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In-Depth Information
A has a smaller value of
f
2
than point B, but a larger value of
f
1
.
Correspondingly, point B has a smaller value of
f
1
than point A, but a larger
value of
f
2
. Single-objective optimization has been widely used to address
multi-objective optimization problems but it has a limited capability.
Objectives are often non-commensurable and are frequently in conflict with
one another. Within a single-objective optimization framework, multiple
objectives are often tackled by the “weighted-sum” approach of aggregating
objectives. This has a number of significant shortcomings, not least of
which is the diculty of assigning appropriate weights to reflect the relative
importance of each objective.
Besides providing the desired family of solutions approximating to the
non-dominated solution set, the multi-objective particle swarm optimizer
uses dynamic weights instead of fixed weights to obtain the Pareto solutions.
4.5. Particle Swarm Algorithm for Multi-Objective
Optimization
As mentioned in Section 4.3, alloy design is a challenging multi-
objective optimization problem, which consists of finding the optimal
chemical compositions and processing parameters for a pre-defined property
requirement. Neurofuzzy modeling has been used to establish the properties
prediction models which facilitate the Particle Swarm Optimization (PSO)
based multi-objective optimization mechanism. An evolutionary adaptive
PSO algorithm has been developed to improve the performance of the
standard PSO.
Based on the established tensile strength and impact toughness
fuzzy prediction models, the proposed optimization algorithm has been
successfully applied to the optimal design of heat-treated alloy steels.
The experimental results have shown that the algorithm can locate the
constrained optimal solutions quickly and provide a useful and effective
guide for alloy steels design.
4.5.1.
Particle swarm optimization algorithm
The particle swarm algorithm works by “flying” a population of co-
operating potential solutions, called particles, through a problem's solution
space, accelerating particles towards better solutions. The particles in PSO
consist of a d-dimensional position vector
x
, and a m-dimensional velocity
vector
v
,sothe
i
th member of a population's position is represented
