored individuals after detected changes and tend to work better in periodically changing environments.
- Prediction-based methods reuse existing information to estimate future environmental states, but inaccurate models can direct search poorly.
- The proposed framework treats historical Pareto sets or fronts as correlated information and avoids requiring an IID assumption.
3 Transfer Learning based Dynamic Multiobjective Optimization Algorithm
Tr-DMOEA maps source and target solution distributions into a latent space using transfer component analysis, then uses transferred Pareto-front knowledge to generate an initial population. This population can be supplied to population-based optimizers to reduce search cost.
- The method maps distributions from different environments into a latent space where they are similar while preserving data variance.
- Domain adaptation reuses knowledge from a source domain for a related but distinct target domain.
- Transfer Component Analysis: Transfer component analysis uses kernel-based representations to reduce source-target distribution differences while retaining statistical variation.
- Tr-DMOEA: The motivation is to reduce computational resource consumption when searching for Pareto-optimal solutions in expensive dynamic problems.
- Tr-DMOEA: The approach addresses non-IID distributions across environments through domain adaptation rather than traditional machine learning alone.
- Tr-DMOEA treats the current Pareto-optimal front as the source domain and next-time feasible solutions as the target domain.
- Tr-DMOEA: The transfer component generates an initial population from the already found Pareto-optimal front for searching the next-time front.
14 end
Tr-IPG maps past Pareto-optimal solutions into a latent space, searches for corresponding individuals in the changed objective space, and generates an initial population pool. Its population output allows integration with population-based multiobjective algorithms, while sampling and optimization choices determine computational cost.
- Transfer Component Analysis uses samples from times t and t + 1 to produce a transformation matrix W for constructing the latent space.The matrix maps solutions from the current Pareto-optimal front into the latent representation.
- Tr-IPG maps the obtained Pareto-optimal front into a latent space, then searches for individuals and generates an initial population pool for the next environment.The three steps operationalize transfer from the current problem to Ft+1(·).
- The numbers of sampled current and next-time solutions are resource-dependent: more sampling can improve results but increases computational cost.The sampling sizes are predefined as |Xs| = ns and |Yt| = nt.
- Particle in the Latent Space denotes the set of mapped solutions used to guide the search for decision variables whose next-time objective values are nearby.The search is formulated as a single-objective optimization problem solved with the Interior Point Algorithm.
- Because Tr-IPG outputs a population, it can be combined with any population-based optimization algorithm to obtain a transfer learning based dynamic multiobjective evolutionary algorithm.This design supports reuse across different evolutionary multiobjective algorithms without changing the transfer procedure itself.
- TCA computation is dominated by eigenvalue decomposition, requiring O(d(m1 + m2)^2) time when d nonzero eigenvectors are extracted.The stated complexity depends on the numbers of solutions used to construct the latent space.
4 Empirical Study
The empirical study integrates transfer learning with three population-based multiobjective algorithms and evaluates them on twelve dynamic benchmark functions using IGD- and React-based metrics. Across the experiments, transfer-enhanced algorithms generally improve performance, although gains depend on the algorithm, parameters, and problem characteristics.
- Algorithmic framework: The study incorporates the approach into NSGA-II, MOPSO, and RM-MEDA, producing Tr-NSGA-II, Tr-MOPSO, and Tr-RM-MEDA for dynamic optimization.The three base algorithms represent genetic, particle-swarm, and estimation-of-distribution optimization metaphors.
- Algorithmic framework: Tr-DMOEA integrates transfer learning with population-based multiobjective algorithms and uses past Pareto-optimal-solution knowledge to generate an initial population after environmental changes.The framework is designed to work with any population-based multiobjective algorithm through the Tr-IPG transfer component.
- Experimental design: The experiments use twelve benchmark functions, eight configurations, and twenty changes per function, evaluating MIGD, DMIGD, React, MReact, and DMReact.DMIGD summarizes performance across multiple environments, while React measures recovery speed after changes; smaller React values are better.
- Results: 78% of Tr-NSGA-II tests, 70% of Tr-MOPSO tests, and 73% of Tr-RM-MEDA tests improved over their original algorithms.These correspond respectively to 75, 67, and 70 improving cases out of 96 tests for each algorithm.
- Results: Transfer-enhanced algorithms showed better performance across benchmark characteristics and were more efficient than selected state-of-the-art designs.The comparison included RND and MOEA/D-KF in addition to the original algorithms.
- Results: Tr-NSGA-II and Tr-MOPSO improved DMReact, whereas Tr-RM-MEDA showed reduced robustness under the tested parameter setting.The authors associate the RM-MEDA robustness reduction with a possible loss of solution diversity and identify parameter selection as future work.
5 Conclusion and Future Works
The paper frames DMOP optimization as a Non-IID learning problem and integrates transfer learning with evolutionary algorithms to reuse past Pareto-optimal knowledge. Applied to three algorithms, the approach generally improves solution quality and robustness, though its effects can depend on parameter settings and algorithm.
- Motivation: DMOP solutions at different times follow related but non-identical distributions, making classical machine-learning prediction methods difficult to apply.The paper identifies this as a Non-IID problem.
- Approach: Transfer component analysis maps source and target distributions into a latent space while preserving variance, enabling past Pareto-optimal solutions to initialize the next search.The obtained initial population can be used by population-based algorithms at the next time instance.
- Evaluation: The framework is incorporated into NSGA-II, MOPSO, and RM-MEDA and compared with original and competing algorithms on twelve benchmark functions.The approach is intended to be broadly compatible with population-based evolutionary algorithms.
- Findings: The experiments broadly validate improved solution quality and robustness from introducing transfer learning into dynamic optimization algorithms.The paper presents this work as a potential avenue for designing effective and efficient evolutionary algorithms for DMOPs.
6 supplemental Materials
The supplemental materials provide detailed MIGD results for six algorithms across twelve testing functions and eight environments. They also include tables for additional benchmark functions and summarize performance changes using ROC values.
- Detailed Results: The supplemental section contains twelve tables recording MIGD values for six algorithms across twelve testing functions and environments C1 through C8.The algorithms include NSGA-II, Tr-NSGA-II, MOPSO, Tr-MOPSO, RM-MEDA, and Tr-RM-MEDA.
- Detailed Results: ROC denotes the ratio of change in MIGD values, with boldface marking experiments where performance improved.This convention is used in the detailed result tables.