Applying Multi-Objective Optimization Algorithms to Mechanical Engineering

Applying Multi-Objective Optimization Algorithms to Mechanical Engineering

Preeti Shivach (Graphic Era University, India), Lata Nautiyal (Graphic Era University, India) and Mangey Ram (Graphic Era University, India)
DOI: 10.4018/978-1-5225-3035-0.ch014
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Abstract

In today's scenarios, the utilization of simulation and optimization in the field of designing is achieving wider recognition in the various zones of commerce as the computational competences of computers upsurge day by day. The result is that the uses for numerical optimization have increased tremendously. Design process in engineering is a distinct practice of solving the problems where a group of recurrently indistinct objectives has to be well-adjusted deprived of violating any given circumstances. Consequently, it seems quite ordinary to consider a design process as an optimization process. The design process could be articulated as to allocate values to the system parameters to confirm that the state variables and the characteristics are as suitable as possible through an inclusive range of operating and environmental variables. This is a complex multi-objective optimization problem (MOOP). This chapter discusses the use of MOO algorithms in mechanical engineering.
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Introduction

To improve the designing process of engineering there is a powerful tool called optimization. It is the act of finding the finest solution under particular conditions. It is more effective than conventional trail-and-error process of designing. In today’s scenarios, the utilization of simulation and optimization in the field of designing is achieving wider recognition in the various zones of commerce as the computational competences of computers upsurge day by day. The result is that the uses for numerical optimization have increased tremendously. There are many optimization approaches developed and used in the literature. These approaches are grounded on non-linear, linear and geometric programming etc. Most recent methods are neural network, genetic algorithms and stimulated annealing. These methods are also called non-traditional optimization methods. Engineering design problem generally consists of blend of numerical simulation, logical designs and list selection. Hence, non-gradient methods are sound suited to this type of problems.

Engineering design problems of real world can be categorized by more than one objective. Therefore, the designing problem in engineering can be viewed as a multi-objective problem. The design process requires a large number of goals to be satisfied and deal with various design variables. Some of these objectives may be conflicting to each other it means we work to achieve a particular objective there might be some objective which we are losing. For example, the automobile design could be realized as a multi-objective problem with two contradictory goals, namely, the minimization of weight and the maximization of the crash resistance. Though, consequences of reduction in the weight of the automobile is, increase in the crash resistance, and vice-versa.

Design variables are a factor that the designer or engineer might “alter” with the purpose of modifying the objects he is designing. The types of design variables are:

  • Independent Variables

  • Dependent Variables

  • State Variables

  • Operating Variables

  • Environment Variables

Independent variables are the measures the engineer deals with precisely, such as physical properties and lubrication properties, etc. Dependent variables are factors the engineer can’t precisely allocate values to but through independent parameters the designer deals with them. State variables are a transitional type of design parameters between independent and dependent. Operating variables are those factors that can be altered after the designing process. The last type of factors (also called external variables) is the environmental features that have impact on the design when used.

Therefore, the designing problem can be expressed as to allocate values or costs to the various design factors with the purpose of ensuring that the variables and the features are as suitable as promising through an inclusive span of environmental and operating variables. This is certainly a complex MOOP.

Single Objective Optimization

Single objective optimization problems (SOOP) are those problems that have only one goal to be achieved. It can be stated as:Find a vector X = {x1, x2, x3, …, xn}T that minimizes objective function f(x)With the constraints; gj(x) ≤ 0, j = 1, 2, 3, …, mhl(x) ≤ 0, l = 1, 2, 3, …, pwhere, X is the vector of design variables.

The above problem is called a SOOP, since there is only one objective to be minimized.

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