MOO has been used in the food industry. The earliest works in the food industry began in the late 1970s, with the bi-objective optimization method applied to determine the optimal flow pattern in a multieffect evaporator system reported by Nishitani and Kunugita (1979). From then until the year 2007, nearly 30 applications of MOO in the food industry have been reported in around 40 journal papers. However, apart from the early works by Nishitani and Kunugita (1979, 1983), further applications of MOO in the food industry were not reported in journals until 1995.
TABLE 8.4
MOO Applications in Heat Processing of Food
Number Application Objectives Selected Decision Variables Method=Comments References
1 A multieffect evaporator
system for milk concentration
Minimization of heat transfer area and steam consumed
Flow pattern, heat transfer area in each effect (assumed to be the same in all effects), and steam consumption
Enumeration of allflow patterns followed by selection of noninferior solutions
Nishitani and Kunugita (1979)
2 Single-effect evaporator
for milk concentration
Minimization of exergy and total investment cost
Steam temperature, temperature of the preheated feed entering the evaporator, and vapor temperature in the evaporator
«-constraint method along with the max-sensitive method Nishitani and Kunugita (1983) 3 Processing of apples by dewatering and impregnation (DIS) followed by air drying
Minimization of processing time and energy consumption, and maximization of product quality parameters: reduction of shrinkage, softening of texture, product stability, and preservation of color
Solution concentration, solution temperature, soaking time, air relative humidity, and air drying time
Experimental data were modeled using multiple linear regression. MOO was carried out using these models and their visualization in the form of response surfaces
Themelin et al. (1997) (continued) ß 2008 by Taylor & Francis Group, LLC.
TABLE 8.4 (continued)
MOO Applications in Heat Processing of Food
Number Application Objectives Selected Decision Variables Method=Comments References
4 Dryers for sliced potato Minimization of color
deterioration and minimization of unit product cost
Drying air temperature and humidity, and drying air temperature change through the conveyor-belt
First principles model and no- preference method were employed. Both Kiranoudis et al. (1999) and Kiranoudis and Markatos (2000) optimized the design of a conveyor- belt dryer; the former with only the product color deterioration parameters as the objectives whereas the latter included unit product cost as well. Similar studies for a fluidized-bed dryer were reported by Krokida and Kiranoudis (2000a and b) Kiranoudis et al. (1999); Kiranoudis and Markatos (2000); Krokida and Kiranoudis (2000a and b) 5 Optimal control of enzyme drying in a batchfluidized-bed dryer Maximization of profit (which increases with product quality) and minimization of energy costs
Trajectories of air temperature and humidity
Weighting method wasfirst used to scalarize the problem. The centered finite differences method and the control parameterization method were then used to solve the problem
Quirijns et al. (2000) ß 2008 by Taylor & Francis Group, LLC.
6 Rice drying Maximization offinal product quality and minimization of drying time
Air temperature and relative humidity as functions of time
Thefirst principles model was validated and then used for optimization by sequential quadratic programming along with«-constraint method
Olmos et al. (2002)
7 Food processing by
conduction heating
Minimization of surface cook value and processing time
Variable retort temperature profile represented by sine and exponential functions
An artificial neural network model was developed based on simulated data from thefirst principles model, and then used for optimization by a genetic algorithm along with «-constraint method Chen and Ramaswamy (2002) 8 Food processing by conduction heating Maximization of volume- average retention of thiamine for two geometries: spherical andfinite cylinders
Variable retort temperature profile
The weighting method and lexicographic ordering were used along with a modified complex method
Erdogdu and Balaban (2003)
9 Blanching-freezing
system
Productivity, costs, quality, and treatment flexibility
Different types of blanchers and freezers
An analytical hierarchy process was employed for choosing the optimal system Bevilacqua et al. (2004) ß 2008 by Taylor & Francis Group, LLC.
TABLE 8.5
MOO Applications in Fermentation
Number Application Objectives Selected=IndependentDecision Variables Method=Comments References
1 Table olive preparation
systems
Minimization of total investment cost and annual product cost, both per ton of prepared olive
Percentage of olive prepared as green olive, percentage of factory total capacity used for preparation of green olive, quantity of prepared olive per year, and total capacity of the factory
The problem, including cost equations and data, was presented in detail. The nonconvex MOO problem was solved using a modified weighting method
Kopsidas (1995)
2 Estimation of model
parameters in ethanol production
Minimization of the mean least squares error in two or more experiments
Eleven parameters in the kinetic model for ethanol production using a high-ethanol tolerant yeast
Weighted min–max method was used to convert the MOO problem into a single-objective problem and then solved by hybrid differential evolution
Wang and Shue (2000)
3 Gluconic acid
production
Maximization of productivity andfinal concentration of gluconic acid, and minimization of thefinal substrate concentration
Batch time, initial substrate concentration, and initial biomass
An evolutionary algorithm was used to generate Pareto-optimal solutions, which were then ranked using net flow method. Effect of controlling the overall mass transfer coefficient was studied. Halsall-Whitney and Thibault (2006) studied three algorithms for generating Pareto- optimal solutions Halsall-Whitney et al. (2003); Halsall-Whitney and Thibault (2006) 4 Selective product enhancement for Aspergillus niger fermentation Maximization of catalase enzyme and minimization of protease enzyme, and vice versa
Sucrose and nitrogen concentrations in the feed, initial broth volume and trajectories of sucrose, nitrogen and hydrogen peroxide additions
«-constraint method along with differential evolution was employed for solving the MOO. Simulation results were verified experimentally
Mandal et al. (2005) ß 2008 by Taylor & Francis Group, LLC.
