A Novel Optimization Algorithm for Echium amoenum Petals Drying

: A novel multi-objective optimization algorithm was developed, which was successfully applied in the drying process. The e ﬀ ect of drying parameters (air velocity ( v d ), drying temperature ( T d )) on the energy consumption (EC) and the quality parameters of Echium amoenum petals in ﬂuidized drying were experimentally studied. The following quality parameters were examined: the color di ﬀ erence, the bioactive compounds as losses of total antioxidant capacity (TAC) and losses of phenolic (TPC), ﬂavonoids (TFC) and anthocyanin (A). The six optimization objectives included simultaneous minimization of the quality parameters and energy consumption. The objective functions represent relationships between process variables and optimization objectives. The relations were approximated using an Artiﬁcial Neural Network (ANN). The Pareto optimal set with a nondominated sorting genetic algorithm was developed. No unequivocal solution to the optimization problem was found. Cannot be obtained E. amoenum petals characterized a low color change at low energy consumption due to its ﬂuidized drying. Unique Pareto optimal solutions were found: T d = 54 ◦ C and v d = 1.0 m / s–for the strategy in which the lower losses of TAC, TFC and A are most important, and T d = 59.8 ◦ C and v d = 0.52 m / s–for the strategy in which the lower losses of TPC and TFC are important with accepted EC values. The results of this research are essential for the improvement of industrial dehydration of E. amoenum petals in order to maintain their high content of bioactive compounds with low energy consumption and low colour change


Introduction
Many biochemical reactions in the body produce active oxygen species that are capable of destroying biomolecules [1]. The production of nitrogen oxide derivatives and forms of active oxygen is one of the causes of cancers and cardiovascular diseases [2]. Antioxidants are effective compounds that can prevent the oxidation of macromolecules such as proteins, nucleic acids and lipids [3]. These compounds trap free radicals and cause detoxification [4]. Some of these compounds are made with antioxidant or anti-oxidant properties as secondary metabolites of plants in nature, including compounds such as phenols, flavonoids, steroids, and terpenoids [5,6]. Dried petals of Borage Iranian (Echium amoenum Fisch. and C. A. Mey) contain considerably high amounts of phenol, flavonoids and anthocyanins [7] that play a major role in antioxidant activity [8]. For this reason, traditional medicine it is used as a drug for the treatment of depression [9], neurological problems [10][11][12], obsessive-compulsive disorder [10,13], anxiety [14], as an analgesic [15], for the prevention of inflammation and irritation of the kidneys and ducts, for rheumatism and heart disease [9], for colds, pneumonia, bronchitis [16,17], as a mucolytic drug, blood purifier, healer of soda affects the price of the dried petals (and poor-quality product is worthless), the drying process should be carried out with the lowest possible energy expenditure.
The presented study investigated the effect of drying process variables (air temperature (T d ) and air velocity and (v d )) on the following quality parameters of E. amoenum petals: the color difference and the bioactive compounds as loss of total antioxidant capacity, loss of total phenolic content, loss of total flavonoids content, anthocyanin loss and energy consumption for fluidized drying. The study focuses on multi-objective optimization (MOO) of the process variables. The goal in an MOO problem is to optimize the several objective functions simultaneously and thus finding the best parameters for E. amoenum petals drying process.

Material
Fresh E. amoenum petals were harvested in Afratape village, Golestan Province, Iran. The samples were collected every day and were kept in the refrigerator at 4 ± 0.5 • C before the beginning of the tests. The initial moisture content of the freshly harvested E. amoenum petals was about 8.67-10.29 d.b. and was reduced to the final moisture content about 0.058-0.041 d.b. at the end of the drying process for the safe storage.

