Proceedings of the Third International Conference on Modeling, Simulation and Applied Optimization Sharjah,U.A.E January 20-22 2009
A HYBRID APPROACH TO SOLVE THE MIDO PROBLEM IN THE SYSTHESIS OF RICE DRYING PROCESSES Wongphaka Wongrat
Abdunnaser Younes
Ali Elkamel
Peter L. Douglas
University of Waterloo Department of Chemical Engineering Waterloo, ON, Canada N2L 3G1
[email protected]
ABSTRACT There is a growing need to find optimal configurations and optimal operating conditions for rice drying systems that ensure high quality of processed rice grain. Since the synthesis problem can be formulated as a mixed-integer dynamic optimization (MIDO) problem, this paper proposes a hybrid algorithm that combines a stochastic method (genetic algorithm) and a deterministic method (control vector parameterization) as a tool to solve it. The results of applying the proposed method show that high quality of rice grain can be preserved for any drying configuration as long as the operating conditions of the drying process produce the least amount of moisture gradient within the rice grain. 1.
developing simplified models for each particular unit operation employed in rice drying processes. Since drying process happening in unit operations of any drying system is simultaneous heat and mass transfer process which can be commonly explained by heat and mass transfer equations; therefore, the synthesis problem of rice drying processes using theoretical models is of the interest in this work. Theoretically, heat and mass process are explained by a system of differential equations and the synthesis problem involves discrete decision variables; hence, these components form a MIDO problem. This kind of problem is difficult to solve because it is highly nonlinear and multimodal. Many solution methods, both deterministic and stochastic, have been proposed to solve the MIDO problem but no specific method has been claimed yet to be very efficient one to solve any kind of problem.
INTRODUCTION
Rice needs to be dried from harvested moisture content to the safe storage level to prevent deterioration; however, rice grain is very sensitive to the mode of drying. Improper drying will cause fissuring in the rice grain and thus reduce yield of head rice, which has higher market value than broken rice. The term “head rice” is defined as rice kernel comprised of three-fourth or more of the original length [1]. To dry rice, many drying systems are used nowadays depending on many factors such as investment cost, term of uses and available technology. Nevertheless, the most popular one (used worldwide) is called multistage drying system is the focus of this work. This method uses alternating sequences of drying, cooling and/or tempering units: Drying units for removing moisture content within the rice grain, cooling units for lowering grain temperature and removing some amount of water from grain and tempering units for equalizing moisture gradient developed during drying process. Phongpipatpong and Douglas [2] stated that there is only limited extension of well-developed integrated process design method in agricultural industries. Therefore, they first addressed the synthesis problem of rice drying processes using simplified models developed from a set of experiment data to find the optimal operating strategy and the optimal configuration for multi-stage rice drying system. Aside from their ease of use, simplified models are only valid within their experimental condition so that there is a need for
In this work, a hybrid method combining a genetic algorithm (GA) with control vector parameterization (CVP) is proposed as a tool for solving the synthesis problem. In the following section, the synthesis problem of rice drying processes will be stated. The solution strategy will be proposed in Section 3. After that, results and discussions of tuning the algorithm’s parameters and optimal solution of the synthesis problem will be shown in Section 4. Finally, the conclusion of this work will be given in Section 5. 2.
THE SYNTHESIS PROBLEM
As mentioned before, improper mode of drying operation will lower the yield of head rice and various configurations of drying system have been used nowadays. Therefore, there is a need for the application of process synthesis in rice drying processes. The synthesis problem in this work can be stated as “Given initial and final moisture contents of rice grain, what is the optimum configuration and operating conditions that maximize the head rice yield?”
This work considers five alternatives that are found in practical multi-stage drying systems. These alternatives are illustrated in Figure 1 as drying-cooling (alternative 1); drying-tempering (alternative 2); cooling-tempering (alternative 3); drying-cooling-tempering (alternative 4); and drying-tempering-cooling (alternative 5). As the name
ICMSA0’09-1
Proceedings of the Third International Conference on Modeling, Simulation and Applied Optimization Sharjah,U.A.E January 20-22 2009
states, multi-stage drying system generally required more than one pass of drying to prevent the loss of head rice by gently drying rice. Note that S1j to S4j and M1j to M4j are dummy splitting and mixing nodes respectively which do not actually exist in a real drying system but they are used for the ease of understanding the connectivity of various units in the superstructure. From Figure 1, rice at initial moisture content (Mi) will pass through multi-pass sequence of drying (Dj), cooling (Cj), and tempering (Pj) units till the moisture content of rice grain reaches the safe storage level (Mf). Table 1 represents the specific conditions considered in this work. j+1th pass
M1j
Dj
S2j
M2j
Cj
S3j
M3j
Pj
S4j
Moutj
Minj
Mi
S1j
M4j
Mf
Figure 1. Superstructure of rice drying processes.
