Planning algorithm for training cosmonauts in ISS
We consider the problem of trainings planning on ISS. Shown that the problem is a combination of a k Partition Problem and an Assignment Problem. NP-compleeteness is proofed. A heuristic and an exact algorithms are proposed.
We consider the problem of planning the ISS cosmonaut training with different objectives. A pre-defined set of minimum qualification levels should be distributed between the crew members with minimum training time differences, training expenses or a maximum of the training level with a limitation of the budget. First, a description of the cosmonaut training process is given. The model are considered for the volume planning problem. The objective of the model is to minimize the differences between the total time of the preparation of all crew members. Then two models are considered for the timetabling planning problem. For the volume planning problem, two algorithms are presented. The first one is aheuristic with a complexity of O(n) operations. The second one consists of a heuristic and exact parts, and it is based on the npartition problem approach.
The central question that motives this paper is the problem of making up a freight train and the routes on the railway. It is necessary from the set of orders available at the stations to determine time-scheduling and destination routing by railways in order to minimize the total completion time. In this paper it was suggested formulation of this problem by applying integer programming.
We consider the problem of planning the cousmonaut's time in ISS with given set of tasks, time planning horizon and load constraints. Shown that the problem is NP-hard in a strong sense. The heuristic algorithm was proposed. Proved that proposed algorithm is exact for problem with requirement of performing all tasks. Program C++ was written and algorithm's work was qualitatively analyzed.
In this article, the fairdivision problem for two participants in the presence of both divisible and indivisibleitems is considered. Three interrelated modifications of the notion of fairdivision–profitably, uniformly and equitably fairdivisions–were introduced. Computationally efficient algorithm for finding all of them was designed. The algorithm includes repetitive solutions of integer knapsack-type problems as its essential steps. The necessary and sufficient conditions of the existence of proportional and equitable division were found. The statements of the article are illustrated by various examples.
In this paper, we will show that the width of simplices defined by systems of linear inequalities can be computed in polynomial time if some minors of their constraint matrices are bounded. Additionally, we present some quasi-polynomial-time and polynomial-time algorithms to solve the integer linear optimization problem defined on simplices minus all their integer vertices assuming that some minors of the constraint matrices of the simplices are bounded.