Experimental study on classical and metaheuristics algorithms for optimal nano-chitosan concentration selection in surface coating and food packaging

Highlights

• Algorithm solved the problem of hydrophobic functional food packaging fabrication.

• Neither additional chemicals nor extra initial test were used in the present work.

• POA, WOA and GOA were applied and compared to find the optimal chitosan NPs.

• It can be applied for the previous optimization studies as well as the future ones.

• POA optimizes experimental replicate models, represented apple nano coating.

Abstract

In this study the Lagrange interpolation optimization algorithm based on two variables with respect to all experimental replicates (POA), was compared with two other heuristics methods (WOA and GOA). Modification of the apple surface by an edible nano coating solution in food packaging was used as case study. The experiment was performed as a factorial test based on completely randomized design by 100 permutations data sets. Results showed a significant difference between the three optimization methods (POA, WOA and GOA) which indicates the necessity of optimization and also efficiency of the present POA. The optimum result by POA, similar to a rose petal property, could rise 72% in surface contact angle (CA). The scanning electron microscopy (SEM) images of the derived surfaces showed almost a uniform spherical nanoparticles morphology. Remarkable advantages of this new approach are no additional material requirement, healthful, easy, inexpensive, fast and affordable technique for surface improvement.

Introduction

Recently, manipulation of the polymeric strands has been extremely investigated to improve the applicability and enhance their performances in many applications such as food packaging and processing or storing (Juang et al., 2016, Li et al., 2018, Louzi and Campos, 2019, Stroea et al., 2019, Tikhonov et al., 2019). Although synthetic polymers have poor inhibition capability against oxygen, carbon dioxide, organic matter vapors and flavors, but they are highly susceptible to the absorption of food flavor as well as to migration to the food (Hong et al., 2005). In addition, their biodegradation process is occurred very slowly in comparison with the biopolymers (Abdul Khalil et al., 2017, Cardoso et al., 2014). Despite these disadvantages, they are widely used as the most common materials for food packaging purposes (Belmonte et al., 2016, Kaplan et al., 2019).

Moreover, there are several advantages for using biopolymers (Cazόn et al., 2017) including low-cost materials, high biodegradability and biocompatibility, non-toxicity, antioxidant, antibacterial, anti-functional and anticancer properties (Mujtaba et al., 2019). They are also employed as the multi-responsive agents for targeted drug-delivery due to their high efficiency in controlled drug release (Corazzari et al., 2015, Elsabee and Abdou, 2013). As a disadvantage, it is not possible to use them individually for food packaging due to their weak sewing, mechanical resistance (Hong et al., 2005), and also less relative deterioration against water vapor (Lee et al., 2008). Thus, to improve the applicability of the synthetic polymers and biopolymers for food packaging aims, they are conventionally covered with an edible layer, which include higher resistance to the corruptive agents and moisture resistance (Hong et al., 2005). In this way, the first and foremost obstacle is high hydrophobicity of the non-polar polymers (Belmonte et al., 2016, Hong et al., 2005, Rezaei et al., 2019) that makes it too difficult to cover them with the polar polymeric textures such as starch and chitosan (CS) (that are highly hydrophilic) (Bezerra de Aquino et al., 2015, Fajardo et al., 2010). To overcome this issue, two strategies have been suggested: 1) Decreasing the hydrophobicity of the synthetic polymers via reported strategies like pretreatment (Alves et al., 2014, Dai and Xu, 2019, Honarvar et al., 2017, Romani et al., 2019, Wang et al., 2019, Zhu, 2019). This strategy may lead to some disadvantages such as making the polymer less potent against microbial attack (Cardoso et al., 2014). Furthermore, these methods are relatively expensive and need some intricate tools. 2) Increasing the hydrophobicity of the mentioned edible biopolymers, which are considered for super-hydrophobic surface coating, and also can reduce the waste of foods despite its poor thermal stabilities (Zhang et al., 2019). For instance, the hydrophilicity of the cellulose nanofiber with chitosan (CNF-CS) has been reduced via incorporation of the various polymeric matrices into the CS films to enhance the preservation capability of this agent, as an active antimicrobial agent for food packaging. In fact, this agent has better biocompatibility in composite form with CNF for replacing petroleum-based synthetic packaging (Deng et al., 2017). It is also shown in another study, an edible super-hydrophobic coating with more than 150° CA, which is the main evaluating hydrophobicity index of solid surfaces (Zhao and Jiang, 2018), has been fabricated using beeswax and coffee (Zhang et al., 2019).