Table 1. The specific conditions considered in this work Condition 1 2 3 4
Description Initial moisture content (Mi) is 34% dry basis (d.b.) Maximum number of passes is 8 The final moisture content(Mf) should be less than 14% dry basis (d.b.) Maximum head rice yield = 70%
Solutions for the synthesis problem considered in this work should identify the following variables: - Total number of passes required for drying rice from initial moisture content (Mi) to final moisture content (Mf). - The configuration of unit operation in each pass (j), whether it consists of a drying unit (Dj), a cooling unit (Cj), a tempering unit (Pj), or a combination of them. - Operating conditions (control variables) of unit operations which exist in the flowsheet in each pass. For a drying unit, they are drying air temperature (TDj), relative humidity of drying air (RHDj) and drying time (tDj); for a cooling unit, they are cooling air temperature (TCj), relative humidity of cooling air (RHCj) and cooling time (tCj); and finally for a tempering unit, it is tempering time (tPj). The bounds on the control variables are shown in Table 2.
Table 2. Bound of control variables Variable TDj (oC) RHD (%) TCj (oC) RHCj (%) tDj (hrs) tCj (hrs) tCj (hrs)
Lower bound 35 5 20 5 0 0 0
3.
Upper bound 80 80 30 80 2 4 6
SOLUTION STRATEGY
For the synthesis problem, both discrete and continuous decisions have to be made in order to find the optimal configuration and optimal control strategy; however, due to the huge total number of possible configurations (58= 390,625) in discrete space and the complex system of differential-algebraic equations derived from theoretical models in continuous space for each configuration, no MIDO algorithms have been claimed yet to be rigorous optimization approach for solving this kind of problem. Recently, many researchers have paid their attention to the development of hybrid optimization method for solving the real-world optimization problem. Principally, the idea of hybrid method is to combine and extend the strengths of individual well-developed techniques and at the same time alleviate their weakness [3]. Hence, we present a hybrid method that combines GAs and CVP as a tool to tackle the MIDO problem. GAs are well-known stochastic search techniques which search for optimal solutions in a manner similar to the mechanisms of natural selection. The basic idea of a GA is to start from initially generated set of random solutions called population from the solution space. Each candidate solution in the population called chromosome will undergo the evolutionary mechanism of GA through selection, crossover and mutation process to explore and exploit the existing solution in a current generation in hope that the better one will be generated in a next generation. A review of GAs, their implementation issues and limitations in chemical engineering can be found in [3]. CVP is a deterministic optimization method widely used for solving optimization problems involving systems of differential equations or transient processes. The basic idea of CVP approach is to iteratively solve nonlinear programming (NLP) problem which is derived from transforming infinite-dimensional optimization problem into finite-dimensional one by discretizing control variables with well-known functions varying from simple piecewise constant to complicated polynomial one and estimating values of state variables by solving an initial value problem (IVP) of ordinary differential equations (ODEs). In each iteration, the value of objective function will be improved from finding the gradients of objective function and state variables with respect to the control parameters [4]. In this work, we take the advantage of the population to population approach of GAs to perform an efficient global search of a high dimensional combinatorial optimization problem (formed by discrete space of this work) and the same time, we use the simplicity of CVP method to transform the dynamic
ICMSA0’09-2
Proceedings of the Third International Conference on Modeling, Simulation and Applied Optimization Sharjah,U.A.E January 20-22 2009 optimization problem into an NLP problem using a differential equation solver. The algorithm structure for the complete hybrid method is presented in Figure 2.
Start
without replacement. Finally, the termination criteria will be checked if the number of generation reaches the maximum number. If the number of current generation is less than the specified number, the same GA procedure will be repeated, otherwise the algorithm will be stopped and optimal configuration and optimal operating conditions will be found.
Set GA parameters Initialize population Gen=0
4. CVP method
Fixed configuration
Evaluate Chromosome
Dynamic Optimization
Apply elitist strategy
Discretize control parameter
Apply tournament selection
Solve Initial value problem
Delete duplicate chromosomes
NLP
Gradient
gen=gen+1
Apply 2-Point Crossover
EXPERIMENTATION
Is optimality?
No
The proposed solution method presented in the previous section was implemented in MATLAB 2006b and run on AMD Athlon 3.21 GHz under Windows operating system to solve the synthesis problem. The problem is to maximize the grain quality (Q) at the end of drying process subjected to a set of differential-algebraic constraints; heat and mass transfer models corresponding to each unit operation represented in the superstructure, bounds on control and state variables and target moisture content at the final time. In this study we have used the head rice yield model developed by Abud-Archila et al. [1] and heat and mass transfer models developed by Abud-Archila et al. [5]. Their process models considered rice grains as two compartments corresponding to brown rice and hull as shown in Figure 3.
Apply inversion mutation
Internal mass transfer coefficient
External mass transfer coefficient
Apply uniform mutation
Yes
β2
β1
Is gen
