This paper considers routing for a group of unmanned aerial vehicles within a promising last-mile delivery system. The routing problem is reduced to the bi-criteria single-depot multiple traveling salesman problem and formalized using a directed graph. Being NP-hard, this problem cannot be efficiently solved by standard exact optimization methods. Therefore, heuristic algorithms should be applied to obtain good approximate solutions in a short time. The problem is solved using NSGA-II, the widespread elitist non-dominated sorting genetic algorithm that demonstrates good results in multicriteria optimization. Some chromosome representation and crossing and mutation operators are implemented in the algorithm. A simulation software tool is presented to investigate the influence of the crossing operators used on the convergence speed of the algorithm. Finally, several genetic crossing operators (Partially-Mapped Crossover, Order Crossover, Cycle Crossover, and Combined Hierarchical Crossover) are compared in terms of efficiency.

Abstract—Deterministic continuous finite-dimensional stationary linear dynamic control systems with many inputs and many outputs are considered. Authors assume that the dynamics matrix can be both stable and unstable, but its eigenvalues are different, do not belong to the imaginary axis, and their pairwise sum is not equal to 0. The problems of constructing spectral solutions of the equations of state and matrices of gramian controllability of these systems, as well as the associated energy functionals of the degree of stability and reachability with the aim of optimal placement of sensors and actuators of multi-connected control systems and complex networks are considered. To solve the listed problems, the article uses various models of the system in state space: a general representation, as well as a representation in various canonical forms. To calculate the spectral decompositions of controllability gramians, pseudo-Hankel matrices (Xiao matrices) are used. New methods have been proposed and algorithms have been developed for calculating controllability gramians and energy metrics of linear systems. The research results can be used for the optimal placement of sensors and actuators of multi-connected control systems or for control with minimal energy in complex networks of various natures.

As its main goal, the article advocates the rationality of the concept of equilibrium in secure strat- egies (EinSS) and the organic proximity of the logic of this concept to the logic underlying the classical approach to solving game-theory problems through Nash equilibrium. The article examines in detail the sys- tem of EinSS definitions through the prism of the Nash equilibrium concept. Based on this analogy, the con- nection between the existence of EinSS and the existence of a Nash equilibrium is established.

V.V. Leontief's open dynamic model with continuous time is considered as a linear dynamic system with control. In the model under study, the function of non-productive consumption serves as control. The necessary conditions for the closure of the technological set are obtained.

Venus has a global rift system stretching for thousands of kilometers. Moreover, there is now evidence of modern volcanism on Venus. Intraplate earthquakes, moonquakes, and marsquakes show that seismic activity can be associated not only with plate tectonic events, volcanism can act as a trigger, and there is no doubt that Venus is a seismically active planet. For upcoming seismic experiments on Venus [3–5] it is important to know in which areas the stresses are large enough to cause quakes.