Abstract

The design and optimization of a large-scale systems are the most difficalt problems. A large-scale system consists of a number of subsystems. For example, in a harvest for harvesting one can separate the following subsystems: the frame, driver's cab, platform, engine, transmission, and steering system. Different departments of the design office engaged in creating a machine optimize their ‘own’ subsystems, while ignoring others. A machine assembled from ‘autonomously optimal’ subsystems turns out to be far from perfect. A machine is a single whole. When improving one of its subsystems, we can unwittingly worsen others. This implies that it is not always possible to solve optimization problems directly even for determination of the feasible solution set. The correct determination of the feasible solution set was a major challenge in engineering optimization problems. In order to construct the feasible solution set, a method called the Parameter Space Investigation (PSI) has been created and successfully integrated into various fields of industry, science, and technology. The methods of approximation of the feasible solution and Pareto optimal sets and the regularization of the Pareto optimal set are described in our paper. These methods are applied to solving the multicriteria optimization problems of large- scale systems. For example, they were applied in an agricultural engineering to a harvester for harvesting design.

Highlights

  • Let us consider a system whose operation is described by a system of equations or whose performance criteria may be directly calculated

  • We assume that the system depends on r design variables D1,...,Dr representing a point D = (D1,...,Dr) of an r-dimensional space

  • In the general case, when designing a machine, one has to take into account the design variable constraints, the functional constraints, and the criteria constraints [1].These constraints defines the feasible solution set D

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Summary

Introduction

Let us consider a system whose operation is described by a system of equations or whose performance criteria may be directly calculated. We assume that the system depends on r design variables D1,...,Dr representing a point D = (D1,...,Dr) of an r-dimensional space. In the general case, when designing a machine, one has to take into account the design variable constraints, the functional constraints, and the criteria constraints [1].These constraints defines the feasible solution set D. A set P  D is called the Pareto optimal set if it consists of Pareto optimal points. One has to determine a design variable vector point Į 0 P, which is most preferable among the vectors belonging to set P. When solving a multicriteria optimization problem, one always has to find the set of Pareto optimal solutions

The feasible and pareto optimal sets approximation
Approximation of feasible solution set
Approximation of pareto set
Decomposition and aggregation of large-scale systems
Construction of hierarchically consistent solutions
Conclusions

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