## 1 Introduction  
In the agro-food industry, olive oil production is one of the industrial practices in Mediterranean countries that contribute to the economy at higher levels [1]. During the extraction process, olive mill wastewater (OMW) is generated in higher amounts (in the successive steps of leaf removal, olive washing, grinding, beating and separation of oil) and considered as an environmental hazardous stream due to the high pollutant load, high concentrations of recalcitrant compounds, long-chain fatty acids, phenolic compounds, solids and biotoxicity [2]. Consequently, OMW treatment is not an easy task, and nowadays, most of the waste streams are, on the one hand, considered to be byproducts with a potential for revalorization in the framework of a circular economy approach, whilst, on the other hand, the revalorization of OMW by adopting low-cost treatments appears to be nearly impossible due to its characteristics [3]. Removal of solids from OMW is the first mandatory step, suggested to be performed initially, and possible by using coagulant materials or by centrifugation methods. Coagulation is defined as a chemical process used in wastewater treatment to remove suspended solids and to improve the removal of the chemical oxygen demand (COD). By employingthis process, the tendency of small particles in an aqueous suspension to combine with one another can be significantly improved. The interaction among the particles results in the formation of larger aggregates that can be removed from the water by sedimentation and/or filtration as the process of coagulant cumulation to wastewater, in order to destabilize the colloidal particles promoting agglomeration, forming larger particles, which can be easily removed by sedimentation [4; 5]. Several synthetic (inorganic and synthetic organic) and natural organic coagulants (NOC) are commonly used in conventional water treatment processes; however, synthetic inorganic coagulants such as FeCl\({}_{3}\), polyaluminum chloride (PAC) and aluminum sulfate, Al\({}_{2}\)(SO\({}_{4}\))\({}_{3}\cdot\)14H\({}_{2}\)O (alum), are the most accepted and practiced in large-scale wastewater treatment plants [6]. Alum is efficient in turbidity removal [7] which will enhance the photocatalysis process. [PERSON] et al. [8] treated OMW with the coagulation and flocculation method prior to anaerobic degradation using alum and achieved 47% removal of COD, 27% total phenols, and 39% total organic carbon (TOC). [PERSON] et al. [9] worked on OMW with several coagulants, and they observed that alum efficiency was less when compared to acid crackling; however, the raw OMW in their work contained high COD, at 69.4 g/L, and they achieved 20% of COD with 400 mg/L of the alum dosage and a pH of 8. [PERSON] et al. [5] achieved 57.1% of COD removal with an 800 mg/L dosage of alum at pH 4.5. This shows that OMW requires extensive optimization since the characteristic changes depending on the month, olive fruit type, extraction method and region. Considering these facts, further optimization of coagulation and flocculation of OMW is needed since the required dosage of coagulant, optimal pH and other suitable conditions should be optimized [5]. In fact, this process consumes a lot of time and resources, leading to unsustainable operating cost issues in factories. This prevents the successful use of the coagulation and flocculation process since uncertainty prevails. Statistical techniques should be employed to study the optimization problem in a feasible way, but stochastic processes require very large sample data to be supported [10; 11]. Considering, together, the need and difficulty in selecting a suitable coagulant dosage for OMW treatment, one of the most popular statistical techniques, that is, grey relational analysis, was selected in this work, targeting the optimization of controlled parameters such as TOC, COD, phenols, and turbidity.