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Design optimization of gearboxes has been a subject of considerable
interest, especially in the present with
the rise in demand for power transmission applications. Gear drives are usually
preferred to transmit power because of their compactness ability to transmit
higher power and a wide range of the
velocity ratios. But as the size of the gears reduces, gears are prone to the various type of failures, for instance, the stresses increase and the
probability that a component fail increases. With the ever-growing power
requirements for all the applications and like of the space to accommodate the
growing equipment size needs arises to optimize the size weight power and other
required factors.

Optimization is the process of adjusting the inputs or characteristics
of a device, mathematical process, system, or experiment to find the minimum or
maximum output or result 1. To achieve this, the
objectives which are to be optimized are expressed in mathematical equations
which are known as objective functions,
cost functions, or fitness functions, which are subjected to a set of
constraints (design requirements) and based on this, various designs are
described using the design variables. Due to the size and high complexity of
the design problem, even the most skilled design engineers will not be able to consider
all the variables simultaneously. This is where the design optimization comes
in. It is the application of numerical algorithms and techniques to engineering
systems to assists the design engineers in improving the desired parameter of
the system. In general, optimization methods can be categorized into Single-Objective
Optimization (SO) or Multi-Objective Optimization (MO) depending on the number
of objective functions.

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The following sections of the current chapter present important definitions
and concepts which are significant to multi-objective optimization; after which
follows the literature review, objectives and scope, and organization of the

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