A Decentralized Multi-objective Optimization Algorithm

During the past few decades, multi-agent optimization problems have drawn increased attention from research community. When multiple objective functions are present among agents, many works optimize sum of these functions. However, this formulation implies a decision regarding relative importance each objective: optimizing is special case multi-objective problem in which all objectives prioritized equally. To enable more general prioritizations, we distributed algorithm that explores Pareto optimal solutions for non-homogeneously weighted sums This exploration performed through new rule based on agents’ priorities generates edge weights communication graph. These determine how agents update their variables with information received other network. Agents initially disagree functions, though they driven to agree upon them as optimize. As result, still reach common solution. The network-level weight matrix (non-doubly) stochastic, contrasting subject doubly-stochastic. New theoretical analyses therefore developed ensure convergence proposed algorithm. paper provides gradient-based algorithm, proof solutions, and rates It shown initial influence rate choices affect its long-run behavior. Numerical results different numbers illustrate performance effectiveness