Degenerate optimization problems of economy and power engineering

Optimization of large economy and power engineering systems leads to degenerate solutions of a high dimensionality. This is a very strong mathematical complication. It however allows the future evolution of power engineering to be considered both as based on joint operation of nuclear power plants (NPP), coal-fired power plants (PP) and gas-fired PPs, and based on only NPPs. This requires a system optimization of the NPP parameters.Computational studies on optimal high-dimensionality systems have led to the degenerate space of admissible economy and power engineering solutions to be understood as a set of points on a lunar surface with a finite number of craters. Such degenerate space may be referred to as “non-convex, non-concave”.In other words, an N-dimensional degenerate “non-convex, non-concave” space of a high-dimensionality optimization problem (N ≥ 10,000) looks like a “lunar surface” with craters of different depths. Craters form the neighborhood of locally optimal plans, and the locally optimal plan as such is on the bottom of a crater. The crater depth defines the value of the functional being optimized. Occasionally, the deepest but different craters include equally deep craters, that is, craters with equal values of the locally optimal plan functionals. The local optimum (local plan) in different craters may differ structurally, and the optimization problem functionals for these points may be equal in value.Calculations show that equally sized craters (with equal values of economy and power engineering development locally optimal plan functionals) occasionally include craters with locally optimal plans of economy and power engineering evolution (in a diversity of the potential combinations of economy and energy technology states) based only on coal- or gas-fired PPs, or on coal-/gas-fired and nuclear PPs, or on NPPs. By weighing the values of the locally optimal plan functionals in different craters, one can find an optimal solution – a locally optimal plan with the best functional value (e.g., in the event of the functional minimization, with the minimum objective functional value out of the entire number of the considered craters).