ABSTRACT
Multiobjective (MO) optimization is an emerging field which is increasingly being implemented in many process-related industries on a global scale� A near-complete understanding of the concerned process mechanisms is crucial for the formulation of the optimization model� Identifying the process-related uncertainties and the process characteristics (such as the existence of nonlinearities, variations in the input, and the process bounds) helps to strengthen the formulation of the process model� The MO models of extraction processes usually form a characteristically complex optimization problem which is relevant to many chemical and pharmaceutical industries� Finding an effective strategy for obtaining the optimal settings for the extraction process is central to solving such problems�
Multicriteria or MO scenarios have become increasingly prevalent in industrial engineering environments (Statnikov & Matusov, 1995)� MO optimization problems are commonly tackled using the concept of Pareto-optimality to trace out the nondominated solution options at the Pareto curve (Zitzler & Thiele, 1998; Deb, Pratap, Agarwal, & Meyarivan, 2002)� Other methods include the weighted techniques which involve objective function aggregation resulting in a master weighted function� This master weighted function is then solved for various weight values (which are usually fractional) (Fishburn, 1967; Luyben & Floudas, 1994; Das & Dennis, 1998; Triantaphyllou, 2000)� Using these techniques, the weights are used to consign relative importance or priority to the objectives in the master aggregate function� Hence, alternative near-optimal solution options are generated for various values of the scalars� In this chapter, the normal boundary intersection (NBI) scheme (Das & Dennis, 1998) is presented as a scalarization tool to construct the Pareto frontier� In Sandgren (1994) and Statnikov and Matusov (1995), detail examples and analyses on MO techniques for problems in engineering optimization are presented�
Over the past years, MO optimization has been introduced and applied into many engineering problems� Some of these developments are briefly discussed in the following� In Aguirre, Zebulum, and Coello (2004), a MO evolutionary algorithm with an enhanced constraint handling mechanism was used to optimize the circuit design of a field programmable transistor array (FPTA)� The authors used the inverted shrinkable Pareto archived evolution strategy (ISPAES) for the MO optimization of the circuit design� Another MO problem involving engineering design was solved by Reddy and
Kumar (2007)� In that work, a MO swarm intelligence algorithm was developed by incorporating the Pareto dominance relation into the standard particle swarm optimization (PSO) algorithm� Three engineering design problems-the “two bar truss design” (Palli, Azram, McCluskey, & Sundararajan, 1999), “I-beam design” (Yang, Yeun, & Ruy, 2002), and the “welded beam design” (Deb, Pratap, & Moitra, 2000) problems-were successfully solved by Reddy and Kumar (2007)� In the area of thermal system design, the MO optimization of an HVAC (heating, ventilating, airconditioning, and cooling) system was carried out by Kusiak, Xu, and Tang (2010)� In that work, a neural network was used to derive the MO optimization model� This model was then optimized using a multiobjective PSO algorithm (MOPSO)� Using this algorithm, the authors identified the optimum control settings for the supply air temperature and static pressure to minimize the air handling unit energy consumption while maintaining air quality� Another application of the non-dominated sorting genetic algorithm (NSGA-II) to engineering system design was done by Nain, Giri, Sharma, and Deb (2010)� In Nain et al� (2010), the authors optimized the structural parameters (area and length of the thermoelectric cooler [TEC] elements) of the TEC� The coefficient of performance (COP) and the rate of refrigeration (ROR) were successfully maximized in that work�
Recently, MO optimization methods have also expanded the power and energy industries� For instance, in Van Sickel, Venkatesh, and Lee (2008), the MO optimization of a fossil fuel power plant was done using multiobjective evolutionary programming (MOEP) and MOPSO algorithms� The MO techniques in that work were applied to develop reference governors for power plant control systems� MO optimization of reference governor design for power plants was done by Heo and Lee (2006)� In that work, PSO variant algorithms were used to find the optimal mapping between unit load demands and pressure set point of a fossil fuel power plant� By this approach, the optimal set points of the controllers under a large variety of operation scenarios were achieved� Similarly, in the works of Song and Kusiak (2010), temporal processes in power plants were optimized using MO techniques� In that work, the central theme was to maximize the boiler efficiency while minimizing the limestone consumption� Two approaches-the data mining (DM) and evolutionary strategy algorithms-were combined to solve the optimization model� In Song and Kusiak (2010), the MO optimization of temporal-dependent processes were successfully completed by identifying the optimum control parameters� One other area in which MO optimization has been applied with considerable success is the field of economic/ environmental dispatch for power systems� For instance, in the works of Gunda and Acharjee (2011), a MO economic/environmental dispatch problem was solved using the Pareto frontier differential evolution (PFDE) approach� By using this technique, the authors managed to minimize the fuel consumption and emissions with minimal energy loss� This triple-objective problem was successfully solved without the violation of the system’s security constraints� Another similar problem was tackled in King, Rughooputh, and Deb (2005)� In that work, power generation optimization was done to minimize the total fuel costs as well as the amount of emission�
