Page 283 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchanger networks 269

Similar to the genetic algorithm, it is also in principle a random method and
generally can handle discontinuous, nondifferential, and nonconvex function.
Unlike the genetic algorithm, the convergence property of the simulated
annealing algorithm can be proved theoretically, and the accepted points
are in Boltzmann distribution at a constant temperature. The genetic algo-
rithm begins from many initial points and is inherently parallel, while the sim-
ulated annealing algorithm starts from a single point. By using the Metropolis
rule to accept the worst solution in a fraction, the fraction gradually
approaches to zero. It is possible to jump out of a local optimum to search
for the global optimum. The solution points in the simulated annealing algo-
rithm satisfy Boltzmann distribution.

6.5.3 Particle swarm optimization algorithm

The particle swarm optimization is a heuristic algorithm originally proposed
by Kennedy and Eberhart (1995). It works like the movement of a bird flock
in which the individual birds are guided by their own experience and the
experience of the neighboring birds. In the particle swarm optimization,
the bird flock is represented as a population (called a swarm) of candidate
solutions (called particles). If improved positions are being discovered by
one or some individual particles, the movement of the swarm will be
attracted and move to these positions in their own ways, and during the
movement, their own experience will be updated. Similar to the genetic
algorithm, the particle swarm optimization is less sensitive to the starting
point of a solution, and due to the stochastic velocity and acceleration of
the particle movements, the local optimum traps can be avoided.
Silva et al. (2008, 2010) applied the particle swarm optimization
approach to the synthesis of heat exchanger networks. Huo et al. (2013) pre-
sented a two-level approach, in which the operators of the genetic algorithm
handled the structure optimization, while the lower level handled the con-
tinuous variables with a standard particle swarm optimization algorithm.
Although the standard particle swarm optimization algorithm is capable
of detecting the region of attraction, it cannot perform a refined local search
to find the optimum with high accuracy. In fact, if a particle has learned from
its neighboring particles and has flied to the region of attraction, it should be
able to make an own search for the best position. Wang et al. (2017) pre-
sented a comprehensive simultaneous synthesis approach based on stagewise
superstructure to design cost-optimal heat exchanger network. They
employed a two-level optimization algorithm for solving the synthesis