5 Fed-batch bioreactors for (a) lysine and (b) protein by recombinant bacteria
Maximization of lysine productivity and yield
Feed rate trajectory andfinal time for lysine production
NSGA-II was used for solving the multi-objective optimal control problem in the two applications, which were studied as single- objective optimization problems in the earlier studies
Sarkar and Modak (2005)
Maximization of protein production and minimization of inducer volume added
Nutrient (glucose) feeding rate and Inducer feeding rate for protein production
6 Batch plant design for
the production of four recombinant proteins: insulin, vaccine for Hepatitis B, chymosin (a food-grade protein), and cryophilic protease (a detergent enzyme)
Four cases of 2 and 3 objectives from
minimization of investment cost, and environmental impact (EI) due to biomass, and EI due to solvent
Number and size of the different equipments, and operating variables used in the process
Discrete event simulator for simulating and checking feasibility of the batch plant and the multi- objective GA (MOGA) were used. Both mono- and multiproduct scenarios were considered for each case
Dietz et al. (2006)
Three cases: maximization of net present value (NPV); maximization of NPV and minimization of product delay=advance criterion; and maximization of NPV and flexibility criterion, and minimization of product delay=advance criterion
Number and size of the different equipments, and operating variables used in the process
A fuzzy approach was proposed to account for uncertain demand, in the optimization of batch plant design for multiple objectives by MOGA
Dietz et al. (2008) (continued) ß 2008 by Taylor & Francis Group, LLC.
TABLE 8.5 (continued)
MOO Applications in Fermentation
Number Application Objectives Selected=IndependentDecision Variables Method=Comments References
7 Optimal design of a
bioreactor for growing Saccharomyces cerevisiae in sugar cane molasses
Maximization of profit and minimization offixed capital investment
Height of the fermentor, feed flow rate, concentrated feed flow rate, and specific growth rate
NSGA-II, normal boundary intersection (NBI) and normalized normal constraint methods were used, and their performance was compared and discussed. Bifurcation analysis to assess the stability of Pareto-optimal solutions is suggested to aid in the selection of a compromise solution
Sendin et al. (2006a)
8 Metabolic pathways for
ethanol production by Saccharomyces cerevisiae
Maximization of ethanol production and minimization of thefive dependent metabolic concentrations
Maximum enzyme activities characterizing different metabolic pathways
Five different MOO methods: weighted sum method, goal attainment method, NBI method, multi-objective indirect optimization method, and multi- objective evolutionary algorithm were used for the case study, and their relative performance was discussed
Sendin et al. (2006b)
9 Glutamine production Maximization of glutamine
concentration and glutamate concentration
Concentrations of glucose and ammonium sulfate in the production medium
Response surface methodology combined with desirability function approach (involving weights) was used to solve the MOO problem to determine the optimal medium. The resulting solution has higher product yields and lower costs, compared to the original medium
Li et al. (2007) ß 2008 by Taylor & Francis Group, LLC.
TABLE 8.6
MOO Applications in Separation Processes
Number Application Objectives Selected=IndependentDecision Variables Method=Comments References
1 Dialysis of beer to
produce low-alcohol beer using hollow-fiber membrane modules
Two cases: (1) maximization of alcohol removal from beer and minimization of‘‘taste chemicals or extract’’ removal and (2) maximization of alcohol removal, and minimization of‘‘taste chemicals or extract’’ removal and cost
Flow rate of pure water on the shell side, inner radius of a single hollow fiber, length of the fiber, fractional free area in the shell, and thickness of the hollowfiber membrane
NSGA was used for solving bi-objective problems. For the tri-objective problem,«-constraint wasfirst used to reduce it to a bi-objective problem, whose solution by NSGA gave a unique solution for each value of«. The inner radius of the hollowfiber was found to be the most important decision variable in most cases
Chan et al. (2000)
2 Membranefiltration
of wine
Maximization of quality parameters and permeate filtration flux
Membrane pore size, recycleflow rate, and type of pretreatment
Measured data on objectives and decision variables were regressed. Minimum loss method (similar to Weighting method) was used for solving the MOO problem for three different cases of champagne and wine produced from different sources
Gergely et al. (2003)
3 Glucose-fructose
separation using simulated moving bed (SMB) and Varicol processes
Two cases: (1) maximization of fructose productivity and purity and (2) maximization of glucose productivity and fructose productivity
Switching period, raffinate flow rate, and eluentflow rate
NSGA method was used for both operation and design optimization. This is one of the three applications presented in Yu et al. (2004) Subramani et al. (2003); Yu et al. (2004) (continued) ß 2008 by Taylor & Francis Group, LLC.
