Syst. This article has been republished with minor changes. 01 Nov November 1, 2022 Biol. Mech. Evol Comput 19(1):4576, Bandyopadhyay S, Saha S (2013) Some single- and multiobjective optimization techniques. After viewing product detail pages, look here to find an easy way to navigate back to pages you are interested in. Sharma, S., Kumar, V. A Comprehensive Review on Multi-objective Optimization Techniques: Past, Present and Future. IEEE Access 8:8085580878, Tang J et al (2021) A review on representative swarm intelligence algorithms for solving optimization problems: applications and trends. Comparison of multi-objective optimization methodologies for : Please try again. MOO was introduced by Vilfredo Pareto. Please try again. Gamboa, M.G.C. J. Suppl. On the contrary, optimization will continue on the second objective and with new constraints on the solution obtained from the first objective. Cited by lists all citing articles based on Crossref citations.Articles with the Crossref icon will open in a new tab. The weights on the scalarization method are equal weights, ROC weights, and RS weights. Register to receive personalised research and resources by email. 29, 100313 (2019), K. Bora, S. Saha, S. Agrawal, M. Safonova, S. Routh, A. Narasimhamurthy, Astro. In recent years, multi-objective optimization (MOO) techniques have become popular due to their potentiality in solving a wide variety of real-world problems, including bioinformatics,. While the inside building can be seen in Figure 6. Surv Oper Res Manag Sci 20(2):3542, MathSciNet In: Arai K, Kapoor S, Bhatia R (eds) Intelligent computing. Fundamentals of Optimization Techniques with Algorithms , Language where (according to example Figure 3), (Q1,Q2) are the coordinates for the Utopia point of the objective function f1(x) whose minimum value is searched for, and objective function f2(x) which needs the minimum value to be determined,(Q1,Q2) are the point coordinates on the POF, and (Q1norm,Q2norm) are normalization point coordinates in the problem areas. Correspondence to Borsa Istanb Rev 22:01, Xu Q, Xu Z, Ma T (2019) A short survey and challenges for multiobjective evolutionary algorithms based on decomposition. IEEE/ACM Trans Comput Biol Bioinform 4(2):279292, Hosseini SH, Vahidi J, Kamel TSR, Shojaei AA (2021) Resource allocation optimization in cloud computing using the whale optimization algorithm. 450, 128 (2018), D. Dutta, J. Sil, P. Dutta, Expert Syst. Trans Evol Comput 19(5):694716, Li K, Deb K, Zhang Q, Kwong S (2015) An evolutionary many-objective optimization algorithm based on dominance and decomposition. 22(6), 14777 (2019), B. Xue, M. Zhang, W.N. Vega-Rodrguez, C.J. 10391044, S. Yadav, A. Ekbal, S. Saha, Soft. The computation time using the exhaustive process is 3.72 times longer compared to the GA optimization. Suganthan, Swarm Evolut. Publisher ADS After we know we have arrived at the best . 9951015, S. Das, S.S. Mullick, P.N. 17, 129 (2016), G.M. Knowl. Figure 7. It also analyzed reviews to verify trustworthiness. The mapping between the solution vector and the objective function vector can be seen in Figure 1 (Deb, 2001). Given this mapping, the convexity of a solution space and an objective function space is crucial in determining the problem-solving algorithm. Springer, Cham, pp 8293, Panda M, Azar A (2020) Hybrid multi-objective Grey Wolf search optimizer and machine learning approach for software bug prediction: hybrid multi-objective Grey Wolf search optimizer for software bug prediction. The vector is determined and uses the limit (upper limit in case of minimization) for all problems. We dont share your credit card details with third-party sellers, and we dont sell your information to others. Most tumors are misdiagnosed due to the variability and complexity of lesions, which reduces the survival rate in patients. Med. There is a term that exists which is referred to as non-dominated solution or Pareto efficient. Evol. In: 2014 IEEE workshop on advanced research and technology in industry applications (WARTIA), pp 10641067, Wang Z, Zhang X, Zhang Z, Sheng D (2021) Credit portfolio optimization: a multi-objective genetic algorithm approach. 14(2), 357367 (2021), C.B. (b) The p3 solution is better when compared to the p9 solution for at least one objective function. 19, T.Takahama, S.Sakai, In IEEE congress on evolutionary computation (IEEE, 2010), pp. statement Multi Objective Optimization Techniques And Applications In Chemical Engineering With Cd Rom Advances In Process Systems Engineering can be one of the options to accompany you taking into consideration having additional time. Secondly, a problem would appear if the plural problem that is optimized is not convex. Comput. 