Drying Process
To conduct experiments, a pilot-scale FBD was constructed in the Department of Agricultural Machinery Mechanics of Azadshahr University. FBD consists of three electric heaters, each of 800 W for heating air, a 1.5 kW fan for circulating air, a drying chamber with dimensions of 0.3 × 0.3 × 0.9 m and a switchboard to control and regulate drying temperature (with accuracy ±0.1 • C) and air velocity (with accuracy ±0.1 m/s). The relative humidity of the drying air was about 35%. The size of its gas distribution chamber is approximately 0.25 × 0.25 × 0.3 m, made with a stainless-steel plate of 1 mm thickness. A perforated distributor plate, with a thickness of 1 mm and holes of 3 mm in diameter, was firmly fixed to the bottom of the chamber.
At the beginning of each experiment, the air temperature and velocity were fixed when there was no sample in the FBD. To stabilize the drying conditions, the dryer was operated with no sample in the chamber for 30 min. The loading density of fresh E. amoenum petals was 1.4 kg/m 2 . More details of the device and the testing method can be found in previous research studies [40].

Color Measurement
Color preserving is crucial when processing food and herbs. Indeed, the first quality feature that a consumer notices when deciding to buy is product color. The machine vision was used to capture fresh and dried E. amoenum petals. The visual system consists of a black wooden box with dimensions of 50 × 50 × 50 cm, four fluorescent lamps of 18 W located on the wall of the box at 45 • for illumination, and a Sony Cyber-shot DSC-W370 digital camera with 14 Mpx of the resolution, which was placed vertically at a distance of 22.5 cm from the samples. Digital images were processed by MATLAB software in Lab color model to evaluate color changes. The color difference (CD) was calculated based on the following optimized formula by the CIE committee where ∆L, ∆C, ∆H are the differences in brightness, chroma, and hue angle of the dried sample from the reference (fresh) sample, respectively, K L , K C , K H are the parameter factors that describe the effect of the change from reference conditions (for reference conditions, they are all in 1), and S L , S C , S H are the weighting functions (S L = 1, S C = 1 + 0.045C, and S H = 1 = 0.015C).

Extract Preparation
Rufino et al. [41] procedure was used to prepare the extract. The dried sample was ground and passed through a sieve (40-mesh). A total of 2 g of sample powder was added to 4 mL of 50% ethanol (v/v). The mixture was mixed to homogenize it and was then was kept at room temperature. After 1 h, the supernatant was transferred to a volumetric flask. A total of 4 mL of 70% acetone was added to the rest of the extract and homogenized using a mixer and kept at room temperature for 1 h. the obtained supernatant was transferred to the same flask containing the first supernatant and the solution volume was brought to 100 mL by distilled water and mixed well. Extraction was performed in triplicate for each treatment.

Determination of Antioxidant Activity by DPPH Method
To assess the antioxidant potential by DPPH free radical scavenging, changes in (DPHH) absorbance are examined. 1, 1-diphenyl-2-picrylhydrazyl (DPPH) is a stable free radical that can accept an electron or hydrogen molecule and become a neutral and stable molecule. DPPH has a strong absorption at a wavelength of 517 nm due to its odd electron; at this stage, the methanolic solution of DPPH is a deep purple color. In the presence of antioxidants, the odd electron can become an electron pair. Regarding the number of electrons received, absorption is reduced. At this stage, the color of the solution turns yellow/colorless. Using this absorption change, the ability of different compounds for free radical scavenging can be measured. The amount of change in the absorption of each sample depends on the ability of the radical adsorbent.
To determine the antioxidant activity, 1 mL of DPPH methanol solution (1 mM), was mixed with 3 mL of sample extract. The mixtures were maintained in a dark place at room temperature; after 30 min, the absorbance was read at 517 nm. The experiment was repeated three times for each sample solution. Antioxidant activity was calculated as the inhibition percentage was calculated by where A sample is the absorbance of DPPH with the extracts and A control is the absorbance of DPPH without the extracts.

