Abstract
Data-driven optimization has found many successful applications in the real world and received increased attention in the field of evolutionary optimization. Most existing algorithms assume that the data used for optimization are always available on a central server for construction of surrogates. This assumption, however, may fail to hold when the data must be collected in a distributed way and are subject to privacy restrictions. This paper aims to propose a federated data-driven evolutionary multi-/many-objective optimization algorithm. To this end, we leverage federated learning for surrogate construction so that multiple clients collaboratively train a radial-basis-function-network as the global surrogate. Then a new federated acquisition function is proposed for the central server to approximate the objective values using the global surrogate and estimate the uncertainty level of the approximated objective values based on the local models. The performance of the proposed algorithm is verified on a series of multi-/many-objective benchmark problems by comparing it with two state-of-the-art surrogate-assisted multi-objective evolutionary algorithms.
Highlights
Many optimization problems have several conflicting objectives that need to be optimized concurrently, which are known as multi-objective optimization [11], and manyobjective optimization when the number of objectives is larger than three [28]
A pile of successful multi-objective evolutionary algorithms (MOEAs) have been developed, which can largely be categorized into decomposition-based MOEAs, such as the multi-objective evolutionary algorithm based on decomposition (MOEA/D) [53] and reference vector guided evolutionary algorithm (RVEA) [6]; Pareto-dominance based, e.g., the elitist non
That most MOEAs require a large number of function evaluations before a set of diverse and well-converged non-dominated solutions can be found, which makes it hard for them to be directly applied to solve a class of data-driven optimization problems [24], whose objectives can be evaluated by means of conducting time-consuming computer simulations or costly physical experiments
Summary
Many optimization problems have several conflicting objectives that need to be optimized concurrently, which are known as multi-objective optimization [11], and manyobjective optimization when the number of objectives is larger than three [28]. Note that many MOEAs combine decomposition or Pareto dominance with other criteria to address various challenges in multi-objective optimization [55]. It is well recognized, that most MOEAs require a large number of function evaluations before a set of diverse and well-converged non-dominated solutions can be found, which makes it hard for them to be directly applied to solve a class of data-driven optimization problems [24], whose objectives can be evaluated by means of conducting time-consuming computer simulations or costly physical experiments. Data-driven surrogate-assisted evolutionary algorithms were first developed for single-objective optimization [23] In this part, we briefly illustrate the concept of multi-objective optimization, RBFN surrogate, federated learning and acquisition function. This layer calculates the distance between a sample point x ∈ Rd and the ith center, φ (||x − ci ||), where φ(·) represents a radial basis function, and in this work we select the Gaussian function with a spread δi as the basis function, φ
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