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OUTLINE
INTRODUCTION
IN SEARCH OF THE OPTIMUM
COMBINING DIRECT SEARCH TECHNIQUESWITH SIMULATION
EVOLUNTIONARY ALGORITHMS
STRATEGIC AND TACTICAL ISSUES
FORMULATING AN EXAMPLE OPTIMIZATIONPROBLEM
REAL-WORLD SIMULATION OPTIMIZATIONPROJECT
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INTRODUCTION
Simulation models are built for manyreasons
To gain understanding of a system,
o orecas e ou pu o e sys em,
To compare one system to another, or
To find the optimal solution
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INTRODUCTION
To find the optimal solution: The simulation isused to answer questions like What are theoptimal setting for (1) to minimize (orMaximize) ..(2).?
Optimization is the process of trying differentcombination of values for the variables thatcan be controlled to seek the combination ofvalues that provides the most desirable output
from simulation model.
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INTRODUCTION
Consider the simulation model as a blackbox that imitates the actual system
In the question before, the first blank, (1)
called decision variables or factors) andthe second blank, (2) represents theperformance measures of interest (output
responses) [See Fig. 11.1]
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INTRODUCTION
The objective is to seek the optimal valuefor each decision variables that minimizes(or maximizes) the expected value of the
Note: the expected value is estimated byaveraging the models output over multiplereplication or batch intervals.
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INTRODUCTION
The formal structure of the simulationoptimization problem:
Objective function:
n or ax , ,, n
Subject to:
Lower Bound(i) X(i) Upper Bound(i)
Where, E[f(X(1),X(2),,X(n))] denotes theexpected value of the objective function
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INTRODUCTION
The search for the optimal solution can be
Done manually, or
Automated with algorithms
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INTRODUCTION
Interfacing optimization algorithms thatcan automatically generate solutions andevaluate them in simulation models is a
Saving the analyst time
A logical method is used efficiently explore therealm of possible solutions, seeking the best
The method often find several exemplarysolutions for the analyst to consider
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INTRODUCTION
In 1995, PROMODEL developedSimRunner based on the research ofBowden (1992) on the use of modern
machine learning.
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IN SEARCH OF THE OPTIMUM
The way to find the optimal solution involves5 steps (Akbay 1996)
Step 1: Identify all possible decision
system
Step 2: Based on the possible values ofeach decision variables, identify allpossible solutions
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IN SEARCH OF THE OPTIMUM
Step 3:Evaluate each of these solutionsaccurately
Step 4: Compare each solution fairly
ep : ecor e es answer
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IN SEARCH OF THE OPTIMUM
If the output from the simulation model for allpossible values of the decision variables isrecorded and plotted, the resulting plot would becalled the response surface (See Fig. 11.2)
For well-posed problems, there are severaloptimization methods that can find the optimalsolution,Newton-Raphson method
Linear Programming
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IN SEARCH OF THE OPTIMUM
Unfortunately, most realistic problems are notwell-posed and do not lend themselves to beingsolved by these optimization methods.
The response surface produced by stochastic
,multimodal, and noisy.
Heuristic techniques consistently provide good,or near optimal, solutions within the reasonableamount of search time.
It may find the optimal solution but there is noguarantee that it always will do so.
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COMBINING DIRECT SEARCHTECHNIQUES WITH SIMULATION
Direct Search techniques are a class of searchtechniques designed to seek optimal values forthe decision variables for a system so as tominimise, or maximise, the output measure ofinterest from the system.
Require no additional information about thefunction that generates the output
Suited for optimization task when mathematicalmodels do not exist.
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COMBINING DIRECT SEARCHTECHNIQUES WITH SIMULATION
SimRunner has an optimization moduleand a module for determining the requiredsample size (replication) and a models
- .The optimization module can optimize
integer and real decision variables.
Methods used i.e., Tabu search andevolutionary algorithms.
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EVOLUNTIONARY ALGORITHMS (EAs)
EA s are a class of direct searchtechniques that are based on conceptsfrom the theory of evolution.
EA s mani ulate a o ulation of solutionsto a problem in such a way that poorsolution fade away and good solutionscontinually evolve in their search for theoptimum
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EVOLUNTIONARY ALGORITHMS
EA s differ from traditional nonlinearoptimization techniques in many ways the most significant difference is that they
population of solutions as opposed tosingle solution.
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EVOLUNTIONARY ALGORITHMS
The most popular EA s are geneticalgorithms
Four major steps are needed to applyan EA:
Step 1: Generate an initial population ofsolutions to the problem by distributing
them throughout the solution space
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EVOLUNTIONARY ALGORITHMS
Step 2: Accurately compute the fitness(response) of each solution
Step 3: Based on the fitness of the
solutions select the best solutions andapply idealized-type genetic operators toproduce a new generation of offspringsolutions.
Step 4: Return step 2 as long as thealgorithm is locating improved solutions.
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EVOLUNTIONARY ALGORITHMS
Discuss the illustration of an EvolutionaryAlgorithms Search of a Response Surface(See Fig. 11.3)
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STRATEGIC AND TACTICAL ISSUES
The analyst must first ensure that the simulationmodel accurately mimic the real system
Another issue very relevant to simulation isefficiency of the simulation study (measured interm of the amount of time necessary to conductexperiment with the simulation model.Operational Efficiency
Statistical Efficiency
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General Optimization Procedure
Step 1: Identify the decision variables to affect the outputof the simulation
Step 2: For each decision variable, define its numericdata type (integer or real) and its lower bound and upperbound.
Step 3: Construct the objective function to measure theutility of the solution tested by the EA
Step 4: Select the size of the EAs population (number ofsolutions) and begin the search.
Step 5: After the search concludes, the analyst select
further evaluation some of the top solutions found by thealgorithm.
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FORMULATING AN EXAMPLEOPTIMIZATION PROBLEM
Problem description (See page 297) Step 1: three decision variables, the number of parts to
be stored in each buffer Q1,Q2,Q3
Step 2: Q1,Q2,Q3 are integer; 1Q(i) 15
Max[$10(Throughput)-$1000(Q1+Q2+Q3)]
Step 4: three profiles aggressive, moderate, andcautions corresponding to EA population sizes of small,medium, and large.
Step 5: After the search concludes, the analyst shouldstudy the solutions found by the algorithm.
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FORMULATING AN EXAMPLEOPTIMIZATION PROBLEM
Consider The allocation of buffer storagebetween workstations described in Section11.6.1.
.SimRunner optimization of the bufferallocation problem using an aggressiveoptimization profile.
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Buffer Allocation Problem
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Buffer Allocation Problem
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REAL-WORLD SIMULATIONOPTIMIZATION PROJECT