Measurement of Total Phenolic Content (TPC)
The total phenol content (TPC) was determined using Folin-Ciocalteu assay by a UV/Vis spectrophotometer. A total of 10 mg m/L of the extract was mixed with 1 mL of Folin-Ciocalteu's reagent, and after 3 min, 0.8 mL of Na 2 CO 3 (2%) was added, and then the volume was increased to 10 mL with water/methanol (4:6). After 30 min, the absorbance of the samples was measured at 740 nm. Tannic acid (0-800 mg/L) was used as the standard calibration curve, the TPC was reported to mg of tannic acid equivalent per gram of extract. The experiments were repeated in triplicate and their mean was reported.

Measurement Anthocyanin Content (A)
For determination of anthocyanins content (A), 0.1 g of the sample was soaked in 10 mL of acidified methanol (methanol/HCl = 99:1, v/v). The extract was maintained for 24 h in the dark at 25 • C. The extract was then centrifuged at 5000 rpm for 5 min. Absorption of the supernatant was measured at 550 nm. The Dowd method, modified by Arvouet-Grand et al. [42], was used to measure the total amount of flavonoids. Briefly, in this method, 5 mL of 2% AlCl 3 in methanol was mixed with the same volume of aqueous extract. After 10 min, the absorbance of the extract solution and the blank solution (containing 5 mL of the extract with 5 mL of ethanol without AlCl 3 was read at 415 nm. Then, the total flavonoid content was determined using the quercetin standard curve (0-100 mgL) and was expressed as mg of quercetin equivalent per gram of dry mass of petals.
Losses of phytochemical properties of E. amoenum petals were calculated as the percentage difference between the mentioned contents for dried (d) and fresh (f ) materials according to the following formulas

Energy Consumption
The total energy consumption (EC) required for drying per kilogram of dried petals consists mainly of the thermal energy (E th ) needed to remove water from the crops, and the mechanical energy (E mec ) needed for the conveyance or airflow, which was calculated by [43] E th = A csa v a ρ a C a ∆Tt (7) where A csa is the cross-section area (m 2 ), v a is the dryer air velocity (m/s), ρ a is the air density (kg/m 3 ), C a is the air specific heat capacity (kJ/(kg·K)), ∆T is the temperature difference ( • C), t is the drying time (s). The mechanical energy used for conveyance or airflow by a fan was calculated by [44] E mec = ∆Pv a A csa t (8) where ∆P is the pressure drop of the crop (Pa).

Objective Functions
Objective functions used by MOOGA algorithm represent relationships between T d , v d (process variables; drying air temperature: 40, 50, and 60 • C, air flow velocity: 0.5, 0.75, and 1.0 m/s) and energy consumption (EC) for the drying process and quality characteristics of the dried material obtained (CD, A loss , TAC loss , TFC loss , TPC loss ). Details about the used data are presented in Table 1.
The relations were approximated using ANN which topology is shown in Figure 1 (three-layer NN). The ANN task was to map input variables: T d and v d on to six outputs (CD, A loss , TAC loss , TFC loss , TPC loss ) to obtain high correlation coefficient (R) and the lowest Mean Squared Error (MSE). The inputs and outputs of ANN were normalized (divide by maximum values, respectively) to obtain the range 0-1.
The actual values of the input variables were chosen randomly from a fixed set of data in each case. For this set of data, three levels of drying air temperature and three levels of air flow velocity were used (see Table 2). Seventy-three repetitions were performed for each level (3·T d ·3·v d ). A total of 657 different results was obtained.   Chosen cases (657 cases from the experiments) were randomly divided into the following sets: 98 samples (15%), 461 samples (70%) for testing, and 98 samples (15%) for validation sets. The network used the default Lavenberg-Marquardt (L-M) algorithm for the training procedure. L-M locates the local minimum of a multivariate function, expressed as the sums of squares of several of non-linear, real-valued functions as demonstrated in paper [45]. In this study, the maximum number of epochs to train, the initial momentum and mu increase factor term were: 100, 0.4 and 10, respectively. The minimum value of MSE was always reached well within that number. The training process was repeated several times in order to obtain the best performance of ANN. All trials were implemented in MATLAB Neural Networks Toolbox R2018a. Moreover, the optimal experiment that minimizes the number of ANN models trained and validated and maximized the model accuracy has been done. The architecture of ANN parameters such as the number of neurons in the hidden layer, activate function in hidden and output layers and statistical values MSE and R were estimated in Table 3. It can be seen from Table 3, the lowest MSE = 0.000292 and high R-value = 0.9922 for Item 3 was obtained.