TABLE 8.6 (continued)
MOO Applications in Separation Processes
Number Application Objectives Selected=IndependentDecision Variables Method=Comments References
Maximization of throughput and minimization of desorbent consumption
Operating parameters of the different operating schemes
A superstructure optimization problem for SMB process is considered. «-constraint method and an interior point optimizer (IPOPT) for solving single-objective problems were used
Kawajiri and Biegler (2006)
Maximization of throughput, product purity and recovery of the valuable component recovery, and minimization of solvent consumption in the desorbent stream
Four zone velocities and step time This study includes more objectives than the previous studies on SMB, where two or three objectives were considered. NIMBUS with IPOPT was employed for solving the MOO problem Hakanen et al. (2007) 4 SMB bioreactor for high fructose syrup by glucose isomerization Maximization of productivity of fructose and minimization of desorbent used
Three cases with the same objectives but different decision variables from: switching time, volumetric flow rate in zone III, volumetric flow rate of desorbent, separator length, reactor Length, and number of columns in separator zones 2 and 3
NSGA-II with jumping genes (NSGA-II-JG) was used for MOO of both operation and design of the SMB bioreactor. The SMB bioreactor used is a separative bioreactor Zhang et al. (2004) 5 SMB bioreactors for sucrose inversion to produce fructose and glucose
Two sets: (1) maximization of concentrated fructose productivity and minimization of solvent consumption and (2) maximization of fructose massflow rate and minimization of solvent consumption
Three or more decision variables from: switching time, raffinate flow rate, desorbentflow rate, column length, and configuration
NSGA-II-JG method was used for MOO of several cases: operation and design of SMB bioreactors and modified SMB bioreactors including reactive Varicol system
Kurup et al. (2005) ß 2008 by Taylor & Francis Group, LLC.
TABLE 8.7
Miscellaneous Applications of MOO in Food Engineering
Number Application Objectives Selected=IndependentDecision Variables Method=Comments References
1 Extrusion process in
cattle food granulation
Minimization of product moisture content, product friability, and process energy consumption
Flour temperature and drawplate profile
Both Massebeuf et al. (1999) and Mokeddem and Khellaf (2007) described a diploid GA and used it for the same application
Massebeuf et al. (1999); Mokeddem and
Khellaf (2007)
2 Optimization of process
conditions for the modification of starch
Maximization of conversion and product quality
System temperature, water fraction, starch fraction, molar ratio of NaOH to sodium monochloroacetate (SMCA), molar ratio of SMCA to starch and reaction time
Pareto sets were generated from experimental data using the backward elimination strategy to eliminate factors. Optimization was done using MS Excel
Tijsen et al. (1999)
3 Proportional-integral
(PI) controller design
Minimization of integral of time weighted absolute error (ITAE), integral of square of manipulated variable changes (ISDU), and settling time of a controller
PI controller parameters, namely, proportional gain and integral time
For generating Pareto-optimal solutions, single and dual population evolutionary algorithms (SPEA and DPEA) were found to be more efficient than grid search algorithm (GSA) when the optimization problem has many decision variables. DPEA was found to be more robust and faster than the other two methods Halsall-Whitney and Thibault (2006) 4 Properties of whey protein-methyl cellulosefilms
Minimization of water vapor permeability, and maximization of tensile strength and elongation
Ratio of glycerol to total polymers Complex method was used in combination with the weighting method. The sensitivities of the solution were checked to ensure that the results were not sensitive to the weighting factors selected
Turhan et al. (2007) ß 2008 by Taylor & Francis Group, LLC.
From then, an incre asing numbe r of studies on MOO in food engine ering can be found in journ als (Figur e 8.4). In fact, the numbe r o f journa l papers on MOO in food enginee ring in the last 3 y ears has incre ased to 15 compa red to 9 in the previou s two 3-year perio ds.
Most app lications of MO O in the food indus try involve eith er the optimi zation of plant operating condition s or the opti mizatio n of the plant desig n. The appli cations of MO O in the food indus try can be grouped into four mai n catego ries : (1) heat processing, (2) ferm entation, (3) separa tion proces ses, a nd (4) miscellan eous.