3 (a)), we want a car with good mileage, so we will turn 'ON' the torch and move towards the last car we can see i.e. In the MOO, determining the optimal value can be done by the exhaustive method which is to check the overall solution. Lopes, A.A. Freitas, IEEE Trans. Wiley, New York, Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, Part I: solving problems with Box constraints. Tech. Kumar, V., & Sahoo, A. K. (2015). In the Pareto method, several terms in the Pareto optimal solution need to be noted. . Processes 8(5):508, Reynolds R, Liu D (2011) Multi-objective cultural algorithms. The weighted approach used is RS weights for power consumption, SNR, and load variance (Gunantara and Dharma 2017). If j is less than the number of P add j with one, and go back to step c. If the opposite, go to step e. If member number -j from P dominates i, add i with one and go back to step b. Mosa, Appl. Selecting the best key player is by assuming that the selected key player is needed to perform well collectively or as a whole. This is a preview of subscription content, access via your institution. Although process optimization for multiple objectives was studied by several researchers back in the 1970s and 1980s, it has attracted active research in the last 10 years, spurred by the new and effective techniques for multi-objective optimization. multi-objective optimization (also known as multi-objective programming, vector optimization, multicriteria optimization, multiattribute optimization or pareto optimization) is an area of multiple criteria decision making that is concerned with mathematical optimization problems involving more than one objective function to be optimized Dyn. Registered in England & Wales No. Multiobjective Optimization Problem - an overview | ScienceDirect Topics In the Pareto method, there is a dominated solution and a non-dominated solution obtained by a continuously updated algorithm. : Alok, N.Kanekar, S.Saha, A.Ekbal, In 2014 9th International Conference on Industrial and Information Systems (ICIIS) (IEEE, 2014), pp. Learn more about Institutional subscriptions, [Source: https://pymoo.org/visualization/star.html]. : This book brings together the latest findings on efficient solutions of multi/many-objective optimization problems from the leading researchers in the field. Gokulnath, S. Shantharajah, Clust. 2015 International Conference on Communications . Knowl. Larger weights for power consumption produce performance of power consumption is better compared to smaller weights. 82(4), 361 (2019), H. Al-Sahaf, Y. Bi, Q. Chen, A. Lensen, Y. Mei, Y. Learn. https://doi.org/10.1007/s11831-022-09778-9, https://doi.org/10.33552/CTCSE.2019.02.000529, https://doi.org/10.4018/978-1-5225-3035-0.CH014, https://doi.org/10.20944/preprints201805.0221.v1. Propellant consumption should be carefully calculated for the purpose of carrying more . 485492 (2006), D.Zhang, B.Wei, In Mechatronics and Automation (ICMA), 2014 IEEE International Conference on (IEEE, 2014), pp. Instead, our system considers things like how recent a review is and if the reviewer bought the item on Amazon. Results show that first, with varied weights, the performance of SNR with GA method is better than the PSO method. 20(5), 792 (2016). You are not required to obtain permission to reuse this article in part or whole. Figure 9 shows five non-dominated solutions solutions are stars sign with numbers. Meanwhile, the objective function is said to be convex if it satisfies the following equation (Boyd & dan Vandenberghe, 2004):(2) f(x+(1)y)f(x)+(1)f(y),(2). The minimum weight design will not necessarily give the minimum cost design because of the different cost-toweight ratios of the materials used. In: Current trends in civil and structural engineering. Due to the flexibility of this rule-based controller, its application to a multi-source hybrid powertrain can be considered. Try again. Google Scholar, C.A.C. This paper briefly explains the multi-objective optimization algorithms and their variants with pros and cons. A review of some of the MOO settlement methods shows that a complex method of solving and difficult mathematical equations are used. IGI Global, Hershey, Pang LM, Ishibuchi H, Shang K (2020) Decomposition-based multi-objective evolutionary algorithm design under two algorithm frameworks. Springer, Cham, pp 672681, Yue C, Liang J, Qu B, Han Y, Zhu Y, Crisalle OD (2020) A novel multiobjective optimization algorithm