Optimization of greenhouse climate management during winter period is an issue that intensely preoccupied researchers over the last two decades as it is directly linked to energy saving, products quality, and reduction of chemical inputs. Goal of this project was the use of Branch and Bound algorithms in order to obtain the optimize greenhouse climate control. For this purpose a biophysical simulator were used and experiments were carried out in the farm of the University of Thessaly in the region of Volos (Greece), during the autumn and winter periods of 2005 and 2007. Branch and Bound algorithms used for two different climate scenarios and the results showed the difference between the classical greenhouse climate control and the control according B & B optimization technique. Finally results showed the contribution of optimization technique to increase tomato production and to reduce energy consumption.
Most of the greenhouse climate control problems show large number of possible
solutions, which are therefore entered the need for finding the best "route" or optimal
solution
The heating of the greenhouse by the sum of the temperatures (Integrated
Temperature Control) during the day has already been applied in several floriculture
Many experimental projects are referred to optimization of greenhouse climate.
The optimal control is one of the processes studied further
The principle of Bellman
Material & Methods
Branch and bound (BB or B&B) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as general real valued problems. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree (Figure 1) with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm. S (Α)
The method of branching and bounding (Branch & Bound) has found application
in solving various and important optimization problems, eg, in integer programming,
nonlinear problems, programming problems, plant sitting problems
S S1 S3 S1 S3
S4
S31 S32
S1
S2
S3
S4 (Β) S21
S22 S31
S32 (C) 2.1
Optimization Method for Greenhouse Climate Control
Optimization of the biophysical simulator with the use of Branch & Bound method uses a space selection strategy in order to be investigated in accordance with the algorithms (1), (2) below. The algorithm (1), is responsible for setting the (Vh) ventilation (system controller) inside the greenhouse where pb1, pc1, pRΤ, the values of the variables that have to be optimized in order to give the best solution. At the same time the algorithm (1), uses the biophysical simulator and more specifically the results obtained for the relative humidity (RH) and the air temperature inside the greenhouse (Ti), during the process of optimization.
The algorithm (2) below is responsible for determining the operation of the (Vt) heating system (system controller) within the greenhouse.
Vt = 0.1⋅ (1 + (
RH − pRT ( Abs ⋅ (RH − pRT )) + 0.5 )) + e ⋅
1 ( pb1−Ti )
pc1 e ⋅
1 ( pb2p−c2DTi ) (1) (2) (3) (4) where pb2, pc2, pRΤ, the values of the variables that have to be optimized in order to give the best solution. At the same time the algorithm (2), uses the biophysical simulator and more specifically the results obtained for the relative humidity (RH) and the air temperature difference inside and outside the greenhouse (DTi), during the process of optimization.
The problem to be solved is to minimize the objective function J to a range of possible solutions, S:
min J = ∑ (Fcon) − ∑ (D.W .F ) where
∑ (Fcon) is the total energy gives the heating system inside the greenhouse, while respectively ∑(D.W.F) the resulting dry weight of mature fruit.
The limiting function used to optimize the biophysical simulator using Branch & Bound method shown below:
min J (one) > max J (other )
Function (4) reject some subset of possible solutions by further exploring inside, to find the possible solution when the above condition is true, that the optimal minimal solution that offers the particular subset is greater than the largest value of another subset. 2.2 Climate and Biological Measurements
The measurements that used to optimize the model were data for tomato
production and development simultaneously with the greenhouse climatic data,
during the autumn and winter periods of 2005 and 2007. For the experimental
periods were used also calculated values by the modified TOMGRO
This section presents results of treatment followed during the experimental measurements and optimum proposed in accordance with the branch & bound method. The results are giving detailed greenhouse climatic conditions and all features related to the development and production of tomato plants. From these were selected and are presented in the following sections the results concerning: a. number of plants node, b. shoot dry weight, c. leaves dry weight, d. whole plant dry weight, e. simulation curve of windows opening, f. air temperature inside the greenhouse, g. temperature of the greenhouse cover. Values that are used as input variables for the number of nodes, dry weight of leaves, stems and fruits are the same that used of the modified TOMGRO. 3.1 Results of the first simulated period
Initially a variation was observed in greenhouse air - cover temperature and presented in Figures 2 and 3. The optimum calculated values fall short of measured values and this is due to the diversification arising from the way of windows opening. Control of when and how much, windows are opening through the use of the algorithm (1) are indicated in Figure 5. Time variation of window opening rate leads to both reduce the temperature and reduce the humidity inside emissions (data not shown).
