105
4Optimization Techniques
This chapter provides information related to iSIGHT’s optimization techniques. The
information is divided into the following ctions:
“Introduction,” on page106 introduces iSIGHT’s optimization techniques.
“Internal Formulation,” on page107 shows how iSIGHT approaches optimization.
“Selecting an Optimization Technique,” on page112 lists all available
optimization techniques in iSIGHT, divides them into subcategories, and defines
them.
“Optimization Strategies,” on page121 outlines strategies that can be ud to lect optimization plans.
“Optimization Tuning Parameters,” on page124 lists the basic and advanced tuning parameters for each iSIGHT optimization technique.
“Numerical Optimization Techniques,” on page147 provides an in-depth look at various methods of direct and penalty numerical optimization techniques.
Technique advantages and disadvantages are also discusd.
“Exploratory Techniques,” on page175 discuss Adaptive Simulated Annealing and Multi-Island Genetic Algorithm optimization techniques.
“Expert System Techniques,” on page178 provides a detailed look at iSIGHT’s expert system technique, Directed Heuristic Search (DHS), and discuss how it
allows the ur to t defined directions.
“Optimization Plan Advisor,” on page190 provides details on how the
Optimization Plan Advisor lects an optimization technique for a problem.
“Supplemental References,” on page195 provides a listing of additional
references.
106Chapter 4 Optimization Techniques
Introduction
This chapter describes in detail the optimization techniques that iSIGHT us, and how
they can be combined to conform to various optimization strategies. After you have
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chon the optimization techniques that will best suit your needs, proceed to the
Optimization chapter of the iSIGHT Ur’s Guide. This book provides instructions on
creating or modifying optimization plans. If you are a new ur, it is recommended that
you understand the basics of optimization plans and techniques before working with
the advanced features. Also covered in the iSIGHT Ur’s Guide are the various ways
to control your optimization plan (e.g., executing tasks, stopping one task, stopping all
tasks).
Approximation models can be utilized during the optimization process to decrea
processing cost by minimizing the number of exact analys. Approximation models
are defined using the Approximations dialog box, or by loading a description file with
predefined models. Approximation models do not have to be initialized if they are ud
inside an optimization Step. The optimizer will check and initialize the models, if
necessary. For additional information on using approximation with optimization, e
Chapter8 “Approximation Techniques”, or refer to the iSIGHT Ur’s Guide.
iSIGHT combines the best features of existing exploitive and exploratory optimization
techniques to supplement your knowledge about a given design problem. Exploitation
is a feature of numerical optimization. It is the immediate focusing of the optimizer on
a local region of the parameter space. All runs of the simulation codes are concentrated
in this region with the intent of moving to better design points in the immediate
vicinity. Exploration avoids focusing on a local region, but evaluates designs
throughout the parameter space in arch of the global optimum.
Domain-independent optimization techniques typically fall under three class:
numerical optimization techniques, exploratory techniques, and expert systems. The
techniques described in this chapter are divided into the three categories.
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This chapter also provides information about optimization techniques including their
purpo, their internal operations, and advantages and disadvantages of the techniques.
For instructions on lecting a technique using the iSIGHT graphical ur interface,
refer to the iSIGHT Ur’s Guide.
Internal Formulation 107Internal Formulation
Different optimization packages u different mathematical formulas to achieve
results. The formulas shown below demonstrate how iSIGHT approaches optimization. The following are the key aspects to this formulation:
All problems are internally converted to a single, weighted minimization problem.
More than one iSIGHT parameter can make up the objective. Each individual objective has a weight multiplier to support objective prioritization, and a scale factor for normalization. If the goal of an individual objective parameter is maximization, then the weight multiplier gets an internal negative sign.刹车痕迹
If your optimization technique is a penalty-bad technique, then the minimization
奔溃的意思problem is the same as described above with a penalty term added.
Objective :
Minimize
Subject to :
Equality Constraints:Inequality Constraints:
Design Variables: for integer and real
or iSIGHT Input Parameter member of t S for discrete parameters
Where :
SF = scale factor with a default of 1.0
W = weight a default of 1.0W i SF i ---------i ∑F i ×x ()h k x ()T et arg –()W k SF k
-
--------0k 1=;=×…K ,W j SF j
---------LB g j x ()–()×0≤W j SF j ---------g j x ()UB –()×0j 1…L ,,=;≤LB SF -------iSIGHTInputParameter SF ------------------------------------------------------------------------------UB SF
-------≤≤
108Chapter 4 Optimization Techniques
The penalty term is as follows:
ba + multiplier * summation of (constraint violation ** violation exponent)
The default values for the parametesr are: 10.0 for penalty ba, 1000.0 for反璞归真的意思
penalty multiplier, and 2 for the violation exponent. The defaults can be
overridden with Tcl API procedures discusd in the iSIGHT MDOL Reference
Guide.
All equality constraints, h(x), have a bandwidth of
泽诺尼亚4+-DeltaForEqualityConstraintViolation. This bandwidth allows a specified range
within which the constraint is not considered violated. The default bandwidth is
.00001, and applies to all equality constraints. You can override this default with
the API procedure api_SetDeltaForEqualityConstraintViolation.
All inequality constraints, g(x), are considered to be nonlinear. This tting cannot be overridden. If an iSIGHT output parameter has a lower and upper bound, this
tting is converted into two inequality constraints of the preceding form. Similar
to the objective, each constraint can have a weight factor and scale factor.
iSIGHT design variables, x, can be of type real, integer, or discrete. If the type is real or integer, the value must lie within ur-specified lower and upper bounds. If
no lower and upper bound is specified, the default value of 1E15 is ud. This
default can be overridden though the Parameters dialog box, or through the MDOL
description file.
凉拌鲫鱼的做法川味There is one default bound for each optimization plan, and a common global
(default) bound value (1E15). During the execution of an optimization plan, the
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plan's bound value overrides the common value. When no optimization plan is
ud, the default common value is ud.
The significance of the default bound is that, from the optimization techniques
point of view, iSIGHT treats each design variable as if it has both a lower and
upper bound. If the type is discrete, iSIGHT expects that the value of the variable
will always be one of the values provided in the ur-supplied constraint t.
Internally, iSIGHT will have a lower bound of 0, and an upper bound of n-1, where
n is the number of allowed values. The t of values can be supplied through the
interface, or through the API procedures api_SetInputConstraintAllowedValues
and api_AddInputConstraintAllowedValues. The optimization technique controls
the values of the design variables, and iSIGHT expects the technique to insure that
they are never allowed to violate their bounds.
Internal Formulation109 To demonstrate the u of iSIGHT’s internal formulation, some simple modifications to the beamSimple.desc file can be made.
Note:This description file can be found in the following location, depending on your operating system:
UNIX and Linux:
$(ISIGHT_HOME)/examples/doc_examples
Windows NT/2000/XP:
$(ISIGHT_HOME)/examples_NT/doc_examples
More information on this example can be found in the iSIGHT MDOL Reference Guide.
For illustrative purpos, there are two objectives in this problem:
minimize Deflection
minimize Mass
The calculations shown in the following ctions were done using the following values as parameters:
BeamHeight = 40.0
FlangeWidth = 40.0
WebThickness = 1.0
FlangeThichness = 1.0
After executing a single run from Task Manager, the corresponding output values can be obtained:
Mass = 118.0
Deflection = 0.14286
Stress = 21.82929
