Swarm Intelligence in Pulp and Paper Process Optimization

Abstract

We have learned much by studying the behavior of groups, or swarms of biological organisms. The intriguing aspect of such swarms is the fact that they exhibit complex collective behavior despite the simplicity of the individuals that make up the swarm. Models of these systems have been used successfully to solve difficult and complex real world optimization problems. This chapter focuses on the model inspired by the intelligent foraging behavior of honey bee swarm, proposed by Karaboga in 2005 and employed to solve optimization problems arising in pulp and paper industry. Pulp and paper industry comprises of a large number of processes, namely, economic optimization of a Kraft pulping or cooking problem, optimal boiler load allocation, maximizing the production rate, trim loss optimization, and optimization of supply chain system where optimization can be applied.

Appendix

Benchmark Functions

• 1. The sphere function is described as follows:

  $$\displaystyle{ f_{1}(x) =\sum _{ i=1}^{n}x_{ i}^{2} }$$

  where the initial range of x is [−100, 100]ⁿ, and n denotes the dimension of the solution space. The minimum solution of the sphere function is x ^∗ = [ 0, 0, ⋯ , 0 ] and f ₁(x ^∗) = 0.

• 2. The Griewank function is described as follows:

  $$\displaystyle{ f_{2}(x) = \frac{1} {4,000}\left (\sum _{i=1}^{n}(x - 100)^{2}\right ) -\left (\varPi _{ i=1}^{n}\cos \left (\frac{x_{i} - 100} {\sqrt{i}} \right )\right ) + 1 }$$

  where the initial range of x is [−600, 600]ⁿ. The minimum of the Griewank function is x ^∗ = [ 100, 100, …, 100 ] and f ₆(x ^∗) = 0.