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Simulation Optimization Using a Hybrid Scheme … 127

simplifications, such as the linearization of the system (Dangerfield and Roberts, 1996).
On the other hand, policy optimization based on algorithmic search methods that use
simulation represent the most general mean for stability analysis of nonlinear systems,
due to its effectiveness in handling the general cases and most of special problems that
arise from nonlinearity. However, the objective functions are chosen to represent the
stability conditions to each model. The use of a generic objective function applied to
stabilize SC models independent of their linear or nonlinear structure has not been found
in the literature surveyed so far.

PARTICLE SWARM OPTIMIZATION

Optimization techniques based on evolutionary algorithms belong to the class of
direct search strategies, where every considered solution is rated using the objective
function values only. Therefore, no closed form of the problem and no further analytical
information is required to direct the search process towards good or preferably optimal
elements of the search space. For that reason, evolutionary search strategies are well
suited for simulation optimization problems. Additionally, because of their flexibility,
ease of operation, minimal requirements and global perspective, evolutionary algorithms
have been successfully used in a wide range of combinatorial and continuous problems.
The first work in PSO is accredited to Eberhart and Kennedy (1995). Later Shi, made
a modified particle swarm optimizer (Shi and Eberhart, 1998) and was first proposed for
simulating social behavior (Kennedy, 1997). Recently, some comprehensive reviews on
theoretical and experimental works on PSO has been published by Bonyadi and
Michalewicz (2017) and Ab Wahab (2015).
Particle swarm optimization is an algorithm that finds better solutions for a problem
by iteratively trying to improve a candidate solutions comparing with a given measure of
quality. It solves a problem by having a population of candidate solutions, called
particles, and moving these particles in the search-space giving a mathematical formula
over the particle's position and velocity. Some limitations of PSO have been identified by
Bonyadi and Michalewicz (2017). They classify the limitations related to convergence in
PSO into groups: convergence to a point (also known as stability), patterns of
movements, convergence to a local optimum, and expected first hitting time.
PSO performs a population-based search to optimize the objective function. The
population is composed by a swarm of particles that represent potential solutions to the
problem. These particles, which are a metaphor of birds in flocks, fly through the search
space updating their positions and velocities based on the best experience of their own
and the swarm. The swarm moves in the direction of “the region with the higher objective
function value, and eventually all particles will gather around the point with the highest
objective value” (Jones, 2005).