Abstract
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.
Highlights
In both technical practice and theoretical research, there are a large number of multi-objective optimization (MOP) problems that need to be optimized synchronously for multiple objectives [1,2,3].When solving multi-objective optimization problems, the traditional method is to convert this problem into a single-objective problem based on prior knowledge and to use single-objective optimization methods to obtain a satisfactory Pareto optimal solution [4]
In order to test the performance of the new hybrid algorithm, two types of test function were selected to compare the performances of the original multi-objective evolutionary algorithm (MOEA)/D, MOEA/ACD, MOEA/ ACD-neighborhood sizes (NS), EN-MOEA/D, and EN-MOEA/ACD-NS
A set of unconstrained functions proposed by Van Veldhuizen in 1999 can comprehensively test a multi-objective optimization algorithm, and is in accordance with the design criteria of the MOP test function proposed by Whitley et al [46,47]
Summary
In both technical practice and theoretical research, there are a large number of multi-objective optimization (MOP) problems that need to be optimized synchronously for multiple objectives [1,2,3]. This paper proposes a multi-objective evolutionary algorithm (MOEA) for MOP problems in order to obtain a set of Pareto optimal solutions [5,6]. With the development of technology, it is very convenient to obtain atmospheric ducts from GNSS phase delay and propagation loss observation data [30], so we tried to retrieve the atmospheric ducts by placing a receiver on the ground to receive the signal from the GNSS and use a new algorithm to analyze it This method will would save a lot of costs in the retrieval of atmospheric ducts. We propose a hybrid decomposition-based multi-objective evolutionary algorithm with adaptive neighborhood sizes (EN-MOEA/ACD-NS), which dynamically imposes some constraints on the objectives, and compare the improved algorithm with the MOEA/D, MOEA/ACD, MOEA/ACD-NS, and EN-MOEA/D on the MOPs and unconstrained function (UF) problems in the Congress on Evolutionary Computation (CEC) 2009 standard test instances [31]. This new algorithm will provide a new method and save a lot of costs for the retrieval of atmospheric ducts, which is of great significance for the research of atmospheric ducts
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