4 Simulation Optimization

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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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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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Step 3:Evaluate each of these solutionsaccurately

Step 4: Compare each solution fairly

ep : ecor e es answer


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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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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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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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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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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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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

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4 Simulation Optimization