1. Introduction
The discharge of massive quantities of industrial-colored effluents into water bodies has become a major concern [
1]. Globally, the annual release of dyestuff into the environment is reported to be 0.28 million tons, from different sources including the textile, leather goods, cosmetic and food industries [
2]. These synthetic dyes are toxic for humans, fauna and flora even at low levels [
3]. They can be carcinogenic and cause dermatitis and allergic sensitization [
4]. Therefore, it is very important to utilize an effective treatment process for these types of wastewaters before discharging into the environment. Due to the resistance of textile wastewaters to biodegradation and their toxic effects on microorganisms, the use of alternative treatment methods to achieve the aim of mineralizing or transforming refractory molecules into others which could be further biodegraded is of great importance. The application of combined physical and chemical processes, such as coagulation, flocculation, filtration and adsorption, has been developed [
5]. Researchers continue to explore more efficient techniques to address the drawbacks of the previous methods, such as low efficiency, high volumes of sludge and high operating/capital costs [
6]. The ozonation process, mostly used with catalysts (i.e., the catalytic ozonation process, COP), is an efficient treatment when mineralization is desired [
7]. Gutowska et al. [
8] concluded that ozonation is more effective compared to the Fenton process for the degradation of reactive orange 113 dye. COP is classified in the category of advanced oxidation processes (AOPs), which are widely used in water treatment processes [
9].
Ozone is a powerful oxidant and an effective purifier in water and wastewater treatment. Especially, ozonation treatment is widely applied to mineralize organic pollutants in water. However, when ozone is used alone, mineralization is not completely effective and some toxic and resistant byproducts (such as ketone, aldehyde, carboxylic acid and bromate) are generated [
10]. To reduce these problems, the catalytic ozonation process (COP) is used to treat wastewaters containing high concentrations of refractory complexes based on the formation of very reactive groups, particularly hydroxyl radicals. This process is used to degrade a variety of organic compounds [
11].
Recently, the combination of ozone with heterogeneous catalyst has attracted a lot of attention from researchers of water and wastewater treatment [
12]. During COP, highly reactive free radicals, especially hydroxyl (
), are produced; they have outstanding ability in the rapid degradation of recalcitrant and toxic organic compounds [
13]. The hydroxyl radical is the second strongest oxidant, with an oxidation potential of 2.8 V (whereas fluorine has the highest electrochemical oxidation potential of 3.03 V). It rapidly and non-selectively attacks the carbon–hydrogen bonds of organic components and converts them to simple and mineral compounds [
14]. Many synthesized catalysts—including metal oxides [
9,
15], metal oxides attached on support [
13,
16] and iron-based [
11,
12]—have been studied in COPs. Among them, magnetic Fe
3O
4 has received increasing attention in water treatment due to its magnetic properties, low cost, recyclability and non-toxicity [
17]. In addition, Fe
3O
4 contains both Fe
2+ and Fe
3+ in the octahedral sites and accelerates the reaction of electron transfer during ozonation, which can facilitate the production of free radicals and improve the oxidation efficiency. Therefore, magnetic Fe
3O
4 catalysts have been successfully applied in COPs and are shown to exhibit high catalytic activity for the reduction of organic pollutants [
16,
18].
Determining the effects of various operational parameters in AOPs is very difficult because of the complexity of reactions. This problem leads to uncertainty during the design of industrial chemical reactors. Obviously, this problem cannot be solved by simple linear multivariate regression. Hence, artificial neural networks (ANNs) can be considered as a promising alternative modeling approach. Multilayer perceptron (MLP) is a class of ANNs that is widely used in data-based modeling and machine learning concerning chemical processes [
19,
20]. One of the characteristics of modeling based on MLP is that it does not require the mathematical description of the phenomena involved in the process. Hence, MLP can be useful in the simulation of complex AOPs. So far, MLP has been widely used in the modeling of AOPs. Cüce et al. [
21] used MLP in the modeling of Fenton and photo–Fenton processes. Photocatalytic degradation of dispersed dye by ZnO nano catalyst was modeled using MLP, by Kıranşan et al. [
22]. ANN modeling of different combinations of AOPs includes sonocatalytic degradation [
23], the solar photocatalytic process [
24] and photo-electrocatalysis of organic pollutants [
25]. COP is also included in this list due to the complexity of its reaction mechanism [
26]. Asgari et al. [
27] applied ANNs to the modeling of the catalytic ozonation of textile wastewater using carbon doped/MgO nano catalyst. Fluoxetine was degraded during COP, and this process of modeling and optimization was performed [
28].
Process optimization is one of the main goals of modeling. In this regard, the development of data-based models such as MLP is a step towards achieving this goal. Presently, the use of multi-objective optimization (MOO) has found a special place in many continuous, semi-batch and batch processes of chemical engineering [
29]. Unlike single-objective optimization, the solutions obtained from MOO are a set of non-dominated (Pareto-optimal) solutions; one of them can be selected as the optimal alternative using weighting methods and multi-criteria decision making (MCDM) [
30].
In this paper, an ANN model was first developed using the experimental data of an AR88 degradation in an ozonation reactor with Fe3O4 nano catalyst in semi-batch mode. Then, MOO was carried out by considering the objective functions to maximize the degradation efficiency of AR88 and to minimize the catalyst dosage simultaneously, to obtain Pareto-optimal solutions. Finally, an optimal alternative was selected by using two weighting methods—i.e., criteria importance through intercriteria correlation (CRITIC) and entropy, followed by the technique for order of preference by similarity to ideal solution (TOPSIS) and multi-attributive border approximation area comparison (MABAC) methods. To the best of our knowledge, MOO/MCDM of the COP of AR88 has not been reported in the literature so far.
The rest of this paper is organized as follows: In
Section 2, the synthesis of the nano catalyst is summarized. Then, the setup of COP and the conditions of experiments, along with the lower and upper limits of operating variables, are given. In
Section 3, the theory of MLP, the building of the MLP model, the optimization method and the theory of MCDM are described. The simulation results and the trends of variables are given in
Section 4 and
Section 5, respectively. The optimization results and the selection of an optimum solution using MCDM are covered in
Section 6. Finally, the main findings of this study are summarized in
Section 7.
6. MOO/MCDM of Catalytic Ozonation Process
The simultaneous maximization of %DE and minimization of the catalyst concentration were considered for the COP of AR88.
Figure 11 shows the Pareto-optimal solutions obtained by the MOPSO algorithm. Clearly, the %DE of AR88 increases with the increase in Fe
3O
4 concentration; thus, there is a trade-off between the two selected objective functions. Further, the Pareto-optimal front has a wide range and good distribution.
For selecting one of the Pareto-optimal solutions, the CRITIC and entropy methods were applied to these non-dominated solutions and the objective weights were calculated. The values of weights are given in
Table 5. The CRITIC method gives nearly equal weights for both objective functions. However, the entropy weights have more difference and catalyst concentration has a high weight. With the CRITIC weights, the TOPSIS and MABAC methods were applied, and the optimal solutions recommended by these MCDM methods are shown by the (
Δ) and (
◊) symbols in
Figure 11, respectively.
The optimal solutions recommended by TOPSIS and MABAC are different when using CRITIC weights (
Table 6). A low degradation efficiency and Fe
3O
4 concentration is preferred by the TOPSIS method, whereas MABAC selected the moderate %DE (95.05%) and catalyst concertation (0.152 g/L). The recommended solution when using entropy weights was the same for both TOPSIS and MABAC (
Table 6). Note that TOPSIS and MABAC, both using entropy weights, may or may not give the same recommended solution depending on the application [
30].