Multi-Objective Optimization Problem
The MOO task consisted in the determination of the set of optimal conditions of the drying process. All the functions were minimalized (EC, CD, A loss , TAC loss , TFC loss , TPC loss ) subject to constraints on the process variables (drying parameters: T d , v d ). Equation (9) presents the mentioned MOO problem.
The Pareto front for this multiobjective optimization problem was generated using a nondominated sorting genetic algorithm (NSGA II). The algorithm was implemented in MATLAB Global Optimization Toolbox R2018a. Subsequent steps of this algorithm are presented, i.e., in [46]. The genetic algorithm parameters are shown in Table 4.

Data
The statistics of the used data are presented in Table 1.

Objective Functions
To approximate functional relations between air drying temperature, drying air velocity (T d and v d ) and energy consumption drying and quality parameters (CD, A loss , TAC loss , TFC loss , TPC loss ) of dried E. amoenum petals, different ANN structures (with various transfer functions) were tested. Considering the lowest MSE, the best result (MSE = 0.00029) was obtained for the ANN structure which consisted of eight nodes in the hidden layer (see Figure 1, Table 2).
The hidden and output layers of the best ANN structure processed data with a log-sigmoid transfer function both in output and hidden layers, respectively, as demonstrated in Figure 1 (see Table 3, Item 3). The ANN training phase was stopped at the 21st iteration as shown in Figure 2. It can be seen that test set error and validation error have similar characteristics. The following final MSE values were obtained: 0.00075, 0.00029, 0.0021 for training, validation and test sets, respectively. Therefore, the final mean-square error is small. Linear regression between the network outputs and the corresponding targets is shown in Figure 3. The following R: 0.9933, 0.9974, and 0.9818 for training, validation and test sets, respectively, indicated that data from the ANN were in agreement with the experimental data. Finally, the R-value is over 0.99 for the total response (see Figure 3).  The ANN training phase was stopped at the 21st iteration ( Figure 2). The following final MSE values were obtained: 0.00075, 0.00029, 0.0021 for training, validation and test sets, respectively. The R of 0.9933, 0.9974, and 0.9818 for training, validation and test sets, respectively, indicated that data from the ANN were in agreement with the experimental data ( Figure 3). The hidden and output layers of the best ANN structure processed data with a log-sigmoid transfer function ( Figure 1).
The energy consumption for drying process was determined with the following formula (from ANN, taking into account multiplication by EC max ) whereas quality parameters of dried petals from formulas (from ANN, taking into account multiplication by the appropriate quality parameters maximum values) Appl. Sci. 2020, 10, 8387 9 of 22 where F (i=1÷8) from and D ji are shown in Table 5. Equations (10)-(15) (respected normalization) were used for algorithm (Equation (9)).
The validation of the model (ANN) using the validation set and, additionally, all data, to demonstrate the reliability of predicted values was conducted. The R for validation and all data was 0.9974 and 0.9922 (Figure 3), whereas mean square errors (MSE) were 0.00026 and 0.00029, respectively. This confirms the accuracy and consistency of the proposed model.