for sparse signal reconstruction. Google Scholar, K. Deb, In Springer Handbook of Computational Intelligence (Springer, Berlin, 2015), pp. Learn more about Institutional subscriptions, Abd Elaziz M, Abualigah L, Ibrahim RA, Attiya I, M Zhou (2021) IoT workflow scheduling using intelligent arithmetic optimization algorithm in fog computing. : Syst. Menhas, M. Fei, In Life System Modeling and Intelligent Computing (Springer, Berlin, 2010), pp. In: 2017 IEEE congress on evolutionary computation (CEC), Mirjalili SM, Merikhi B, Mirjalili SZ, Zoghi M, Mirjalili S (2017) Multi-objective versus single-objective optimization frameworks for designing photonic crystal filters. . PubMedGoogle Scholar. Otherwise, the process stops and denotes P as a non-dominated set. Nat Comput Int J 17(3):585609, Falcn-Cardona JG, Coello CAC (2018) A multi-objective evolutionary hyper-heuristic based on multiple indicator-based density estimators. The results show some alternatives in the selection of relays. Meanwhile, if the SNR value from S to D is less than two power two spectral efficiency, then two dual-hop procedure is chosen. Evol. Although process optimization for multiple objectives was studied in the 1970s and 1980s, it has attracted active research in the last 15 years, spurred by the new and effective techniques for multi-objective optimization (MOO). The first is called the Multi-Criteria Decision Making (MCDM) approach which can be characterized by the use of mathematical programming techniques and a decision mak- ing method in an intertwined manner. The settlement method will then be applied to the ad hoc network. Data Min. The multi-objective optimization problem is defined as: E1 where F1 (P) and F2 (P) are the objective functions to be minimized over the set of permissible decision vector P, as follow in the next Subsections 2.1 and 2.2. Comput. In: Optimization of manufacturing processes. Health Inform. Results for one simulation are used to find the cooperative path pair. , Item Weight 3099067 The selected cooperative path pairs are 1 (132232) and 2 (141432). Nguyen, H.B. 2015), there are shell and tube heat exchangers. Dr. Naveen Saini would liketo acknowledge the support received from the Woosong University Academic research in 2021. In the single-objective optimization problem, the superiority of a solution over other solutions is easily determined by comparing their objective function values In multi-objective optimization problem, the goodness of a solution is determined by the dominance Dominance Bring your club to Amazon Book Clubs, start a new book club and invite your friends to join, or find a club thats right for you for free. Some introductory figures from : Deb Kalyanmoy, Multi-Objective Optimization using Evolutionary Algorithms, Wiley 2001 Implementation of Constrained GA Based on NSGA-II. The -constraint method (Haimes, Lasdon, & Wismer, 1971) optimizes only one problem while the other problems are transformed into limits. : Chen, Y.L. It was implemented on MAT LAB. List prices may not necessarily reflect the product's prevailing market price. In: TENCON 20172017 IEEE Region 10 conference, pp 27472752, Kvasov DE, Mukhametzhanov MS (2018) Metaheuristic vs. deterministic global optimization algorithms. Anyone you share the following link with will be able to read this content: Sorry, a shareable link is not currently available for this article. Appl. 88, 571 (2018), C.A.C. In: 2019 International conference on computer, information and telecommunication systems (CITS), pp 15, Xu Q, Xu Z, Ma T (2020) A survey of multiobjective evolutionary algorithms based on decomposition: variants, challenges and future directions. 105(13), 211 (2009), S. Makhija, S. Saha, S. Basak, M. Das, Astro. Optimization has been playing a key role in the design, planning and operation of chemical and related processes for nearly half a century. , Dimensions Association for Computing Machinery, New York, pp 595603, Peitz S, Dellnitz M (2018) A survey of recent trends in multiobjective optimal controlsurrogate models, feedback control and objective reduction. Unable to add item to List. In: Proceedings of the genetic and evolutionary computation conference, GECCO 18. (TOMM) 16(1s), 1 (2020), N. Saini, S. Saha, V. Potnuru, R. Grover, P. Bhattacharyya, IEEE Intell. Association for Computing Machinery, New York, pp 635642, Dede T, Kripka M, Toan V, Yepes V, Venkata Rao R (2019) Usage of optimization techniques in civil engineering during the last two decades. It has been found that using evolutionary algorithms is a highly effective way of finding