Optimization algorithms may be classified into two main categories. Exact Algorithms which are not working well in high dimensional problems, also their performance may be too long; and Approximate Algorithms which may achieve good results near to the optimum solution in the accepted and reasonable time (Fig. 1); which can be categorized to heuristics and metaheuristics, where their significant difference is that heuristics are more problem-dependent than metaheuristics (Abdel-Basset et al., 2018). Meta-heuristic optimization algorithms become more and more popular in many applications due to their many beneficial attributes (Mirjalili & Lewis, 2016). Because the metaheuristic can't solve all optimization problems and they only have good performance in the specific given problem (Abdel-Basset et al., 2018), so the enormous number of metaheuristics has been developed for various types of problems such as continuous, discrete, unconstrained, multi-objective, etc.

Exploration and exploitation are the main functions of metaheuristics (Abdel-Basset et al., 2018). Due to this, metaheuristics can be classified into two main grouped: the first one: algorithms which simulate natural phenomena, human behavior in modern real life or even mathematics, and the second one: algorithms which didn’t use any simulation for determining their search strategy (Abdel-Basset et al., 2018).

Algorithms in the first category also can be divided into:

BIOLOGY BASED METAHEURISTICS {Genetic Algorithm (GA) (Holland. 1992); and genetic programming (Koza, 1990)}; swarm intelligence (SI){Particle Swarm Optimization (PSO) (Eberhart & Kennedy, 1995); artificial Fish Schooling algorithm (AFSA) (Li, 2003); Artificial Bee Colony (ABC) (Karaboga and Basturk, 2007), Chicken Swarm Optimization (CSO) (Meng et al., 2014), Harris hawks optimization (HHO) (Heidari ET AL., 2019), Artificial Fish Swarm Algorithm (AFSA) (Li, 2003), Dragonfly algorithm (DA) (Mirjalili, 2016a, Mirjalili, 2016b), Firefly algorithm (FA) (Yang, 2010, Yang, 2010, Tolouei et al., 2020), Social Spider Optimization (SSO-C) Algorithm (Cuevas & Cienfuegos, 2014), intelligent water drops (IWD) algorithm (Mathiyalagan et al., 2013), Pathfinder Algorithm (PFA) (Yapici and Cetinkaya, 2019), Firework Algorithm (FA) (Tan and Zhu, 2010), Seeker Optimization Algorithm (SOA) (Dai et al., 2007), Group Counseling Optimizer (GCO) (Eita and Fahmy, 2014), Mine Blast Algorithm (MBA) (Sadollah et al., 2013), Soccer League Competition (SLC) algorithm (Moosavian and Roodsari, 2014)} which have some advantages over evolution-based algorithms and are easier to implement (Mirjalili & Lewis, 2016); }}

BIO-STIMULATED ALGORITHMS {Gray Wolf Optimizer (GWO) (Mirjalili et al., 2014), Spotted Hyena Optimizer (SHO) (Dhiman and Kumar, 2017), Dendritic Cell Algorithm (DCA) (Greensmith et al., 2008), Artificial Immune System (AIS) (De Castro and Timmis, 2002), krill herd (KH) algorithm (Gandomi and Alavi, 2012), Barnacles Mating Optimizer (BMO) (Askarzadeh & Rezazadeh, 2012), Group Search Optimizer (GSO) (He et al., 2009)}

NATURE-INSPIRED {Cuckoo Optimization Algorithm (COA) (Rajabioun, 2011), The Whale Optimization Algorithm (WOA) (Mirjalili and Lewis, 2016), Grasshopper Optimization Algorithm (GOA) (Saremi et al., 2017), Emperor Penguin Optimizer (EPO) (Dhiman and Kumar, 2018), Flower Pollination Algorithm (FPA) (Yang, 2012), satin bower bird optimization algorithm (SBO) (Moosavi and Bardsiri, 2017), Crow search algorithm (CSA) (Askarzadeh, 2016), Ant Lion Optimizer (ALO) (Mirjalili, 2015a, Mirjalili, 2015b), Moth-Flame Optimization (MFO) algorithm (Mirjalili, 2015a, Mirjalili, 2015b), Tree Growth Algorithm (TGA) (Cheraghalipour et al., 2018), Symbiotic Organisms Search (SOS) (Cheng and Prayogo, 2014), Dolphin echolocation (Kaveh and Farhoudi, 2013), runner-root algorithm (RRA) (Merrikh-Bayat, 2015), Farmland fertility algorithm (Shayanfar and Gharehchopogh, 2018), Marine Predators Algorithm (MPA) (Faramarzi et al., 2020), Multi-Verse Optimizer (MVO) (Mirjalili et al, (2016)), Water Waves Optimization (WWO) (Zheng, 2015); Clonal Selection Algorithm (CLONALG) (Von De Castro & Zuben, 2000), Ant Colony Optimization (ACO) (Dorigo, 1992), Invasive Weed Optimization (IWO) (Mehrabian and Lucas, 2006), Bat Algorithm (BA) (Yang, 2010, Yang, 2010))}