Multi-Objective Optimization
The MOO problem formulated in Equation (9) was solved with the genetic algorithm using the initial population size of 40. Table 3 shows the controlled parameters of NSGA II. The optimization problem converged to the Pareto optimum set after 146 genetic algorithm generations. In the study, the probability of mutation and crossover and were 0.15 and 0.85, respectively. One hundred and eighty design points formed Pareto set given in Table A1. Figure A1 presents the impact of T d and v a on EC, CD, and quality parameters (A loss , TAC loss , TFC loss , TPC loss ) of the Echium amoenum petals (data from Table A1). Figure 4 shows the Pareto fronts for EC and CD, A loss , TAC loss , TFC loss , TPC loss , respectively.
The smallest values of EC were obtained for ID134, ID132, and ID131 (278.3, 288.8, and 295.5 MJ/kg, respectively). It corresponds to the following drying parameters: T d = 60.00 • C and v d = 0.50 m/s, T d = 59.84 • C and v d = 0.50 m/s, T d = 59.77 • C and v d = 0.50 m/s, respectively. However, due to the very small differences between the individual values of drying parameters obtained and the lack of such precise settings, it can be assumed that the best parameters due to energy savings are the following: T d = 60 • C and v d = 0.5 m/s. Assuming that the temperature and velocity of the drying air can be set (in the dryer) with an accuracy of 0.5 • C and 0.02 m/s, drying at T d = 60.0 ± 0.5 • C and v d = 0.5 ± 0.02 m/s allows for obtaining Echium amoenum petals with the following parameters: TAC loss , TFC loss , A loss , TPC loss , CD, EC: 45.5%, 28.0%, 47.3%, 29.8%, 36.7, and 328.8 MJ/kg, respectively (average values for mentioned ranges of T d and v d ).
Pareto front (Figure 4b) indicates the following solutions: ID70, ID75 and ID84, for which EC is 835.6, 804.8, and 766.4 MJ/kg, respectively, and CD are 30.7, 31.6, and 31.8, respectively. These solutions are obtained for the following drying process parameters: air drying temperature 44.47, 45.42, and 45.41 • C, and air-drying velocity 0.50, 0.51, and 0.50 m/s. However, due to the very small differences between each value of T d and v d obtained and the inability to set these parameters so precisely (adjustment by 0.02 • C and 0.01 m/s), it can be assumed that the best parameters due to the simultaneous energy-saving and color preservation are the following: T d = 45.5 • C and v d = 0.5 m/s. However, for these solutions, EC, CD, A loss , TAC loss , TFC loss , TPC loss are respectively about 2.9, 1.7, 1.7, 2.2, 8.6, and 2.5 times higher than their minimum values. CD was always conflicting with other quality parameters (see Figure 4b).
Assuming that the temperature and velocity of the drying air can be set (in the dryer) with an accuracy of 0.5 • C and 0.02 m/s, drying at T d = 45.5 ± 0.5 • C and v d = 0.5 ± 0.02 m/s allows for obtaining Echium amoenum petals with the following parameters: TAC loss , TFC loss , A loss , TPC loss , CD, EC: 36  It can be stated that there is no unequivocal solution to the optimization problem written by Equation (9). The solutions relate to the Echium amoenum petals drying parameters at which the lowest values of individual quality parameters, EC or CD, sometimes groups of the parameters were obtained. However, CD was always conflicting with other quality parameters (see Figure 4b), so this parameter was omitted in further considerations.
The optimization results show ( Figures 5 and 6) that A, TAC, TFC are interrelated. Figure 6 shows the four solutions for the optimization task. The ID92 is characterized by EC = 434.8 MJ/kg (1.6 times higher than EC min ), whereas A loss = 39.0 (the lowest of all obtained optimization solutions), TAC loss = 36.8% (2.4 times higher than TACloss min), TFC loss = 9.4% (1.4 times higher than TFC loss min ), and TPC loss is 37.0% (1.4 times higher than TPC loss min ) (CD = 38.3-2.2 times higher than CD min ). The parameters of the drying process for ID92 are the following: T d = 53.94 • C and v d = 1.00 m/s. The ID109 solution differs only in value of T d (T d is 0.57 • C higher than for ID92 and amounts to 54.51 • C (v d = 1.00 m/s). For this solution, EC is a little lower (420 MJ/kg), but TAC loss is higher (40.1%).
The next ID107 solution (EC = 410.1 MJ/kg) is characterized by the lowest of the four solutions TPC loss = 26.0% (1.2 times higher than TPC loss min ). For this solution, TAC loss is higher than for the previously mentioned ID92 and lower than ID109 (TAC loss = 39.2%-2.5 times higher than TAC loss min), but TFC loss and A loss are already much bigger: TFC loss = 29.6% (4.3 times higher than TFC loss min), and A loss = 48.7% (1.3 times higher than A loss min) , CD is high and amount 37%. The parameters of the drying process for ID107 are the following: T d = 59.82 • C and v d = 0.53 m/s. A similar solution is ID111 for which EC, TFC loss , A loss are lower and amount to 381.3 MJ/kg, 29.1%, 48.12%, while TAC loss and TPC loss are larger (41.2% and 27.0%, respectively); CD is high: 36.9%. The parameters of the drying process for ID111 are very similar to ID107 and amount: T d = 59.85 • C and v d = 0.52 m/s. For this solution, EC is little lower (381.3 MJ/kg), but TAC loss and TPC loss are higher (41.2 and 27.0%, respectively). Figure 6 shows Pareto fronts for EC and, simultaneously, A loss , TAC loss , TFC loss , and TPC loss . Considering the maximum values of TAC loss max = 80.5%, TFC loss max = 70.9%, A loss max = 76.9%, and TPC loss max = 60.6%, it can be assumed that for the four indicated solutions, the losses do not differ significantly and are much smaller than the mentioned maximum losses.