multiple effective solutions in a single simulation run. In every x solution in the decision variable space there is a point on the objective function space. Bohat, In Computational Intelligence: Theories, Applications and Future Directions, vol. Swarm Intell 3:6985, Antonio LM, Berenguer JA, Coello CA (2018) Evolutionary many-objective optimization based on linear assignment problem transformations. Association for Computing Machinery, New York, pp 527534, Jain H, Deb K (2013) An improved adaptive approach for elitist nondominated sorting genetic algorithm for many-objective optimization. fundamentals of optimization techniques with algorithms presents a complete package of various traditional and advanced optimization techniques along with a variety of example problems, algorithms and matlab code optimization techniques, for linear and nonlinear single variable and multivariable models, as well as multi-objective and advanced 164, 45 (2019), N. Saini, S. Saha, D. Chakraborty, P. Bhattacharyya, PLoS One 14(11), e0223477 (2019), N. Saini, S. Saha, A. Kumar, P. Bhattacharyya, In International Conference on Neural Information Processing (Springer, Berlin, 2019), pp. Soft Comput. In: Proceedings of the genetic and evolutionary computation conference, GECCO 19. J. Comput. In: International conference on parallel problem solving from nature, Springer, New York, pp 832842, Eckart Z, Thiele L (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. In multi-objective optimization . An Introduction to Multiobjective Optimization Techniques In our previous work, multi-objective optimization was undertaken to determine the optimal operating conditions in terms of the process parameters that . The POF for minimize objective function f1(x) and maximize objective function f2(x) can be seen in Figure 4 under the curve (a). 403449, K. Price, R.M. 388393 (2006), S. Saha, S. Bandyopadhyay, Pattern Recogn. : The brain tumor is characterized by an anomalous proliferation of brain cells that can either be benign or malignant. 3 (Pearson Upper Saddle River, NJ, USA:, 2009), A.L. Evol. Problems that have more than one objective is referred to as multi-objective optimization (MOO). Home Loo Hay Lee Publications Trans, Multimedia Comput. Most of these objectives are conflicting in nature and require multi-objective solutions. 19801987 (2004), H. Zhang, A. Zhou, S. Song, Q. Zhang, X.Z. Vertical takeoff and vertical landing (VTVL) vehicles, based on throttling liquid rocket engines, are attracting increasing attention for their validation of guidance and control techniques during landing. Please try again. 44, 748 (2019). Comput. 2 (IEEE, 2014), vol. MathSciNet 20(4), 1171 (2015), A.K. Areas covered: Starting with SOO and the ways used to incorporate multiple criteria into it, the present review focuses on MOO techniques, their comparison, advantages, and restrictions. 02TH8600), vol. The POF for the two objective functions, f1(x) and f2(x),with different purposes exist in three more combinations. 34(6), 43 (2019), N.Saini, S.Kumar, S.Saha, P.Bhattacharyya, In 2020 IEEE International Conference on Pattern Recognition (ICPR) (IEEE, 2020), J.M. Multi-Objective Optimization: Techniques and Applications in Chemical 276(12), 35 (2019), S. Saha, A.K. Springer optimization and its applications, vol 145. 24(9), 68516870 (2020), P. Charbonneau, Astrophys. 43, 31 (2018), B.C. Google Scholar, Abdel-Basset M, Mohamed R, Mirjalili S, Chakrabortty RK, Ryan M (2021) An efficient marine predators algorithm for solving multi-objective optimization problems: analysis and validations. Finally, the computational time required for scalarization functions with varying weights has little to no difference. Biol. Optimization Optimization refers to finding one or more . Ramesh, R.J. Sethi, H. Yu, PLoS One 10(2), e0115671 (2015), N. Saini, S. Saha, P. Bhattacharyya, IEEE Trans. Loo Hay Lee - Publications Multi-objective optimization techniques: a survey of the state-of-the https://doi.org/10.4018/978-1-5225-3035-0.CH014, Maltese J, Ombuki-Berman BM, Engelbrecht AP (2018) A scalability study of many-objective optimization algorithms. Proceedings of the EUROGEN2001, Athens, Greece, 1921 September 2001, Zolpakar NA, Lodhi SS, Pathak S, Sharma MA (2020) Application of multi-objective genetic algorithm (MOGA) optimization in machining processes. Sci. To calculate the overall star rating and percentage breakdown by star, we dont use a simple average. Multi-Objective Optimization: Techniques and Applications in Chemical Engineering (Second Edition) (Advances in Process Systems Engineering)$138.02Only 