The MO problem considered in this chapter was formulated by Shashi, Deep, and Katiyar (2010)� This problem involves the optimization of the yields of certain chemical products which are extracted from the Gardenia jasminoides Ellis fruit� The MO
optimization model was developed by Shashi et al� (2010) to maximize the extraction yields of the three bioactive compounds: crocin, geniposide, and total phenolic compounds� The optimal extraction parameters which construct the most dominant Pareto frontier are then identified such that the process constraints remain unviolated� In Shashi et al� (2010), the MO problem was tackled using the real-coded genetic algorithm (RCGA) approach to obtain a single individual optima and not a Pareto frontier� In that work, measurement metrics were not employed to evaluate the solution quality in detail� In addition, the work done in Shashi et al� (2010) focused on modeling the system rather than optimizing it� The authors of that work employed only one optimization technique and did not carry out extensive comparative analysis on the optimization capabilities� Due to the mentioned setbacks, these factors are systematically addressed in this chapter to provide some insights on the optimization of the extraction process�
Over the past years, swarm intelligence-based metaheuristic techniques have been applied with increasing frequency to industrial MO scenarios� Some of the most effective swarm approaches have been devised using ideas from Newtonian gravitational theory (Rashedi, Nezamabadi-pour, & Saryazdi, 2009), dynamics of fish movement (Neshat, Sepidnam, Sargolzaei, & Toosi, 2014), and bird flocking behaviors (Kennedy & Eberhart, 1995)� In this chapter, two swarm-based techniques-PSO (Kennedy & Eberhart, 1995) and the novel Hopfield-enhanced PSO (HoPSO)—are presented and implemented to the extraction problem (Shashi et al�, 2010)� The measurement techniques such as the convergence metric (Deb & Jain, 2002) and the hypervolume indicator (HVI) (Zitzler & Thiele, 1998) were used to analyze the solution spread produced by these algorithms� The HVI is a set measure reflecting the volume enclosed by a Pareto front approximation and a reference set (Emmerich, Beume, & Naujoks, 2005)� The convergence metric on the other hand measures the degree at which the solutions conglomerate toward optimal regions of the objective space� Using the values obtained by the measurement metrics, the correlation between the convergence and the degree of dominance (measured by the HVI) of the solution sets is obtained and discussed� The solutions constructing the Pareto frontier obtained using the developed HoPSO algorithm is also subjected to the analyses mentioned above�
In this chapter, the details on the model as well as the strategies employed to optimize the MO extraction process are discussed� In addition, the procedures involving the overall optimization basis called the NBI are explored� By the implementation of the measurement metrics, the solutions obtained using the metaheuristics are then gauged and analyzed�
The model for MO problem considered in this chapter was developed by Shashi et al� (2010)� This problem involves the optimization of the yields of certain chemical products which are extracted from the G. jasminoides Ellis fruit� The phenolic compounds in G. jasminoides Ellis have high antioxidant capabilities which make this fruit valuable for medicinal uses (Li, Wong, Chen, & Chen, 2008)� Compared to other natural food pigments, the coloring constituents of the fruit of Gardenia are nontoxic and chemically stable (Van Calsteren et al�, 1997)� The constituents present in the Gardenia fruit (Oshima et al�, 1988) are iridoid glycosides (e�g�, gardenoside,
geniposide, gardoside, and scandoside methyl ester)� These constituents could be converted into blue colorants under aerobic conditions by enzymes or some microorganisms� The Gardenia fruit extract in its rudimentary form also contains phenolic compounds with high antioxidant capacity in abundance (Li et al�, 2008)� The MO optimization model in Shashi et al� (2010) was for the extraction process of bioactive compounds from Gardenia with respect to the constraints� The MO optimization model was developed to maximize the yield of three bioactive compounds: crocin ( f1), geniposide ( f2), and total phenolic compounds ( f3)� This model is presented as follows:
→
→
→
f f
f process constraints
Maximize Crocin, Maximize Geniposide, Maximize Total phenolic compounds, subject to .