8.4.1 H
EATP
ROCESSINGFood proces sing by appli cation of heat is divi ded into different class ifi cations based on the type of h eating medium used (Fellows , 2000). Eva poration with steam as the heating medium, dryin g wi th hot air, and conduct ion heati ng are three areas in which MOO has b een appli ed. Most appli cations of MOO in heat processing consisted of an economic objective and other object ives that incl ude environ mental and product quality objectives (T able 8.4).
The earliest work of MOO in heat processing is the optimization of the flow pattern in a multi-effect evaporator by Nishitani and Kunugita (1979). Chen and Ramaswamy (2002) and Erdogdu and Balaban (2003) explored the application of MOO to thermal treatment. The application of MOO to food drying is reported in five applications (Table 8.4): apple drying (Themelin et al., 1997), conveyer-belt dryer design (Kiranoudis and Markotos, 2000), fluidized bed dryer (Krokida and Kiranoudis, 2000a and b), control of a drying process (Quirjns et al., 2000), and batch drying of rice (Olmos et al., 2002). Quirjins et al. (2000) noted the importance of including spatial modeling in
1979 –1995 1996 –1998 1999 –2001 2002–2004 2005 –2007 0 2 4 6 8 10 12 14 Number of jour nal articles
FIGURE 8.4 Number of journal papers on MOO applications in food engineering since 1979. Note that each bar except thefirst one is for a 3 year period.
optimizing the control of the drying process. Olmos, et al. (2002) presented the use of MOO in the batch drying of rice, providing new insights into rice drying, and food quality preservation processes. Bevilacqua et al. (2004) used MOO to determine the best blanching-freezing system for multiple objectives (Table 8.4).
8.4.2 F
ERMENTATIONFermentat ion typicall y refers to the convers ion o f sugar to alcoho l using yea st under anaerob ic condit ions. Stein kraus (1995) de fi ned ferm ented foods as the ‘‘food substrate s that are invade d or overgr own by edible mic roorga nisms whos e enzy mes, particula rly amylases, prote ases, and lipa ses, hydrolyze the polysacch arides, pro- teins, and lipids to nontox ic products wi th fl avors, aromas and text ures pleasant and attractive to the human consum er. If the product s of enzyme activities have unpleasant o dors or undesi rable, unattract ive flavors o r the product s are toxi c or disease produci ng, the foods are describ ed as spoiled. ’’
Ferme ntation in the food indus try is usual ly represented by kinetic model s. The fermentat ion proces s itself can often b e repres ented by a mat hematical model (Winkler, 1990). Product qualiti es often expres sed in terms of the concentrati on of a desir ed acid, product ion rates , and subst rate concent rations are often used as the objectives in MO O probl ems (Table 8.5). Decisi on varia bles include residence time in the biore actor, concent ration of mic roorga nisms and operat ing temp erature. The first appli cation o f MOO to fermentat ion was by Kops idas (1995) in the desig n of table oliv e prepar ation systems (Table 8.5). Wa ng and Sheu (2000) used MO O to estimate the kinet ic model param eters of yeast with high ethanol tolerance. The production of glutami ne and gluconic acid were also optimi zed for mul tiple object- ives (Ha lsall-W hitney et a l., 2 003; Halsall-Wh itney and Thibaul t, 2006; Li et al., 2007).
Recentl y, Sa kar and Modak (2005) and Dietz et al. (2006, 2008) used MOO to optimize the desig n of mul tistage batch bioreactor s (Table 8.5). Sakar and Modak (2005) discussed the useful ness of using MO O met hods in the design o f fed-ba tch bioreactor s listin g vario us con flicting object ives that are usually encount ered in real-world situati ons. MOO was also used for product enhancem ent (Mand al et al., 2005), and Sendin et al. (2006a,b) discussed the MOO of fermentation of sugar cane molasses.
8.4.3 S
EPARATIONP
ROCESSESA wide range of MOO applications in food processing is related to separation processes (Table 8.6). Separation is done either to improve product quality and to obtain a particular extract or to preserve food. Chan et al. (2000) applied MOO to optimization of membrane separation modules. Mathematical models were developed and tuned using the experimental results. The use of MOO in wine filtration was studied by Gergely et al. (2003). The application of MOO to simulated moving beds (SMBs) for food processing can be found in six different studies (Subramani et al., 2003; Yu et al., 2004; Zhang et al., 2004; Kurup et al., 2005; Kawajiri and Biegler, 2006; Hakanen et al., 2007). MOO is particularly applicable to SMBs due to the conflicting objectives
that are associated with the design and operation of SMBs. Of the six studies, three of them were accomplished using NSGA (Table 8.6). Owing to the complexities of