Method of Multiobjective Optimization of Controlled Systems with Distributed Parameters

Design and control of electrotechnological systems

“…for minimization of N I criteria according to (8) subject to the constraints (9) for the a priori value ε 0 of the error of uniform approximation, fixed according to the conditions of inequalities ε0≤max⁡jε0j. This formulation excludes the trivial case of coincidence of solutions of problems (8) and (9) for each of the criteria I j ( p ̄) for all j=1, NItrue¯ (Rapoport and Pleshivtseva, 2018).…”

“…First, the application of various modifications of genetic algorithms (GA) that differ from each other in population aggregation methods for particular efficiency criteria in combination with modern methods of numerical simulation of optimized processes are considered. Second, the alternance method and MOO technique based on optimal control theory are considered and tested based on field analysis code developed in finite element method (FEM) software (Pleshivtseva et al , 2017a; Rapoport and Pleshivtseva, 2018; Pleshivtseva et al , 2017b).…”

“…Recently, the new, constructive method for MOO of control processes of deterministic and not fully defined controlled systems with distributed parameters has been proposed (Rapoport and Pleshivtseva, 2018). The optimization problem is considered under condition when an accuracy of uniform approximation of final object state to the required spatial distribution of controlled function is given in the form (7).…”

“…Investigation, analysis and comparison of different multiple-criteria optimization methods and tools have been implemented on examples of induction heating designing and control problems formulated mathematically regarding the typical optimization criteria (Figure 2) (Pleshivtseva et al , 2017a; Rapoport and Pleshivtseva, 2018; Pleshivtseva et al , 2017b). The typical optimization objectives such as energy consumption, metal loss because of scale formation and heating accuracy are considered as components of vector optimization criterion.…”