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This paper considers the multi-depot vehicle routing problem with object alternation. We propose a formal statement of the problem with two types of objects and a mathematical model with two blocks of Boolean variables. First, the model is studied without gathering vehicles (mobile objects). Then, a special object (a single collection point) is introduced in the model. We show additional constraints of the mathematical model with this object. Special attention is paid to the condition of no subcycles. This condition is considered based on the adjacency matrix. Five greedy algorithms are proposed for solving the problem, two of which are iterative. One of the greedy algorithms is given a probabilistic modification based on the randomization of variables (an adaptive algorithm). Finally, the proposed algorithms are compared in terms of the average value of the objective function and the running time in a computational experiment. Also, the results of another experiment—the parametric tuning of the adaptive algorithm—are presented. [ABSTRACT FROM AUTHOR]

Consideration was given to derivation of the motion equations of a space robotic module with a mathematical model having many degrees of freedom whose number can vary in the course of operation. This problem was solved in a computing environment such as the Maple program package. It was anticipated that the on-line mathematical model would be used to establish a rational in a sense motion control law of such a complicated object. For this purpose the paper solved some problems of decomposition of the resulting mathematical model. The results of computer-aided derivation of the motion equations of several particular schemes of the of the space robotic module were presented to illustrate constructiveness of the proposed mathematical support of problem solution. [ABSTRACT FROM AUTHOR]

We show and validate a mathematical model of multicriterial preferences, in which the preference relation is formed with interval estimates of relative tradeoffs of values of one criteria with values of other criteria. We develop a theory and multicriterial problem analysis methods based on this model. [ABSTRACT FROM AUTHOR]