The ground station scheduling problem is a complex scheduling problem involving multiple objectives. Evolutionary techniques for multi-objective optimization are becoming popular among different fields, due to their effectiveness in obtaining a set of trade-off solutions. In contrast to some conventional methods, that aggregate the objectives into one weighted-sum objective function, multi-objective evolutionary algorithms manage to find a set of solutions in the Pareto-optimal front. Selecting one algorithm, however, for a specific problem adds additional challenge. In this paper the ground station scheduling problem was solved through six different evolutionary multi-objective algorithms, the NSGA-II, NSGA-III, SPEA2, GDE3, IBEA, and MOEA/D. The goal is to test their efficacy and performance to a number of benchmark static instances of the ground scheduling problem. Benchmark instances are of different sizes, allowing further testing of the behavior of the algorithms to different dimensionality of the problem. The solutions are compared to the recent solutions of a weighted-sum approach solved by the GA. The results show that all multi-objective algorithms manage to find as good solution as the weighted-sum, while giving more additional alternatives. The decomposition-based MOEA/D outperforms the rest of the algorithms for the specific problem in almost all aspects.

In this paper, a bilevel multi-objective formulation of the Ground Scheduling Problem is presented. First, the problem is formulated as a bilevel optimisation problem (BOP), wherein the upper level (UL) is a biobjective problem determining the pairs of Ground Station (GS) to Spacecraft (SC) and the starting time of each event with objectives the maximisation of the access windows and the minimisation of the communication clashes of each GS. These two objectives of the UL can be assumed as a measure of the violation of the feasibility of a schedule. The lower level (LL) consists of a single objective optimisation problem that determines the duration of each event, with objectives the communication time requirement of SCs with GS and the total ground station usage, combined together to a weighted sum function. The approach used to solve this multi-objective BOP is a nested approach, where the Pareto front of the upper level is obtained by a multi-objective optimisation algorithm (NSGA2) and the lower level is solved using a GA. The formulation is tested on one small test case from literature and the relevant results are reported.

a b s t r ac tIn this paper, a groundwater management model for which the solution is obtained through a coupled application of simulation and optimization models is analyzed. The most widely used numerical groundwater flow model, MODFLOW, which is a three-dimensional (3-D) model using the finite differences method for solving the governing groundwater flow equations, is used as the flow-simulation model. This model is then connected to the Harmony Search Algorithm, one of the most emerging and successful metaheuristic optimization techniques, which simulates the quest for perfect harmony in music. In this paper, this technique is applied to a classic, theoretical example found in the manual of MODFLOW for comparison purposes, by examining the optimization of its aquifer system in terms of minimizing the pumping cost. For this application, a specially designed computer software programme was developed in MATLAB environment. This software, apart from coupling the simulation and optimization models, provides 2-D and 3-D graphical representations of the results allowing users to have a visual image of the piezometric surface in the whole aquifer system area. More specifically, in the specific management problem, the positions and the total required water demand for the pumping wells from the three aquifers system are pre-defined, while the optimal distribution of the pumping rates is determined through the proposed methodology. The results show that coupling flow-simulation and optimization models could be a very useful procedure when solving complex groundwater management problems.