Design Optimization
What is Design Optimization?
Design optimization is a process of finding the values of input parameters, which lead to the best performance of analytical or simulation model of a product or a manufacturing process under investigation. Ultimately, it answers the following questions:
 How to improve product or process characteristics?
 Which combination of input parameters is the best?
 How to decrease the effect of input parameters variability on the overall product or process behavior?
Create model 
Define variables and goals 
Run optimization 
Key Advantages of Optimization in pSeven
 Efficient solution of complex engineering problems with up to ten objective functions, hundreds of design variables and constraints with a small computation budget.
 A wide range of easytouse proprietary and inhouse developed optimization algorithms with a minimum setup required.
 Automatic algorithm selection that allows users with no specialized competence to solve optimization problems easier.
 Robustness of optimization process to random noise in model responses, as well as to undefined model behavior.
 Parallel execution of optimization procedures allowing to reduce computational time of resourceconsuming problems solution drastically.
Optimization Algorithms
pSeven offers a complete set of inhouse developed methods and algorithms to conduct optimization of one or multiple model objective functions subject to various constraints. It allows to efficiently solve both design optimization problems with fast to evaluate analytical models and the problems where the key challenge is expensive in terms of computing resources simulations.
In addition to inhouse developed methods and algorithms, pSeven also uses popular and wellknown implementations of optimization algorithms and supplements them with inhouse developed features, which makes them even more efficient and unique. The efficiency of optimization problem solution highly depends on optimization method and proper algorithm selection.
Supported Problem Types:

Local Algorithms:

Globalization Algorithms:

With pSeven, the user has to simply set the basic properties of the model (if known), such as model evaluation expensiveness, smoothness of model responses, etc., instead of tedious tuning of optimization algorithm internal parameters. After that automatic and adaptive choice of specific optimization algorithm(s) based on this information is provided by SmartSelection technique. Learn more > 
Along with the automatic algorithms selection convenient for the users, full control over the whole optimization process is available for expertlevel users, making optimization capabilities of pSeven highly customizable.
SurrogateBased Optimization (SBO)
Single and multiobjective surrogatebased optimization in pSeven is based upon a widelyknown approach of fitting a response surface to output values of few points evaluated from the model. After first fitting, it balances between finding the minimum/maximum values and improving the response surface by sampling areas where the chance of improvement may be high.
Implementation of this approach in pSeven is significantly different from other available realizations and is free from the most common drawbacks. The sampling utilizes an inhouse developed Design of Experiments strategy, which respects as much feasible domain of the problem as possible. Techniques for fitting the response surface origin to Gaussian Processes (GP) for constructing approximation models, but are adapted for problems with high dimensionality (up to 100 input parameters) and other realworld applications issues.
Approximation 

Create model 
Define variables and goals 
Run optimization 
Robust Design Optimization (RDO)
Single and multiobjective robust optimization in pSeven supports virtually all possible formulations, including probabilistic and quantile type constraints. It is based on the stateoftheart stochastic approach that supports both direct and surrogatebased optimization, so it is suitable for expensive to evaluate problems.
The basis of this approach is a careful adjustment of the distribution realizations number of uncertain parameters. Only a small number of random realizations away from optimal solution needs to be considered to change the uncertain parameter itself. When the optimal solution is approached, the number of distribution realizations will be increased.
The unique feature of this approach is that it provides both the solution and the corresponding uncertainty estimations of objective and constraints values. Another advantage of robust optimization in pSeven for engineering applications is that explicit distribution law of the uncertain parameters is not required, it is enough to provide their distribution empirically.
Create model 
Define variables and goals 
Provide distributions for variables 
Run optimization 
Advanced Problem Statements
There is also a set of specific aspects of analytical and simulation models that can and must be taken into account during the design optimization process in pSeven:
Problem DimensionalityThis challenge is characterized by a large number of design variables (hundreds), constraints (dozens) and objectives (multiple). 
Problem StatementVarious types of input parameters (continuous, integer, categorical), constraints and objectives (smooth, nonlinear, multiextremal, nondifferentiable, mixed). 
Conflicting objectivesOptimization of two or more conflicting objectives simultaneously creates a Pareto frontier. 
Noisy Objective FunctionsFinite precision of numbers used in computers and special features of numerical methods, in particular, meshing and convergence rules of finite element methods, produces numerical noise. 
Computational TimeCalculation of a single design point can take a significant time. For example, a typical CFD simulation takes up to several hours. That is why it is extremely important for an optimization process to use the simulation model as rarely as possible. 
Uncomputable RegionsTheir presence means that the simulation model is unable to obtain results for certain values of model parameters, for example, when the solution of a nonlinear structural problem is not able to achieve convergence or if an intense turbulent flow motion makes the solution of NavierStokes equations numerically unstable. 