CHEMISTRY BASED METAHEURISTICS {Chemical Reaction Optimization (CRO) (Lam and Li, 2010); Gases Brownian Motion Optimization (GBMO) (Abdechiri et al., 2013) which its complexity is O(n) and results showed that GBMO is efficient in solving SAT problems, especially for large instances, also has a good performance for solving continues SAT problems and performed as GA (Yingbiao, 2005) discrete SAT (Lardeux et al., 2006) versions.}

MUSIC BASED METAHEURISTICS {Harmony Search (HS) (Geem et al., 2001); Method of Musical Composition (MMC) (Gutiérrez et al., 2012)).}

MATH BASED METAHEURISTICS {(Base Optimization Algorithm (BOA) (Salem, 2012); Sine Cosine Algorithm (SCA) (Mirjalili, 2016a, Mirjalili, 2016b))}

PHYSICS BASED METAHEURISTICS {Gravitational Local Search (GLSA) (Webster and Bernhard, 2003), Black Hole Algorithm (BHA) (Hatamlou, 2013a, Hatamlou, 2013b), Colliding Bodies Optimization (CBO) (Kaveh and Mahdavi, 2014), atom search optimization (ASO) (Zhao et al., 2019), Simulated Annealing (SA) (Kirkpatrick et al., 1983); Gravitational Search Algorithm (GSA) (Rashedi et al., 2009); Biogeography-Based Optimization (BBO) (Simon, 2008); Big-Bang Big-Crunch (BBBC) (Erol and Eksin, 2006); Charged System Search (CSS) (Kaveh and Talatahari, 2010); Central Force Optimization (CFO) (Formato, 2007); Artificial Chemical Reaction Optimization Algorithm (ACROA) (Alatas, 2011); Black Hole (BH) algorithm (Hatamlou, 2013a, Hatamlou, 2013b); Ray Optimization (RO) algorithm (Kaveh and Khayatazad, 2012); Small-World Optimization Algorithm (SWOA) (Du et al., 2006); Galaxy-based Search Algorithm (GbSA) (Shah-Hosseini, 2011); Curved Space Optimization (CSO) (Moghaddam et al., 2012); Water Evaporation Optimization (WEO) (Kaveh and Bakhshpoori, 2016)}

SOCIAL AND SPORT BASED METAHEURISTICS {Teaching–Learning-Based Optimization (TLBO) (Rao et al., 2012); League Championship Algorithm (LCA) (Kashan, 2014), Hunting Search (HUS) algorithm (Oftadeh et al., 2010), Queuing search algorithm (QSA) (Zhang et al., 2018), interior search algorithm (ISA) (Gandomi, 2014), Exchange Market Algorithm (EMA) (Ghorbani and Babaei, 2014), Social-Based Algorithm (SBA) (Ramezani and Lotfi, 2013), Hill Climbing Algorithm (HCA) (Brownlee, 2011). Probability-Based Incremental Learning (PBIL) (Dasgupta and Zbigniew, 2013)}

EVOLUTIONARY-BASED {Memetic algorithm (MA) (Moscato, 1989), Genetic Programming (GP) (Koza, 1992)), Evolutionary Programming (EP), Imperialist Competitive Algorithm (ICA) (Atashpaz-Gargari and Lucas, 2007), Yin-Yang-pair, Artificial (Punnathanam & Kotecha, 2016), Neural Networks (ANN) (Hassoun, 1995), Evolution Strategy (ES) (Cai and Thierauf, 1996)}