1 left in stock - order soon. Scenario 2: Applying 1D optimisation on objective-2, i.e. Comput. In the MOO, there is a multi-dimensional space of the objective function vector and the decision variable space of the solution vector. After the algorithm Continuously Updated is done, it then determines the Utopia point. The comparison of these two algorithms s is done because both algorithms have similarities and differences. Some conclusions can be made based on the analysis of optimization results. The Pareto method keeps the elements of the solution vectors separate (independent) during optimization and the concept of dominance is there to differentiate the dominated and non-dominated solutions. The scalarization method incorporates multi-objective functions into scalar fitness function as in the following equation (Murata & Ishibuchi, 1996):(5) F(x)=w1f1(x)+w2f2(x)++wnfn(x).(5). 110, 107649 (2021), Y. Zhang, D. Gong, X. Gelatt, M.P. Uebnice cudzch jazykov Odborn a akademick literatra. To calculate the overall star rating and percentage breakdown by star, we dont use a simple average. Grating lobe and sidelobe suppression using Multi-Objective Optimization Techniques. For this, rules can be modified to include state-of-charge values of all of the storage components . IEEE Trans Evol Comput 18(1):2035, Mukhopadhyay A, Maulik U, Bandyopadhyay S, Coello CCA (2014) A survey of multiobjective evolutionary algorithms for data mining: Part I. IEEE Trans Evol Comput 18(1):419, Nuhanovi A, Hivziefendi J, Hadimehmedovi A (2013) Distribution network reconfiguration considering power losses and outages costs using genetic algorithm. Post-Doctoral Research Visit F/M Post-Doctorant - Multi-robot formation Prez, Appl. Pham, Materials 13(5), 1205 (2020), J. Maturana, F. Lardeux, F. Saubion, J. Heuristics 16(6), 881 (2010), F. Ramezani, J. Lu, J. Taheri, F.K. Sci. Please try again. Two objectives are considered, which are the quality of matches (measuring the extent of the time series of finance whether it is an uptrend, downtrend, or head-and-shoulders) and area (size, through the linear function, the length of the interval described). Larger weights for SNR produce better SNR performance compared to smaller weights. Arch Comput Methods Eng 29:22852308, Pham TX, Siarry P, Oulhadj H (2019) A multi-objective optimization approach for brain MRI segmentation using fuzzy entropy clustering and region-based active contour methods. The performance of the proposed techniques is clearly validated by the experimental analysis incorporated in this study and is the first study that concisely treats fuzzy membership function optimization in terms of an MDP environment it opens up enumerable opportunities for future reinforcement learning endeavors. IEEE Trans Evol Comput 22(2):226244, Malik P, Nautiyal L, Ram M (2018) Applying multi-objective optimization algorithms to mechanical engineering, pp 287301. For example p3 and p9, which are in the Pareto optimal solution. 43(3), 738 (2010), M.K. Renewable contract : Oui. Rep. 7(1), 1 (2017), A. Onan, S. Korukolu, H. Bulut, Inf. In order to determine the shortest Euclidean distance from the Utopia point to the points in the POF, the following equation can be used (Cohanim, Hewitt, and de Weck, 2004):(4) dE=minQ1Q1Q1norm2+Q2Q2Q2norm2,(4). The standard TO application of static structural compliance may be cast as a multiobjective problem if mass is included as an objective rather than a constraint. Although process optimization for multiple objectives was studied by several researchers back in the 1970s and 1980s, it has attracted active research in the last 10 years, spurred by the new and effective techniques for multi-objective optimization. Multi-objective algorithms look for optimal values of design variables such as outer tube diameter, outer diameter, and baffle spacing. This can be seen in Figure 2. 2009 (American Medical Informatics Association, 2009), vol. Low-Cost first, followed by applying 1D optimisation on objective-1, i.e. Google Scholar, Coello CAC, Lechuga MS, Pulido GT (1999) Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. volume230,pages 23192335 (2021)Cite this article. 37(3), 487 (2004), M. Sharma, J.K. Chhabra, Sustain. 