LORA-MaOO: Learning Ordinal Relations and Angles for Expensive Many-Objective Optimization
Keywords: Expensive optimization, many-objective optimization, surrogate-assisted optimization, Gaussian Processes, ordinal regression
Abstract: Many-objective optimization (MaOO) simultaneously optimizes many conflicting objectives to identify the Pareto front - a set of diverse solutions that represent different optimal balances between conflicting objectives. For expensive MaOO problems, due to their costly function evaluations, computationally cheap surrogates have been widely used in MaOO to save evaluation budget. However, as the number of objectives $M$ increases, the cost of using surrogates increases rapidly as many optimization algorithms need maintain $M$ surrogates. In addition, a large $M$ indicates a high-dimensional objective space, increasing the difficulty of maintaining solution diversity.
It is a challenge to reach diverse optimal solutions with a relatively low cost of using surrogates for MaOO problems.
To handle this challenge, we propose LORA-MaOO, a surrogate-assisted MaOO algorithm that learns $M$ surrogates from spherical coordinates, including an ordinal-regression-based surrogate that learns the ordinal relations between solutions (denoted as radial surrogate) and $M$-1 regression-based surrogates that trained on angular coordinates (denoted as angular surrogates).
In each optimization iteration, model-based search is completed with a single radial surrogate, while $M$-1 angular surrogates are used only once for selecting diverse candidates. Therefore, the frequency of using angular surrogates is largely reduced, lowering the cost of using surrogates.
In addition, we design a clustering method to quantify artificial ordinal relations for non-dominated solutions and improve the quantification of dominance-based ordinal relations. These ordinal relations are used to train the radial regression surrogate which predicts how desirable the candidate solutions are in terms of convergence. The solution diversity is maintained via angles between solutions instead of pre-defined auxiliary reference vectors, which is parameter-free. Experimental results show that LORA-MaOO significantly outperforms other surrogate-assisted MaOO methods on most MaOO benchmark problems and real-world applications.
Primary Area: optimization
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Submission Number: 10805
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