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<p>In the context of dynamic multi-objective optimization problems, a shift of Pareto fronts is a consequence of changing environmental parameters. Current state-of-the-art methods define this dynamic nature as unknown time-dependent variables influencing the objective space of the problem. However, when dealing with real-world processes, these time-dependent variables are not always unknown. Processes are characterized by an intricate relationship between a series of decision variables, observed parameters, but also unknown parameters. Observed parameters can be seen as causal responses to underlying unknown environmental variables. This implies that they are at least partially determined by the state of other variables and reveal information about the state of the process that is not known when solely considering the decision variables. This paper discusses the types of uncertainty present in dynamic processes and how these uncertainties can be quantified and handled in surrogate modeling. A novel approach, PSAMOO, is proposed to integrate environmental parameters into parametric surrogate models to achieve more efficient Pareto front tracking in dynamic optimization. An extensive evaluation on dynamic problems shows how epistemic and aleatoric uncertainty can effectively be quantified and accounted for resulting in an improved dynamic Pareto front tracking and approximation.</p>

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Handling uncertainty with parametric surrogate-assisted optimization for dynamic multi-objective problems

  • 期刊论文

  • 发表日期：

    2025年6月4日

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  • Arne De Temmerman,
  • Matthias De Ryck,
  • Mathias Verbeke

摘要

In the context of dynamic multi-objective optimization problems, a shift of Pareto fronts is a consequence of changing environmental parameters. Current state-of-the-art methods define this dynamic nature as unknown time-dependent variables influencing the objective space of the problem. However, when dealing with real-world processes, these time-dependent variables are not always unknown. Processes are characterized by an intricate relationship between a series of decision variables, observed parameters, but also unknown parameters. Observed parameters can be seen as causal responses to underlying unknown environmental variables. This implies that they are at least partially determined by the state of other variables and reveal information about the state of the process that is not known when solely considering the decision variables. This paper discusses the types of uncertainty present in dynamic processes and how these uncertainties can be quantified and handled in surrogate modeling. A novel approach, PSAMOO, is proposed to integrate environmental parameters into parametric surrogate models to achieve more efficient Pareto front tracking in dynamic optimization. An extensive evaluation on dynamic problems shows how epistemic and aleatoric uncertainty can effectively be quantified and accounted for resulting in an improved dynamic Pareto front tracking and approximation.