Krzysztof Arminski, Polish Space Agency; Tomasz Zubowicz, Polish Space Agency; Stefania Wolf, Polish Space Agency; Mikolaj Kruzynski, Polish Space Agency; Zygmunt Anio?, Polish Space Agency; Tymoteusz Trocki, POLSA; Edwin Wnuk, Polish Space Agency
Keywords: sensor network, telescopes, multi-objective optimisation, evolutionary algorithm
Abstract:
The paper contains the results of a research work related to a decision support problem investigating the allocation of operating time of passive optical sensors (telescopes) associated with participation in the operation of a wide-area observation network. The decision task is formulated as a multi-objective optimization problem with constraints extended by a modified Pareto front solution selection method.
For this purpose, the sensor description (elements of the consideration space) have been defined as a tuple consisting of: the name of the sensor; the use (type) of the sensor in the sense of survey or tracking; an indicator defining the quality of the sensor’s performance; the recommended operating time of the sensor to be declared; the maximum (specified by the operator) declared operating time of the sensor; the cost per hour of operating time; the location of the sensor with accuracy to the geographical region (very large area location — VLA). Therefore, a natural choice of manipulated variable in the task is the list specifying the recommended operating time of sensors contending for connection to the sensor network as well as their operating mode in the case of sensors that can operate in multiple modes.
However, the declaration of the sensor’s contribution of operating time to the network is not free and is subject to constraints, which include the following factors: the declared contribution of the sensor’s operating time should be within the accepted limits of the maximum operating time; the declared operating time of survey sensors located in selected geographic areas should not exceed the cumulative limit established; the declared operating time of all survey sensors should not exceed the cumulative assumed limits; in addition, such an analogous set of constraints is adopted for tracking sensors. Finally, the recommended contribution (operating time) of a sensor should not exceed the maximum specified by the operator for each individual facility.
Evaluation of the selection of a given sensor’s time contribution to the work for the designed network is carried out considering the following criteria: the number of sensors providing their services; the quality of the data provided based on the sensor’s operational evaluation performed through the consortium during the selected operational period; the dispersion of sensors across the VLA; and the operating cost of the sensors determined by the sensor-specific hourly observation rate. The solution being sought is to determine a recommendation for the declared contribution of sensor operating time to the network that allows maximization of the first three fit functions while minimizing the last (fourth) cost function.
Given the nature of the multicriteria task and the order of the solution space imposed by the assumptions made, an evolutionary algorithm implemented in the Python language has been used to obtain the numerical solution of the task. To consider the constraints in the optimization task, the penalty function method was used. Thus, the implementation of constraints consisted of adding a penalty to all objective functions. The proposed algorithm has been based on the NSGA-III algorithm.
The main features of the algorithm developed include the fact that it utilised the representation of decision variables in the form of the binary and floating-point numbers with limited precision. Former were used due to, among other things, to allow a selection between sensor modes. In addition, the evolution cycle was based on genetic crossover operators of the following types: simulated binary bounded – for floating point variables, and two point – for all decision variables. For mutation, the operators of polynomial bounded – for floating point variables and flip bit – for binary variables were used. To facilitate the selection of preferable elements from the Pareto front, a solution pre-selection method was used based on the decision-maker’s preference for a portion of the considered front, and then GRC (grey relational coefficient) was applied to evaluate the remaining solutions.
Two experiments are presented in the paper. In the first experiment, all the sensors foreseen to participate in the network were subject to optimisation. The second experiment involved the exclusion of selected sensors from the optimisation, assuming a known constant participation in the operation of the network is assigned and that it is affecting the fulfilment of constraints. This approach can be explained, for example, using expert knowledge to establish the core of the network under construction based on the selected resources. Consequently, these have been omitted during the optimization process.
Subsequently, the results of these experiments were then compared. It turned out that when optimising the time contribution of all sensors, some of them turned out to be strongly preferred by the algorithm, marginalising the uses of others. However, the process was largely an effect of the decision-maker’s preferences. The method adopted for evaluating the network was also not negligible at this point. It is worth noting that the approach used demonstrates that there exists certain equivalence of selected sensors with respect to the criteria considered. Therefore, the section of sensors to construct the network under development requires human intervention and consideration of the criteria not included in the formal definition of the task.
It turns out that the adopted approach allows to effectively support the decision-making process it allows to eliminate decisions that are not rational based on the adopted criteria.
As part of further research, a modification of the evaluation of sensors is planned to better reflect the purpose of network development.
Date of Conference: September 19-22, 2023
Track: SDA Systems & Instrumentation