However, where the quality of the dried product directly affects the price (poor-quality product is worthless), the drying process should be carried out with the acceptable (not always the lowest) energy expenditure. For the strategy in which, apart from EC minimization, the lower losses of TAC, TFC and A are most important, while accepting quite high TPC loss and high CD, the drying parameters of E. amoenum petals are the following: T d = 54.0 • C and v d = 1.0 m/s. Assuming the mentioned accuracy of T d and v d setting, drying at T d = 54.0 ± 0.5 • C and v d = 1.0 ± 0.02 m/s can obtain Echium amoenum petals with the following parameters: TAC loss , TFC loss , A loss , TPC loss , CD, EC: 36.8%, 9.4%, 39.0%, 38.3%, 37.1, and 434.9 MJ/kg, respectively (average values for mentioned ranges of T d and v d ). However, when apart from EC minimization, low losses of TPC and TFC are important; with losses of TAC and CD similar to those mentioned previously, the drying parameters of E. amoenum petals are the following: T d = 59.8 • C and v d = 0.53 m/s. Assuming the mentioned accuracy of T d and v d setting, drying at T d = 60.0 ± 0.5 • C and v d = 0.52 ± 0.02 m/s can obtain Echium amoenum petals with the following parameters: TAC loss , TFC loss , A loss , TPC loss , CD, EC: 44.0%, 28.3%, 47.7%, 29.0%, 36.8, and 349.1 MJ/kg, respectively (average values for mentioned ranges of T d and v d ).
Jafarian et al. [47] optimized a counter-flow indirect dew-point evaporative cooler precise model. In an MOO task, the NSGA II is often used. NSGA II has commonly been used to understand a wide range of problems such as a heating, cooling, and power system integrated with biomass gasification [48,49], waste heat recovery systems [50] and organic Rankine cycle [51]. Moreover, the NSGA II algorithm was widely used in the food industry for the determination of Biot mass number [52] and the mass diffusion coefficient [53] in the drying process. Winiczenko et al. [54,55] successfully applied the algorithm to the rehydration process.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 13 of 23 It can be stated that there is no unequivocal solution to the optimization problem written by Equation (9). The solutions relate to the Echium amoenum petals drying parameters at which the lowest values of individual quality parameters, EC or CD, sometimes groups of the parameters were obtained. However, CD was always conflicting with other quality parameters (see Figure 4b), so this parameter was omitted in further considerations.
The optimization results show ( Figures 5 and 6) that A, TAC, TFC are interrelated.      The next ID107 solution (EC = 410.1 MJ/kg) is characterized by the lowest of the four solutions TPCloss = 26.0% (1.2 times higher than TPCloss min). For this solution, TACloss is higher than for the previously mentioned ID92 and lower than ID109 (TACloss = 39.2%-2.5 times higher than TACloss min), but TFCloss and Aloss are already much bigger: TFCloss = 29.6% (4.3 times higher than TFCloss min), and Aloss = 48.7% (1.3 times higher than Aloss min), CD is high and amount 37%. The parameters of the drying process for ID107 are the following: Td = 59.82 °C and vd = 0.53 m/s. A similar solution is ID111 for which EC, TFCloss, Aloss are lower and amount to 381.3 MJ/kg, 29.1%, 48.12%, while TACloss and TPCloss are larger (41.2% and 27.0%, respectively); CD is high: 36.9%. The parameters of the drying process for ID111 are very similar to ID107 and amount: Td = 59.85 °C and vd = 0.52 m/s. For this solution, EC is little lower (381.3 MJ/kg), but TACloss and TPCloss are higher (41.2 and 27.0 %, respectively). Figure 6 shows Pareto fronts for EC and, simultaneously, Aloss, TACloss, TFCloss, and TPCloss. Considering the maximum values of TACloss max = 80.5%, TFCloss max = 70.9%, Aloss max = 76.9%, and TPCloss max = 60.6%, it can be assumed that for the four indicated solutions, the losses do not differ significantly and are much smaller than the mentioned maximum losses.
However, where the quality of the dried product directly affects the price (poor-quality product is worthless), the drying process should be carried out with the acceptable (not always the lowest) energy expenditure. For the strategy in which, apart from EC minimization, the lower losses of TAC, TFC and A are most important, while accepting quite high TPCloss and high CD, the drying

