Abstract
This chapter presents a comparison of population-based (e.g. Genetic Algorithms (GA), Firefly Algorithm (FA), and Ant Colony Optimization (ACO))and single point search meta-heuristic methods (e.g. Simulated Annealing (SA), Threshold Accepting (TA), and Tabu Search (TS)) applied to an optimal tuning of a universal digital proportional-integral-derivative (PID) controller. The PID controllers control feed rate and maintain glucose concentration at the desired set point for an E. coli MC4110 fed-batch cultivation process. The model of the cultivation process is represented by dynamic non-linear mass balance equations for biomass and substrate. In the control the design measurement, process noise, and time delay of the glucose measurement system were taken into account. To achieve good closed-loop system the constants (Kp, Ti, Td, b, c and N) were tuned in the PID controller algorithm so the controller can provide control action designed for the specific process requirements resulting in an optimal set of PID controller settings. For a time the controllers set and maintained the control variable at the desired set point during the E. coli MC4110 fed-batch cultivation process. Average, best, and worst objective function values and PID controller's parameters were used as criteria to compare the performance of the considered meta-heuristic algorithms. This indicates that the population-based meta-heuristics performs better than the single point search methods. GA and ACO show better performance than FA. It also indicates that TS results are comparable to those of FA. The results show that SA and TA algorithms failed to solve the PID controller tuning problem.
TopIntroduction
In the last 20 years, a new kind of approximate algorithm has emerged which basically tries to combine basic heuristic methods in higher level frameworks aimed at efficiently and effectively exploring a search space. These methods are nowadays commonly called meta-heuristics. The term meta-heuristic, first introduced in (Glover, 1986), derives from the composition of two Greek words. Heuristic derives from the verb heuriskein (euriskein) which means “to find”, while the suffix meta means “beyond, in an upper level”. Before this term was widely adopted, meta-heuristics were often called modern heuristics (Reeves, 1993).
Optimization heuristics are generally divided into two broad classes, namely, constructive methods and local search methods. For a long time local search has not been considered as a mature technique and only recently the method has become an object of increasing interest (Gilli & Winker, 2009). Local search methods are divided into trajectory methods (single point search) and population-based methods. Population-based meta-heuristic methods combine a number of solutions in an effort to generate new solutions that share good merits of the old and are expected to have better fitness. Such methods are iterative procedures that gradually replace solutions with better found ones. This class of algorithms includes but is not restricted to Ant Colony Optimization (ACO) (Dorigo & Stutzle, 2004; Dorigo & Socha, 2007; Bianchi et al., 2009), Evolutionary Computation (EC) including Genetic Algorithms (GA) (Goldberg, 1989), Particle Swarm Optimization (PSO), Firefly Algorithm (FA) (Yang, 2008; Yang, 2009). On the other hand, single point search methods improve upon a specific solution by exploring its neighborhood with a set of moves. Examples of this class are Simulated Annealing (SA) (Kirkpatrick et al., 1983; Metropolis et al., 1953), Thresholds Acceptance (TA) (Dueck & Scheuer, 1990) and Tabu Search (TS) (Glover & Laguna, 1997; Gendreau, 2002; Gendreau & Potvin, 2005; Gendreau & Potvin, 2010).
During the last decade, meta-heuristic techniques have been successfully applied to a variety of areas, including to bioprocess engineering (Roeva, 2010; Angelova & Pencheva, 2011; Angelova, Tzonkov, & Pencheva, 2011; Roeva & Fidanova, 2012; Angelova & Pencheva, 2012a; Angelova & Pencheva, 2012b; Roeva & Trenkova, 2012; Kosev et al., 2012; Angelova, Atanassov, & Pencheva, 2012a; Angelova, Atanassov, & Pencheva, 2012b; Roeva, 2012; Angelova, Melo-Pinto, & Pencheva, 2012; Roeva, 2013; Angelova & Pencheva, 2013; Roeva & Fidanova, 2013). In this work a list of meta-heuristic methods is applied to an optimal tuning of a digital Proportional-Integral-Derivative (PID) controller. The controller is used for control of glucose concentration during an E. coli MC4110 fed-batch cultivation process.
Key Terms in this Chapter
TS: Local search based meta-heuristic, where some of the search directions are forbidden.
Meta-Heuristic: High-level search methodologies used for optimization.
PID Controller Parameters Tuning: Tuning a controller involves setting the proportional, integral, and derivative values to get the best possible control for a particular process.
Ant Colony Optimization: Constructive meta-heuristic based on ant behavior when searching for the food.
SA: Local search based stochastic meta-heuristic.
Cultivation Process: It is encouraging the growth of microbiological culture.
TA: A deterministic analogue of SA.
PID Controller: A proportional-integral-derivative controller is a generic control loop feedback mechanism (controller) widely used in industrial control systems.
Genetic Algorithms: Population based meta-heuristic method which use the idea of Darwinian evolution.
Firefly Algorithm: Population based meta-heuristic method which is inspired from flashing light behaviour of fireflies in nature.