Simulation optimization
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Abstract:
Simulation optimization has received considerable attention from both simulation researchers and practitioners. In this tutorial we present a broad introduction to simulation optimization and the many techniques that have been suggested to solve simulation optimization problems. Both continuous and discrete problems are discussed, but an emphasis is placed on discrete problems and practical methods for addressing such problems.Keywords:
Discrete optimization
Engineering optimization
Many real-world problems such as determining the type and number of wind turbines, facility placement problems, job scheduling problems, are in the category of combinatorial optimization problems in terms of the type of decision variables. However, since many of the evolutionary optimization algorithms are developed for solving continuous optimization problems, they cannot be directly applied to optimization problems with discrete decision variables. Therefore, the continuous decision variable values generated by these metaheuristics need to be converted to binary values using some techniques. In other words, to apply such algorithms to discrete optimization problems, it is necessary to adapt the candidate solution vectors of the algorithms to discrete values and make changes in their working structures. In this study, firstly, adaptation methods that are frequently used in previous studies in transforming metaheuristic optimization algorithms designed for the solution of continuous optimization problems into discrete optimization algorithms are explained. Then, the popular location update strategies used in solving discrete optimization problems are explained. The presented work summarizes the process of adapting continuous optimization algorithms to solve combinatorial problems step by step.
Discrete optimization
Continuous variable
Parallel metaheuristic
L-reduction
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Abstract Mixed-variable optimization problems consist of the continuous, integer, and discrete variables generally used in various engineering optimization problems. These variables increase the computational cost and complexity of optimization problems due to the handling of variables. Moreover, there are few optimization algorithms that give a globally optimal solution for non-differential and non-convex objective functions. Initially, the Jaya algorithm has been developed for continuous variable optimization problems. In this paper, the Jaya algorithm is further extended for solving mixed-variable optimization problems. In the proposed algorithm, continuous variables remain in the continuous domain while continuous domains of discrete and integer variables are converted into discrete and integer domains applying bound constraint of the middle point of corresponding two consecutive values of discrete and integer variables. The effectiveness of the proposed algorithm is evaluated through examples of mixed-variable optimization problems taken from previous research works, and optimum solutions are validated with other mixed-variable optimization algorithms. The proposed algorithm is also applied to two-plane balancing of the unbalanced rigid threshing rotor, using the number of balance masses on plane 1 and plane 2. It is found that the proposed algorithm is computationally more efficient and easier to use than other mixed optimization techniques.
Discrete optimization
Cutting-plane method
Continuous variable
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Most practical application problems are complex optimization problems,which belong to multi-objective optimization problems and simultaneously include the optimization of continuous variables and discrete variables.The existing optimization methods mostly focus on the continuous variables,and little on discrete variables optimization,even lessr on the discrete multi-objective optimization.This article summarizes present methods on the discrete multi-objective optimization,and points out its development trend.
Discrete optimization
Random optimization
Continuous variable
L-reduction
Engineering optimization
Derivative-Free Optimization
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Dimensioning
Discrete optimization
Topology optimization
Continuous variable
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The optimization problems in mechanical engineering were investigated with LINGO7 0 model language. This model can obtain better and reliable optimization results than general optimization method. LINGO7 0 may find optimization problems with continuous variables and may expediently find optimization problems with integer optimization variables in engineering. After introducing the soft LINGO7 0 , some optimization examples were given.
Engineering optimization
Discrete optimization
Multidisciplinary design optimization
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Wireless communication systems are based on many algorithms and theories such as information theory, coding theory, decision/estimation theory, mathematical modeling, optimization theory, and so on. Mathematical optimization techniques play an important role in many practical systems and research areas such as science, engineering, economics, statistics and medicine. The purpose of optimization is to find the best possible value of the objective function. Optimization problems are composed of three elements: objective function, constraints, and optimization variables. Linear programming is a highly useful tool of analysis and optimization. Optimization problems are categorized as convex optimization problems or non-convex optimization problems. Convex optimization covers convexity analysis, modeling and problem formulation, optimization, and numerical analysis. The gradient descent method is one of the most widely used optimization methods because it is simple and suitable for large-scale problems, and also works very well with few assumptions.
Engineering optimization
Derivative-Free Optimization
Discrete optimization
Random optimization
Convexity
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The optimization with discrete parameter is often encountered in mechine optimization design and has always been a difficult problem in the area of engineering optimization design.An optimization approach with discrete parameter us-ing Visual Basic,an object-based visualable program tool is suggested in this paper,which opens a nov alway to solve the optimization problem with discrete variables by taking the parameters optimization for a new type of gear pump as an example.
Discrete optimization
Engineering optimization
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The mixed optimization problems in mechanical engineering were investigated with LINGO9.0 model language.This model can obtain better and reliable optimization results than general optimization method.LINGO9.0 may find optimization problems with continuous variables and may expediently find optimization problems with integer optimization variables and discrete optimization variables in engineering.After introducing the software LINGO9.0 and emphasizing the problems in use,some optimization examples were given and their results are better than that with existing optimization method.
Discrete optimization
Engineering optimization
Multidisciplinary design optimization
Continuous variable
Random optimization
L-reduction
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Discrete optimization
Derivative-Free Optimization
L-reduction
Engineering optimization
Optimization algorithm
Random optimization
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The designing optimization of structural parameters for the frame of four roller rolling mill was achieved by the utilization of cooperated optimization method.According to the thought of carrying out designing optimization upon complex system by designing optimization of multi-branch of learning,let the complex mechanical system be resolved into a number of simple sub-systems for carrying out designing optimization has been put forward.Cooperated optimization is a kind of multi-branch of learning algorithm of designing optimization that has been developed rather quickly in recent years,the method of cooperated optimization being applied to the optimization design of complex engineering system has been described.Within the optimization of systematic level of cooperated optimization,the slack variable is introduced to let the restraint of consistency equality be transformed to the restraint of non-equality.The value adoption of slack variable will affect the convergence speed in the optimization of systematic level.By means of designing optimization of structural parameters for the frame of four roller rolling mill,the general train of thought for carrying out designing optimization of complex mechanical system by the use of cooperated optimization method was presented,thus laid a foundation for solving the problems of designing optimization of more complicated mechanical system.A calculation example proved the effectiveness of solving the designing optimization problems in complex mechanical system by cooperated optimization algorithm.
Engineering optimization
Multidisciplinary design optimization
Discrete optimization
Optimization algorithm
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