# Simulation-based optimization

The idea of **simulation-based optimization** ( **SBO** ) is to combine an optimization component with simulation models that varies certain variables of a simulation model in order to minimize or maximize an objective function.

Simulation modelsare used to forecast complex, real systems that are subject to random influences. Typically, simulation models are used to examine the effects of individual action alternatives without actually implementing them and causing possible negative effects on the real system. As a rule, one limits oneself to a relatively small number of alternative courses of action, plays them through with the help of simulation software, and then selects the best alternative course of action based on a specific objective. The classic method for selecting an alternative course of action is to carry out the simulations with the appropriate software, but then to make the selection largely manually. The simulation-based optimization, on the other hand, aims to automate this selection of the “best” alternative action by aMake an algorithm that uses an underlying simulation model. The basic idea of the SBO is to describe alternative courses of action using variables in a simulation model. An SBO algorithm varies these variables, repeatedly evaluates the solution resulting from the choice of variable values using simulation runs and then returns the best solution found. On the one hand, the optimizer can control the simulator and vice versa.

In analogy to the “classic” optimization, the simulation result for the SBO corresponds to B. can be a cost value, the objective function of an optimization problem, and the variables of a simulation model the variables of an optimization model. A major difference to "usual" optimization problems, however, is that the "target function" in the SBO is stochastic; In other words, it is subject to random fluctuations, depending on which occurring scenario is considered in a simulation run.

## Application examples

Possible objectives from which specific SBO problems can be derived are finding

- the best integration of production and logistics in a company,
- the best layouts, connections and capacities of logistics networks,
- the highest utilization of available human resources,
- the best locations for the distribution of goods,
- the best plan for operating a nuclear power plant,
- the best allocation of doctors and nurses in a hospital,
- the best setting of tolerances in production processes,
- the solution of multi-criteria objectives (Pareto optimality) in production and logistics.

## software

There is an almost unmanageable variety of products on the market for simulation software. Various simulation software packages have now been expanded to include components for the SBO:

- The MATLAB Optimization Toolbox combines various methods of numerical optimization from the field of linear and non-linear optimization. The
*Genetic Algorithm and Direct Search Toolbox*expands the possibilities of optimization through further optimization strategies. - MLDesigner is a multi-domain (DE, FSM, SDF, CT) modeling and simulation tool for the development of complex, embedded systems.
- Plant Simulation has its own SBO component as well as integrated neural networks.
- OpenMDAO is an open source software for multidisciplinary optimization developed by NASA and written in Python .
- OptQuest is connected to 22 products from other software manufacturers, such as B. Arena, Crystal Ball, ProModel, Enterprise Dynamics, Flexsim and SIMUL8. In addition, OptQuest can be integrated into other applications through an API (the OptQuest Engine Callable Library).
- Simulink Design Optimization changes the parameters of a model in such a way that its dynamic behavior at an output follows a specified signal course or a corridor.
- WITNESS has an integrated experimenter that performs automated mass experiments to optimize processes and systems with various algorithms.

## Algorithms

The following classification of the SBO algorithms can be made, which is based on the SBO research directions:

- Algorithms for finite solution spaces: Ranking & Selection, Multiple Comparisons and Ordinal Optimization
- Stochastic Approximation Algorithms (SA) such as FDSA and SPSA
- Response Surface Methodology Algorithms (RSM) such as Sequential RSM with linear regression or neural networks
- Sample Path Optimization (SPO)
- Metaheuristics such as simulated cooling (SA), evolutionary algorithms (EA), taboo search (TS), scatter search (SCS) and particle swarm optimization (PSO)
- Direct search algorithms (DS) such as Pattern Search (PS) and the Nelder-Mead- Simplex-Algorithm , see Downhill-Simplex-Method
- Random Search
- Adaptive and Hybrid Search - Algorithms (determine, stochastic, evolve, genetic, threshold) with Learning Process (ISSOP - Intelligent System for Simulation and Optimization)

## literature

- Michael C. Fu:
*Optimization for simulation: Theory vs. practice*. In:*INFORMS Journal on Computing*14, 2002, 3, ISSN 0899-1499 , pp. 192-215. - Abhijit Gosavi:
*Simulation-based optimization. Parametric optimization techniques and reinforcement learning*. Kluwer Academic Publishers, Boston MA et al. 2003, ISBN 1-402-07454-9 , (*Operations research / computer science interfaces series*25). - Johannes Bayer, Thomas Collisi, Sigrid Wenzel (eds.):
*Simulation in the automotive industry*. Springer, Berlin 2002, ISBN 3-540-44192-1 . - Steffen Bangsow:
*Production simulations with Plant Simulation and SimTalk. Application and programming with examples and solutions*. Hanser Verlag, Munich et al. 2008, ISBN 978-3-446-41490-7 , (*Workbook - Edition CAD.de*), (with 1 CD-ROM). - Wilfried Krug:
*Modeling, Simulation and Optimization for manufacturing, organizational and logistical processes*. SCS - EUROPE BVBA, Delft et al. 2002, ISBN 3-936150-20-6 . - Matthias Böhmer:
*Forward-looking order picking strategies. Simulation-based optimization in the event of fluctuating access numbers*. VDM Verlag Dr. Müller, Saarbrücken 2009, ISBN 978-3-8364-9843-2 .