Pareto Tracer: a predictor–corrector method for multi-objective optimization problems

Martín, Adanay; Schütze, Oliver

doi:10.1080/0305215x.2017.1327579

Cited by 38 publications

(33 citation statements)

References 19 publications

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“…A popular approach for MaOPs is comprised of interactive methods [173][174][175][176][177][178]. These methods do not compute the entire set of optimal compromises, but instead interactively explore the Pareto set.…”

Section: Reduction Techniques For Many-objective Optimization Problemsmentioning

confidence: 99%

“…Starting at the current Pareto-optimal solution, a decision maker can choose in which direction to proceed, i.e., which objective to improve at the expense of some other, currently less important objective. The approach in [178], for example, allows for Pareto-optimal movements both in the decision and objective space. One of the main advantages of interactive methods is the reduced computational effort, especially in the presence of many criteria, since it is not affected significantly by the dimension of the Pareto set.…”

Section: Reduction Techniques For Many-objective Optimization Problemsmentioning

confidence: 99%

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A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

Peitz

Dellnitz

2018

MCA

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Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

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Section: Reduction Techniques For Many-objective Optimization Problemsmentioning

confidence: 99%

Section: Reduction Techniques For Many-objective Optimization Problemsmentioning

confidence: 99%

A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

Peitz

Dellnitz

2018

MCA

View full text Add to dashboard Cite

show abstract

“…Starting at the current Pareto optimal solution, a decision maker can choose in which direction to proceed, i.e., which objective to improve at the expense of some other, currently less important objective. The approach in [178], for example, allows for Pareto optimal movements both in decision and objective space. One of the main advantages of interactive methods, is the reduced computational effort -especially in the presence of many criteria -since it is not affected significantly by the dimension of the Pareto set.…”

Section: Reduction Techniques For Many-objective Optimization Problemsmentioning

confidence: 99%

“…A popular approach for MaOPs are interactive methods [173][174][175][176][177][178]. These methods do not compute the entire set of optimal compromises but instead interactively explore the Pareto set.…”

Section: Reduction Techniques For Many-objective Optimization Problemsmentioning

confidence: 99%

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

Peitz¹,

Dellnitz²

2018

Preprint

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Abstract:Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto optimal solutions have led to a wide range of new applications related to optimal and feedback control which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview over recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

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“…In order to improve the MOEA/D, Zhao et al proposed a method called an ensemble of different neighborhood sizes with online self-adaptation (ENS-MOEA/D), which aims to avoid the local optimum or poor convergence due to the neighborhood sizes [15]. Martín et al developed a novel predictor-corrector method with the aim of finding the zero set of F-an underdetermined system of equations motivated by the Karush-Kuhn-Tucker conditions for MOP problems [16]. Based on the variable neighborhood tabu search, Janssens et al proposed a method to analyze the effect of the algorithmic parameters and instance characteristics on the quality of a Pareto front produced by a multi-objective algorithm [17].…”

mentioning

confidence: 99%

Using the Decomposition-Based Multi-Objective Evolutionary Algorithm with Adaptive Neighborhood Sizes and Dynamic Constraint Strategies to Retrieve Atmospheric Ducts

Mai

Shi

Liao

et al. 2020

Sensors

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The traditional method of retrieving atmospheric ducts is to use the special sensor of weather balloons or rocket soundings to obtain information intelligently, and it is very expensive. Today, with the development of technology, it is very convenient to retrieve the atmospheric ducts from Global Navigation Satellite System (GNSS) phase delay and propagation loss observation data, and then the GNSS receiver on the ground forms an automatic receiving sensor. This paper proposes a hybrid decomposition-based multi-objective evolutionary algorithm with adaptive neighborhood sizes (EN-MOEA/ACD-NS), which dynamically imposes some constraints on the objectives. The decomposition-based multi-objective evolutionary algorithm (MOEA/D) updates the solutions through neighboring objectives, the number of which affects the quality of the optimal solution. Properly constraining the optimization objectives can effectively balance the diversity and convergence of the population. The experimental results from the Congress on Evolutionary Computation (CEC) 2009 on test instances with hypervolume (HV), inverted generational distance (IGD), and average Hausdorff distance ∆ 2 metrics show that the new method performs similarly to the evolutionary algorithm MOEA/ACD-NS, which considers only the dynamic change of the neighborhood sizes. The improved algorithm is applied to the practical problem of jointly retrieving atmospheric ducts with GNSS signals, and its performance further demonstrates its feasibility and practicability. the multi-objective optimization can make full use of multi-source observation information and can improve the reliability of the solution. The traditional method can only obtain a Pareto optimal solution that is not necessarily satisfactory to the decision-maker; the rationality of prior knowledge also affects the selection of the optimal solution. This paper proposes a multi-objective evolutionary algorithm (MOEA) for MOP problems in order to obtain a set of Pareto optimal solutions [5,6]. According to the optimization framework, MOEAs can be roughly divided into three categories, namely: (a) Pareto-based approaches [7], (b) indicator-based approaches [8], and (c) decomposition-based approaches [9].Pareto-based methods sort the individuals according to the dominant relationship among them, and then the optimal solution is selected. The Pareto-based approach is the most popular method in the evolutionary multi-objective optimization community. NSGA-II and SPEA2 are the most representative algorithms, and they are very effective when dealing with two or three objective functions [7,10]. However, when the number of objective functions increases to more than three, most of the solutions in the NSGA-II and SPEA2 search spaces become non-dominated solutions, resulting in a rapid decline in search capabilities.Indicator-based MOEAs use the value of performance indicators to guide the search direction, which drives whole generated solutions to the Pareto solution sets. As the calculation of the Pareto dominance relatio...

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Pareto Tracer: a predictor–corrector method for multi-objective optimization problems

Cited by 38 publications

References 19 publications

A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

A Survey of Recent Trends in Multiobjective Optimal Control—Surrogate Models, Feedback Control and Objective Reduction

A Survey of Recent Trends in Multiobjective Optimal Control -- Surrogate Models, Feedback Control and Objective Reduction

Using the Decomposition-Based Multi-Objective Evolutionary Algorithm with Adaptive Neighborhood Sizes and Dynamic Constraint Strategies to Retrieve Atmospheric Ducts

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