Figures 4 (a-d) are showing the variation of calculated values using the modified TOMGRO, and the optimum values obtained after the use of branch & bound method for the number of nodes, dry weight of stem, leaves and whole plant correspondingly. In Figure 4 (a) observed that the climate change does not change the number of plant nodes formed. Correspondingly there is no change at the number of leaves and the number of produced flowers (data not shown). Variation is observed in Figure 4 (b) showing the dry weight of the shoot. The calculated optimal values are above those calculated by the modified TOMGRO. Reverse change is observed in the dry weight of leaves Figure 4 (c), wherein the optimum values are below those estimated by the modified TOMGRO.
Smaller differences observed in Figure 4 (d) illustrating the total output of the plant biomass. The differences are due to the diversification of air temperature values, Figure 2. Reduction of air temperature leads to a small hysteresis of growth and development of tomato plants. The reduction in biomass production when the plants are in the initial stage of development helps to create more robust plants and there is a regular practice for the producers that mainly use the chemical composition of the nutrient solution and the irrigation dose to achieve it. 3.2 Results of the second simulated period 4 Discussion & Conclusions
The results presented above were according two different climate scenarios within greenhouses, with simultaneous display of the changes caused in the development and production of the tomato crop. The periods used were selected of producer’s interest and was at the start of the growing season and the second in the medium.
The study of the results for the first scenario, it is established that the reduction of air temperature contributes to the reduction of both dry weight of leaves and whole plant. The decrease in air temperature was due to the different treatment of the windows operating system (system controller and B & B method). 10/10/2007 11/10/2007 12/10/2007 13/10/2007
14/10/2007 Days
The practice followed in accordance with the use of branch & bound method leads to an opening of a greenhouse window for longer period than that followed in the experimental procedure. However, the reduction of biomass produced when the plants are in the initial stage of development helps to create more robust plants in the future.
Days Days 3 3 4 4 5 5
Days Days 3 3 4 4 5 5 0,6 1)tn 0,5 -a l (gp 0,4 s tem 0,3 fso tgh 0,2 i e ryw 0,1 D 0
(a) 0
1 (b) 0
1 100% ) (%90% g inn 80% e pO 70% ow 60% d inW50% feo 40% g tan 30% e rce 20% P 10% 0% 15 16 17 18 19 20 25 26 27 28 29
30 21 22 23 24
Air Temperature (oC)
By observing the results of the second scenario it was found that the reduction of production costs by 19.72% led to a corresponding reduction of the biomass production by 15.5% of shoot dry weight, 18.5% of leaves dry weight and 17.4% of whole plant dry weight. However, the reduction caused in plants growth and development can be balanced with an increase in air temperature inside the greenhouse to a period prior to the reduction. 0 28/11/2007 29/11/2007 30/11/2007 1/12/2007 2/12/2007 3/12/2007
4/12/2007
Days
Managing greenhouse climate as mentioned is a daily activity for the producers, which despite its frequency poses many problems. Further analysis of possible climate scenarios will help to create strategies that will shape the conditions for reducing production costs and improving the climate inside the greenhouse units. 15,0 -1t)n14,0 oapn l ( se13,0 oodn f er12,0 b m u N11,0 3,0 -1t)an2,5 lgp2,0 (se tm1,5 fso th1,0 eg i w0,5 ry D 0,0 (a) (b) 0 1
2 0 1 2
Days Days 3 3 4 4 5 5 5,0 -1)tn4,0 a l p g (s3,0 eeva lf2,0 o t h g ie1,0 w ry D 0,0 1)7,0 -ltan6,0 (gp tn5,0 ap l fo4,0 t h ieg3,0 w ryd2,0 lta oT1,0 0,0 0 0 (c) (d) 1 1 2 2
Days Days 3 3
Acknowledgments. This paper is part of the 03ED526 research project, implemented within the framework of the “Reinforcement Program of Human Research 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 4 4 ) % ( g n i n e p O w o d n i W f o e g a t n e c r e P 5 5 Manpower” (PENED) and co-financed by National and Community Funds (25% from the Greek Ministry of Development-General Secretariat of Research and Technology and 75% from E.U.-European Social Fund).