2026, H.Li, F.He, Y.Liang, Q.Quan, Soft Comput. The dominance solution and optimal value in MOO are usually achieved when one objective function cannot increase without reducing the other objective function. It can be solved mathematically if a Pareto optimal solution has been found (Ehrgott, 2005). Springer, Cham, pp 185199, Computer Science and Engineering Department, National Institute of Technology, Hamirpur, Himachal Pradesh, 177005, India, You can also search for this author in The non-dominated solution (p1, p2, p3, p4, p5, and p6) and dominated solution (p7, p8, , p21) can be seen in Figure 3 (Gunantara & Sastra, 2016; Pernodet, Lahmidi, & Michel, 2009). Mathematically, the MOO problem using the Pareto method can be written as follows (Ehrgott, 2005):(3) f1,opt=minf1(x)f2,opt=minf2(x). IEEE Access 9:32293248, Qi Y, Ma X, Liu F, Jiao L, Sun J, Wu J (2014) MOEA/D with adaptive weight adjustment. The List Price is the suggested retail price of a new product as provided by a manufacturer, supplier, or seller. There was an error retrieving your Wish Lists. Alyasseri, Appl. The MOO or the multi-objective optimization refers to finding the optimal solution values of more than one desired goals. In: Evolutionary methods for design, optimization and control with applications to industrial problems. The two configurations have 32 nodes where source specified at node 1, destination is specified at node 32, and the other node acts as relay. multi objective optimization problem Multiobjective optimization involves three stages: model building, search, and decision making (preference articulation). , Hardcover CoRR, abs/1609.04069, Garca-Martnez C, Cordon O, Herrera F (2007) A taxonomy and an empirical analysis of multiple objective ant colony optimization algorithms for the bi-criteria TSP. There was a problem loading your book clubs. Technology Studies Department, Endicott College of International Studies, Woosong University, Daejeon, 34606, South Korea, Department of Computer Science and Engineering, Indian Institute of Technology Patna, Bihar, 801103, India, You can also search for this author in Good Mileage. Feldman, Physica A 478, 20 (2017), ADS 242, pp. In the lexicographic method (Fishburn, 1974), decision-makers are asked to regulate objective functions by relying on their absolute interests. 2, vol. By closing this message, you are consenting to our use of cookies. Atlantis Press, pp 443447, Moshref M, Al-Sayyed R, Al Sharaeh S (2020) Multi-objective optimization algorithms for wireless sensor networks: a comprehensive survey. Vijay Kumar. The computational time difference can be seen if it is compared with the exhaustive method by checking the overall solutions. The ad hoc network model that is used is a model outside the building and inside the building. Fusion 50, 168 (2019), A.A. Bidgoli, H.Ebrahimpour-Komleh, S.Rahnamayan, In 2019 IEEE Congress on Evolutionary Computation (CEC) (IEEE, 2019), pp. The non-dominated set makes up a POF. Cost function ( F 1) The fuel cost is considered as an essential criterion for economics analysis in thermal power plants. Several exercises are included at the end of many chapters, for use by both practicing engineers and students. 1 (World Scientific, Singapore, 2004), E. Zitzler, K. Deb, L. Thiele, Evol. Fundam Inform 106(1):4573, Santana-Quintero L, Arias-Montano A, Coello C (2010) A review of techniques for handling expensive functions in evolutionary multi-objective optimization. In: Proceedings of the Sriwijaya international conference on information technology and its applications (SICONIAN 2019), 2020. Swarm Evol Comput 66:100937, Olmo JL, Romero JR, Ventura S (2012) Classification rule mining using ant programming guided by grammar with multiple Pareto fronts. 49(7), 1482 (2018), J. Liang, W. Xu, C. Yue, K. Yu, H. Song, O.D. Eng. This condition is called Pareto optimality. The number searches of existing path pairs based on the configuration of the model affect the determination of the optimal value on the scalarization method assisted by the GA. Comput. In: Proceedings of the genetic and evolutionary computation conference, GECCO 19. Multiobjective optimization can be defined as determining a vector of design variables that are within the feasible region to minimize (maximize) a vector of objective functions and can be mathematically expressed as follows (1) where x is the vector of design variables, f i ( x) is the i th objective function, and g ( x) is the constraint vector. Netw. In order to capture this renewed interest, this monograph presents the recent and ongoing research in multi-optimization techniques and their applications in chemical engineering.Following a brief introduction and general review on the development of multi-objective optimization applications in chemical engineering since 2000, the book gives a description of selected multi-objective techniques and then goes on to discuss chemical engineering applications.