Algorithms in the second category can be summarized as: TABU SEARCH (TS) was presented by Glover and McMillan (1986) who first used the term “metaheuristic” and can be called is an Evolutionary-based because of its iterative searching (Abdel-Basset et al., 2018); VARIABLE NEIGHBORHOOD SEARCH (VNS) (Mladenovíc and Hansen (1997)). PARTIAL OPTIMIZATION METAHEURISTIC UNDER SPECIAL INTENSIFICATION CONDITIONS (POPMUSIC) (Taillard and Voss, 2002), which is a local search that can optimize large-scale optimization problems. POPMUSIC serves as a general frame comprises other search procedures such as Large Neighborhood Search, Local Optimizations (LOPT), Adaptive Randomized Decomposition, Differential Evolution (DE) (Abdel-Basset et al., 2018).

Various algorithms have been applied for different nano fields. GA was developed to optimize a time-cost trade-off problem. Obtained solutions showed that in some cases of scheduling without this algorithm, resource consumption was exceeded above resource availability (Taheri Amiri et al., 2018). It was also used for enhancing portfolio performance, suggested a two-stage mixed integer mode (Ansari et al., 2019).

To get benefit from the point of power in each algorithm, we apply the hybridization of metaheuristics. GA also was used to optimize the process conditions of Al Matrix nano-composites and optimization of supported nanostructures for the first principles of global structure (Shabani and Mazahery, 2013, Vilhelmsen and Hammer, 2014). Furthermore, the Hybrid Parallel Evolutionary Algorithm (HPEA) was used for optimal searching for new, stable atomic arrangements of two-dimensional graphene-like carbon lattices. The combination of the parallel evolutionary algorithm and the conjugate-gradient technique was used to find stable arrangements of carbon atoms under certain imposed conditions (Mrozek et al., 2015). The K-Means clustering method and the interactive GA were utilized to produce and optimize military camouflage images scored by expert observers (Montazeri et al., 2019). Improved ABC was used to solve spatial optimization problems (Yang et al., 2015). Lagrangian relaxation (LR), PSO, FA, and BA were used to solve LTPS problem (Tolouei et al., 2020). The optimal parameters for the synthesize of nano-particles by the milling process were integrated by the Taguchi method, RSM and GA (Hou, Su, & Liu, 2007). Due to the importance of achieving the maximum absorption coefficient spectrum in the optical applications such as solar cells and plasmonic nanoantenna, according to the importance of achieving maximum absorption coefficient spectrum, the TLBO was proposed to design an array of plasmonic nano bi-pyramids. The results confirmed the strong dependency of the absorption coefficient on the localized position of plasmonic nanoparticles (Akhlaghi et al., 2014). A hybrid technique PSO-GA for solving the constrained optimization problems has been developed. PSO improved the vector while GA has modified the decision vectors (Garg, 2016). FTMA also used for solving global optimization problems, which has a competing performance in terms of speed and evading the local minima (Allawi et al, 2019). A new hybrid HSOS-LO algorithm represented a combination of the canonical SOS and several local search mechanisms aimed at increasing the searching capability in discrete-based solution space (Prayogo et al., 2020). Modified coyote optimization algorithm (MCOA) has been proposed for the optimal power flow (OPF) problem. MCOA reduced fuel cost and power loss (Li et al., 2019). To test the performance of the proposed quantum dolphin swarm algorithm (QDSA), six commonly used large-scale functions, were taken as examples. Furthermore, WOA were used for comparison (Qiao and Yang, 2019). A comparative study of four metaheuristic algorithms (DSA, PSO, ABC, GA) have been proposed and these algorithms were tested on succinic acid production in Escherichia coli. The comparative performances are measured based on production rate, growth rate, and computational time (Mohd Daud et al., 2019). The Adaptive Cuckoo Search (ACS) and PSO algorithms are used to estimate echo bandwidth, arrival time, center frequency, amplitude and phase and these parameters and their performances were compared (Chibane et al., 2019). Alejo-Reyes et al. (2019) studied a novel and non-linear model for minimizing the total cost per time unit, considering ordering, purchasing, inventory, and transportation cost with freight rate discounts. Due to the non-linearity of the proposed model, PSO, GA, and DE, are implemented as optimizing solvers instead of analytical methods. DA, PSO, and recently a hybrid DA-PSO, has been proposed (Khunkitti et al., 2019). A method using PSO, can allow automatically generating extractive summaries from documents by adequately weighting sentences coring features (Villa-Monte et al., 2019). A robust hybrid IDE-ACO were applied for optimizing the truss structures with discrete sizing variables (Mohammad Arjmand et al., 2018). A dynamic distribution model in cold supply chains of dairy products was developed by using an enhanced hybrid metaheuristic approach based on ACO. The proposed distribution model was defined according to CVRP, and the minimum number of vehicles were determined (Khanmohammadzadeh Seresti et al., 2019). ACO system algorithms are proposed to solve the time-dependent problem represented by an extended flight graph. The improved approach to the diversification of search in ACO system algorithms, increased the quality of the constructed routes from different regions. The proposed algorithms are analysed for efficiency based on the analysis of the results of a computational experiment from real data (Hulianytskyi and Pavlenko, 2019). On the premise of guaranteeing the convergence accuracy, the calculation speed of ACO algorithm in the planning for transmission network was effectively improved (Fan, 2019). The Shuffled Frog-Leaping algorithm provides a significant improvement against other existing models in terms of energy consumption and migration of virtual machines using memory, collaboration and sharing information among frogs, high convergence speed and better flexibility against local optimum problem (Sattari-Naeini et al., 2018).

