Single- and Multiobjective Optimization on the Lattice of Cubes

Abstract

This paper gives examples of optimization problems on a lattice of cubes in the single- and multiobjective cases. We describe a method for calculating the local curvature of a given surface of a large-area geological object at each point and for constructing its curvature surface based on these geophysical data. Such information is used in geology and geophysics for detecting the most probable storage areas of hydrocarbons [1–5]. Based on these results, we develop mathematical models and state single- and multiobjective optimization problems on a lattice of cubes for arranging a finite number of oil wells in an explored field. We describe a method for designing an equivalence set for solving multiobjective problems on the lattices of cubes of any dimensions. Finally, we show that a similar approach is applicable for stating and solving optimization problems on a lattice of cubes in different sectors of the economy.