Conclusions
The effect of T d (40-60 • C) and v d (0.5-1 m/s) in fluidized drying on the energy consumption and the quality parameters (TAC loss , TPC loss , TFC loss and A loss ) of E. amoenum petals was studied. A novel multi-objective optimization (MOO) algorithm, based on Pareto optimization, genetic algorithm (GA) and artificial neural network (ANN), was developed. The following optimization objectives of A loss , CD, EC, TAC loss , TFC loss and TPC loss were used for its simultaneous minimization. The objective functions were developed by using ANN. The Pareto optimal set was developed with the non-dominated sorting genetic algorithm II.
It can be stated that there is no unequivocal solution to the optimization problem. The quality of dried E. amoenum petals directly affects the price of the dried flakes (and poor-quality product is worthless). Therefore, the drying process does not have to be carried out with the lowest energy consumed, but only with the low possible energy expenditure.
Cannot be obtained E. amoenum petals characterized a low color change at low energy expenditure for fluidized drying.
The smallest value of energy consumption (EC = 278.3 MJ/kg) was obtained for the following drying parameters: A unique Pareto optimal solution was found at T d = 54 • C and v d = 1.0 m/s-for the strategy in which the lower losses of TAC, TFC and A are most important at the accepted EC value, resulting in 36.8%, 9.4%, 39.0%, 434.9 MJ/kg, 37.1%, 38.3 for TACloss, TFCloss, Aloss, EC, TPCloss, and CD, respectively.
The next unique Pareto optimal solution was found at T d = 59.8 • C and v d = 0.52 m/s-for the strategy in which, the lower losses of TPC and TFC are important at accepted EC values, resulting in 44.0%, 28.3%, 47.7%, 349.1 MJ/kg, 29.0%, 36.8 for TAC loss , TFC loss , A loss , EC, TPC loss , and CD respectively.
The results of this research are essential for the improvement in the industrial dehydration of E. amoenum petals to maintain their high content of bioactive compounds with low energy consumption and low colour change.
Funding: This research received no external funding.

Conflicts of Interest:
The authors declare no conflict of interest.