Simulation-based optimization (also known as simply simulation optimization) integrates
optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
techniques into
simulation
A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of Conceptual model, models; the model represents the key characteristics or behaviors of the selected system or proc ...
modeling and analysis. Because of the complexity of the simulation, the
objective function
In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cos ...
may become difficult and expensive to evaluate. Usually, the underlying simulation model is stochastic, so that the objective function must be estimated using statistical estimation techniques (called output analysis in simulation methodology).
Once a system is mathematically modeled, computer-based simulations provide information about its behavior. Parametric simulation methods can be used to improve the performance of a system. In this method, the input of each variable is varied with other parameters remaining constant and the effect on the design objective is observed. This is a time-consuming method and improves the performance partially. To obtain the optimal solution with minimum computation and time, the problem is solved iteratively where in each iteration the solution moves closer to the optimum solution. Such methods are known as ‘numerical optimization’ or ‘simulation-based optimization’.
In simulation experiment, the goal is to evaluate the effect of different values of input variables on a system. However, the interest is sometimes in finding the optimal value for input variables in terms of the system outcomes. One way could be running simulation experiments for all possible input variables. However, this approach is not always practical due to several possible situations and it just makes it intractable to run experiments for each scenario. For example, there might be too many possible values for input variables, or the simulation model might be too complicated and expensive to run for suboptimal input variable values. In these cases, the goal is to find optimal values for the input variables rather than trying all possible values. This process is called simulation optimization.
Specific simulation–based optimization methods can be chosen according to Figure 1 based on the decision variable types.
Optimization
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
exists in two main branches of operations research:
''Optimization
parametric (static)'' – The objective is to find the values of the parameters, which are “static” for all states, with the goal of maximizing or minimizing a function. In this case, one can use
mathematical programming
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...
, such as
linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear function#As a polynomial function, li ...
. In this scenario, simulation helps when the parameters contain noise or the evaluation of the problem would demand excessive computer time, due to its complexity.
''Optimization
control
Control may refer to:
Basic meanings Economics and business
* Control (management), an element of management
* Control, an element of management accounting
* Comptroller (or controller), a senior financial officer in an organization
* Controllin ...
(dynamic)'' – This is used largely in
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
and
electrical engineering
Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
. The optimal control is per state and the results change in each of them. One can use mathematical programming, as well as dynamic programming. In this scenario, simulation can generate random samples and solve complex and large-scale problems.
[Abhijit Gosavi]
Simulation‐Based Optimization: Parametric Optimization Techniques and Reinforcement Learning
Springer, 2nd Edition (2015)
Simulation-based optimization methods
Some important approaches in simulation optimization are discussed below.
Statistical ranking and selection methods (R/S)
Ranking and selection methods are designed for problems where the alternatives are fixed and known, and simulation is used to estimate the system performance.
In the simulation optimization setting, applicable methods include indifference zone approaches, optimal computing budget allocation, and knowledge gradient algorithms.
Response surface methodology (RSM)
In
response surface methodology
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM ...
, the objective is to find the relationship between the input variables and the response variables. The process starts from trying to fit a linear regression model. If the P-value turns out to be low, then a higher degree polynomial regression, which is usually quadratic, will be implemented. The process of finding a good relationship between input and response variables will be done for each simulation test. In simulation optimization, response surface method can be used to find the best input variables that produce desired outcomes in terms of response variables.
Heuristic methods
Heuristic methods change accuracy by speed. Their goal is to find a good solution faster than the traditional methods, when they are too slow or fail in solving the problem. Usually they find local optimal instead of the optimal value; however, the values are considered close enough of the final solution. Examples of these kinds of methods include
tabu search Tabu search is a metaheuristic search method employing local search methods used for mathematical optimization. It was created by Fred W. Glover in 1986
and formalized in 1989.
Local (neighborhood) searches take a potential solution to a prob ...
and
genetic algorithms
In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to gene ...
.
Metamodels enable researchers to obtain reliable approximate model outputs without running expensive and time-consuming computer simulations. Therefore, the process of model optimization can take less computation time and cost.
Stochastic approximation
Stochastic approximation
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive update rules of stochastic approximation methods can be used, among other things, for solving l ...
is used when the function cannot be computed directly, only estimated via noisy observations. In these scenarios, this method (or family of methods) looks for the extrema of these function. The objective function would be:
: