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abstract

Astronomical scheduling problem has several external conditions that change dynamically at any time during observations, like weather condition (humidity, temperature, wind speed, opacity, etc.), and target visibility conditions (target over the horizon, Sun/Moon blocking the target). Therefore, a dynamic rescheduling is needed. An astronomical project will be scheduled as one or more Scheduling Blocks (SBs) as an atomic unit of astronomical observations. We propose a mixed integer linear programming (MILP) solution to select the best SBs, favors SBs with high scientific values, and thus maximizing the quantity of completed observation projects. The data content of Atacama Large Millimeter/Submillimeter Array (ALMA) projects of cycle 0 and cycle 1 were analyzed, and a synthetic set of tests of the real instances was created. Two configurations, one of 5000 SBs in a 3 months season and another 10,000 SBs a 6 months season were created. These instances were evaluated with excellent results. Through the testing it is showed that the MILP proposal has optimal solutions.

5. Conclusions

This study has proved that the scheduling problem in astronomy is a very challenging problem and there is still enough space to contribute. Even when the proposed algorithm takes advantage of some assumptions that simplifies the real problem, this work was able to produce a mathematical model and a prototype implementation of a scheduling solution that solves successfully a simplified version of ALMA’s scheduling problem considering projected volumes of demand for the next years. This scheduling algorithm features a multi-layer model that performs a schedule process in both long-term and short-term phases. Also, a time discretization and both static and dynamic variables are considered in this scheduling model in which Scheduling Blocks are arranged over the planning time thanks by a MILP-based solver that performs the core task of the scheduling process. The main objectives detailed in Section 1 were accomplished successfully, while their respective results can be checked as follow: 1. A list of static and dynamic parameters, and scheduling constraints of ALMA observatory was researched to build the proposed scheduling algorithm. 2. A mathematical scheduling model based on a MILP approach to solve the simplified ALMA’s scheduling problem was proposed taking in consideration the identified variables, constraints and assumptions described in Section 2. 3. A prototype of the proposed algorithm was programmed in C++ using CPLEX framework. 4. ALMA scheduling data of both Cycle 0 and Cycle 1 was characterized and used to simulate data and test the proposed algorithm. 5. The results of the gap of the obtained solution from the optimal, execution times and internal model attributes was presented by executing synthetical instances over the implementation prototype.