Disadvantage of most of these algorithms is the disuse of all experimental replicates data ({Y_ij}) in each selected Xi to determine the optimum points in an experimental process consists of experimental replicates. The previous methods, based on interpolation for optimization, perform based on the averages of experimental replicated data (consist of standard deviation (STDE)), and they have not been changed yet. Previous algorithms have a step by step pattern. Other methods based on statistical methods, which analyze the discrete systems with experimental replicates data, maybe reliable but are less accurate. In these methods, the use of the experimental replicates averages as an approximated data values instead of the original data lead to error and less reliability. Using tools such as computers, algorithms complexities and removing some experimental data, in order to simplify the models are the reasons for the inefficiency of these methods. Therefore, a new useful, simple and efficient algorithm which can save time, use fewer computer tools, and also apply all experimental replicates data in the optimization process is very important and necessary to raise the accuracy.

This study describes a new meta-heuristic optimization algorithm (namely, Proposed Optimization Algorithm, POA) which is able to include all experimental replicates, and be applied in the field of nano/agriculture. Therefore, an effort has been made to mathematically predict the optimal concentration (OC) of CS biopolymer, in which the hydrophobicity of the CS reaches to its maximum value (Tabasum et al., 2019). To the best of our knowledge, there is no previous study on this subject in the published optimization methods literature. The main difference between the current work and other meta-heuristic algorithms, inspired by the nature (particularly GOA (Saremi et al., 2017)/ and WOA (Mirjalili & Lewis, 2016)), is easy modeling to use by only mathematical knowledge, and interpolation concepts, without any additional hypothesizes for simulation.

Further, experimental screening is carried out to confirm our computational predictions. As the first and foremost excellence of this method, elimination of any chemical additive for increasing the hydrophobicity of the edible polymers, could be referred. Herein, it is clearly demonstrated that the most effective degree of hydrophobicity could be obtained for CS matrix, via a precise optimization method. Then, an objective investigation is done through the surface-coating of an apple that prove well food packaging is performed with no need to additional modifiers. To the best of our knowledge, this is the first report of contributing all experimental replicates data for performing and optimizing a statistical project and also is the first report of increasing the hydrophobicity on agricultural products.

In addition, the results of the present method are shown and compared with the results of other methods in previous studies and also with the two meta-heuristic methods of WOA and GOA. Although, some statistical based methods were shown to reduce the data distances and used all experimental data (Wang et al., 2014) but the present method is an algorithm which models problems consisting discrete data based on consideration of all experimental replicates discrete data with every STDE. Moreover, this algorithm introduces a simple procedure for programming such as discrete data problems in optimization science to apply in hydrophobicity of fruits and modification of polymeric surfaces. Thus, current study follows two main objectives; introducing the new optimization method based on Directed Local Search (POA), and also determining the optimal nano-chitosan (NCS) concentration corresponding to the maximum covered apple surface CA. This will compensate the lack of optimization in similar previous studies; and fabricating the hydrophobic apple surface with the optimal NCS concentrations. Corresponding CA measurements, were done after POA, GOA, WOA performance, respectively. The best method was introduced based on statistical analysis comparison. Finally, summarizes the study and present the chemical/agricultural results.