Definition of the feasible solution set in multicriteria optimization problems with continuous, discrete, and mixed design variables

2009 ◽  
Vol 71 (12) ◽  
pp. e109-e117 ◽  
Author(s):  
Roman Statnikov ◽  
Alex Bordetsky ◽  
Josef Matusov ◽  
Il’ya Sobol’ ◽  
Alexander Statnikov
Keyword(s):  
Multicriteria Optimization ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Solution Set ◽  
Mixed Design ◽  
Design Variables ◽  
Definition Of ◽  
Mixed Design Variables

scholarly journals The vector optimization and modeling of a technical systems

2018 ◽  
Vol 224 ◽  
pp. 04020
Author(s):  
Leonid B. Matusov
Keyword(s):  
Parameter Space ◽  
Multicriteria Optimization ◽  
Feasible Solution ◽  
Solution Set ◽  
Identification Problems ◽  
Design Variables ◽  
Technical Systems ◽  
The Mathematical Model ◽  
Term Identification

The construction a feasible solution set with a given accuracy is a main problem in multicriteria optimization and modeling. In order to construct the feasible solution set, a method called the Parameter Space Investigation has been created and successfully integrated into various fields of industry, science, and technology. Multicriteria modeling (identification) is a new direction that is of great value in applications. In the most common usage, the term “identification” means construction of the mathematical model of a system and determination of the parameters (design variables) of the model. The construction a feasible solution set with a given accuracy is a common way for solving multicriteria optimization and modeling problems. The issues of the estimation of the Parameter Space Investigation method convergence rate, the approximation of the feasible solution set are described. Besides these, the multicriteria identification problems of mechanical systems are discussed too.

Particle Swarm Methodologies for Engineering Design Optimization

2009 ◽  
Author(s):  
Singiresu S. Rao ◽  
Kiran K. Annamdas
Keyword(s):  
Particle Swarm Optimization ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Multiple Objective ◽  
Optimization Approach ◽  
Objective Functions ◽  
Mixed Design ◽  
Swarm Optimization ◽  
Design Variables ◽  
Mixed Design Variables

Particle swarm methodologies are presented for the solution of constrained mechanical and structural system optimization problems involving single or multiple objective functions with continuous or mixed design variables. The particle swarm optimization presented is a modified particle swarm optimization approach, with better computational efficiency and solution accuracy, is based on the use of dynamic maximum velocity function and bounce method. The constraints of the optimization problem are handled using a dynamic penalty function approach. To handle the discrete design variables, the closest discrete approach is used. Multiple objective functions are handled using a modified cooperative game theory approach. The applicability and computational efficiency of the proposed particle swarm optimization approach are demonstrated through illustrate examples involving single and multiple objectives as well as continuous and mixed design variables. The present methodology is expected to be useful for the solution of a variety of practical engineering design optimization problems.

The Application of Artificial Immune System in Mechanical Engineering for Constrained Optimization

2013 ◽  
Vol 273 ◽  
pp. 775-779
Author(s):  
Xue Nong Ran
Keyword(s):  
Immune System ◽  
Constrained Optimization ◽  
Mechanical Engineering ◽  
Artificial Immune System ◽  
Mixed Design ◽  
Artificial Immune ◽  
Design Variables ◽  
Feasible Solutions ◽  
Mixed Design Variables

A hybrid AIS-GA was proposed and tested. The algorithm performed very well in problems presenting continuous, discrete, and mixed design variables, producing feasible solutions in all runs for all problems considered. Also, it is much more easily parallelizable than the previous hybrids, and does not require any user-defined parameter other than the parameters already used by the AIS and the GA.

scholarly journals Malticriteria design of a large-scale mechanical systems

2019 ◽  
Vol 126 ◽  
pp. 00016
Author(s):  
Leonid Matusov
Keyword(s):  
Large Scale ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Steering System ◽  
Solution Set ◽  
Pareto Optimal ◽  
Large Scale Systems ◽  
Design And Optimization ◽  
Pareto Optimal Set

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.

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