Trust-Region Method Based on Probabilistic Models for Multi-Objective Optimization
Primary Area: probabilistic methods (Bayesian methods, variational inference, sampling, UQ, etc.)
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Keywords: Multi-objective optimization, Trust region method, probabilistic models, global convergence.
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Abstract: Multi-objective expensive optimization problems appear in many real-world applications. These problems involve multiple computationally expensive objectives, and their derivative information is usually unavailable or hard to compute. Most existing methods focus on constructing high-quality surrogate models for individual objective functions or aggressive subproblems, and these often come with a prohibitive cost. This paper extends the trust-region method based on probabilistic models to solve multi-objective optimization problems. Specifically, we adopt the decomposition mechanism from MOEA/D to decompose the multi-objective optimization problem into multiple Tchebycheff subproblems. Each subproblem is then approximated using high-quality probabilistic models within a trust region framework. Under certain mild assumptions and the properties of Martingales, we can prove that the proposed method can converge to the Pareto critical point with probability one. Experimental results further illustrate that the proposed algorithm outperforms other representative algorithms on a low budget.
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Submission Number: 9437
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