A Decentralized Multi-objective Optimization Algorithm

During the past few decades, multi-agent optimization problems have drawn increased attention from the research community. When multiple objective functions are present among agents, many works optimize the sum of these objective functions. However, this formulation implies a decision regarding the...

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Vydáno v:Journal of optimization theory and applications Ročník 189; číslo 2; s. 458 - 485
Hlavní autoři: Blondin, Maude J., Hale, Matthew
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2021
Springer Nature B.V
Témata:
Algorithms
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Convergence
Engineering
Mathematics
Mathematics and Statistics
Multiagent systems
Multiple objective analysis
Operations Research/Decision Theory
Optimization
Optimization algorithms
Pareto optimization
Pareto optimum
Priorities
Theory of Computation
Weight
Pareto front
Distributed optimization
Multi-objective optimization
Multi-agent systems
ISSN:0022-3239, 1573-2878
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Shrnutí:During the past few decades, multi-agent optimization problems have drawn increased attention from the research community. When multiple objective functions are present among agents, many works optimize the sum of these objective functions. However, this formulation implies a decision regarding the relative importance of each objective: optimizing the sum is a special case of a multi-objective problem in which all objectives are prioritized equally. To enable more general prioritizations, we present a distributed optimization algorithm that explores Pareto optimal solutions for non-homogeneously weighted sums of objective functions. This exploration is performed through a new rule based on agents’ priorities that generates edge weights in agents’ communication graph. These weights determine how agents update their decision variables with information received from other agents in the network. Agents initially disagree on the priorities of objective functions, though they are driven to agree upon them as they optimize. As a result, agents still reach a common solution. The network-level weight matrix is (non-doubly) stochastic, contrasting with many works on the subject in which the network-level weight matrix is doubly-stochastic. New theoretical analyses are therefore developed to ensure convergence of the proposed algorithm. This paper provides a gradient-based optimization algorithm, proof of convergence to solutions, and convergence rates of the proposed algorithm. It is shown that agents’ initial priorities influence the convergence rate of the proposed algorithm and that these initial choices affect its long-run behavior. Numerical results performed with different numbers of agents illustrate the performance and effectiveness of the proposed algorithm.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01840-z