Multi-objective optimization: Difference between revisions

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In 2013, Ganesan et al. carried out the multi-objective optimization of the combined carbon dioxide reforming and partial oxidation of methane. The objective functions were methane conversion, carbon monoxide selectivity, and hydrogen to carbon monoxide ratio. Ganesan used the Normal Boundary Intersection (NBI) method in conjunction with two swarm-based techniques (Gravitational Search Algorithm (GSA) and Particle Swarm Optimization (PSO)) to tackle the problem.<ref>{{Cite journal|title = Swarm intelligence and gravitational search algorithm for multi-objective optimization of synthesis gas production|journal = Applied Energy|date = 2013-03-01|pages = 368–374|volume = 103|doi = 10.1016/j.apenergy.2012.09.059|first1 = T.|last1 = Ganesan|first2 = I.|last2 = Elamvazuthi|first3 = Ku Zilati|last3 = Ku Shaari|first4 = P.|last4 = Vasant| bibcode=2013ApEn..103..368G }}</ref> Applications involving chemical extraction<ref>{{Cite book|publisher = Springer International Publishing|date = 2015-03-23|isbn = 978-3-319-15704-7|pages = 13–21|series = Lecture Notes in Computer Science|doi = 10.1007/978-3-319-15705-4_2|first1 = Timothy|last1 = Ganesan|first2 = Irraivan|last2 = Elamvazuthi|first3 = Pandian|last3 = Vasant|first4 = Ku Zilati Ku|last4 = Shaari| title=Intelligent Information and Database Systems | chapter=Multiobjective Optimization of Bioactive Compound Extraction Process via Evolutionary Strategies | volume=9012 |editor-first = Ngoc Thanh|editor-last = Nguyen|editor-first2 = Bogdan|editor-last2 = Trawiński|editor-first3 = Raymond|editor-last3 = Kosala}}</ref> and bioethanol production processes<ref>{{Cite book|title = Contemporary Advancements in Information Technology Development in Dynamic Environments|url = https://books.google.com/books?id=L6N_BAAAQBAJ|publisher = IGI Global|date = 2014-06-30|isbn = 9781466662537|first = Khosrow-Pour|last = Mehdi}}</ref> have posed similar multi-objective problems.

In 2013, Abakarov et al. proposed an alternative technique to solve multi-objective optimization problems arising in food engineering.<ref>{{Cite journal|title=Multi-criteria optimization and decision-making approach for improving of food engineering processes|author1=Abakarov. A. |author2=Sushkov. Yu. |author3=Mascheroni. R.H. |year=2012 |journal=International Journal of Food Studies |volume=2 |pages=1–21 |doi=10.7455/ijfs/2.1.2013.a1 |doi-broken-date=181 JanuaryJuly 2025 |s2cid=3708256 |url=http://tomakechoice.com/paper/MCDM&OD_IJFS.pdf}}</ref> The Aggregating Functions Approach, the Adaptive Random Search Algorithm, and the Penalty Functions Approach were used to compute the initial set of the non-dominated or Pareto-optimal solutions. The [[Analytic Hierarchy Process]] and Tabular Method were used simultaneously for choosing the best alternative among the computed subset of non-dominated solutions for osmotic dehydration processes.<ref>{{Cite journal |author1=Abakarov, A. |author2=Sushkov, Y. |author3=Almonacid, S. |author4=Simpson, R. |year=2009| title=Multiobjective Optimisation Approach: Thermal Food Processing.|journal=Journal of Food Science |volume=74 |issue=9|pages= E471–E487 |doi=10.1111/j.1750-3841.2009.01348.x| pmid=20492109|hdl=10533/134983|hdl-access=free}}</ref>

In 2018, Pearce et al. formulated task allocation to human and robotic workers as a multi-objective optimization problem, considering production time and the ergonomic impact on the human worker as the two objectives considered in the formulation. Their approach used a [[Linear programming|Mixed-Integer Linear Program]] to solve the optimization problem for a weighted sum of the two objectives to calculate a set of [[Pareto efficiency|Pareto optimal]] solutions. Applying the approach to several manufacturing tasks showed improvements in at least one objective in most tasks and in both objectives in some of the processes.<ref>{{Cite journal |last1=Pearce |first1=Margaret |last2=Mutlu |first2=Bilge |last3=Shah |first3=Julie |last4=Radwin |first4=Robert |date=2018 |title=Optimizing Makespan and Ergonomics in Integrating Collaborative Robots Into Manufacturing Processes |journal=IEEE Transactions on Automation Science and Engineering |volume=15 |issue=4 |language=en-US |pages=1772–1784 |doi=10.1109/tase.2018.2789820 |s2cid=52927442|issn=1545-5955 |doi-access=free}}</ref>

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=== Evolutionary algorithms ===

[[Evolutionary algorithms]] are popular approaches to generating Pareto optimal solutions to a multi-objective optimization problem. Most evolutionary multi-objective optimization (EMO) algorithms apply Pareto-based ranking schemes. Evolutionary algorithms such as the Non-dominated Sorting Genetic Algorithm-II (NSGA-II),<ref name="doi10.1109/4235.996017">{{Cite journal | doi = 10.1109/4235.996017| title = A fast and elitist multiobjective genetic algorithm: NSGA-II| journal = IEEE Transactions on Evolutionary Computation| volume = 6| issue = 2| pages = 182| year = 2002| last1 = Deb | first1 = K.| last2 = Pratap | first2 = A.| last3 = Agarwal | first3 = S.| last4 = Meyarivan | first4 = T.| citeseerx = 10.1.1.17.7771| s2cid = 9914171}}</ref> its extended version NSGA-III,<ref>{{Cite journal |last1=Deb |first1=Kalyanmoy |last2=Jain |first2=Himanshu |date=2014 |title=An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point-Based Nondominated Sorting Approach, Part I: Solving Problems With Box Constraints |url=https://ieeexplore.ieee.org/document/6600851 |journal=IEEE Transactions on Evolutionary Computation |volume=18 |issue=4 |pages=577–601 |doi=10.1109/TEVC.2013.2281535 |s2cid=206682597 |issn=1089-778X}}</ref><ref>{{Cite journal |last1=Jain |first1=Himanshu |last2=Deb |first2=Kalyanmoy |date=2014 |title=An Evolutionary Many-Objective Optimization Algorithm Using Reference-Point Based Nondominated Sorting Approach, Part II: Handling Constraints and Extending to an Adaptive Approach |url=https://ieeexplore.ieee.org/document/6595567 |journal=IEEE Transactions on Evolutionary Computation |volume=18 |issue=4 |pages=602–622 |doi=10.1109/TEVC.2013.2281534 |s2cid=16426862 |issn=1089-778X}}</ref> Strength Pareto Evolutionary Algorithm 2 (SPEA-2)<ref>Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Performance of the Strength Pareto Evolutionary Algorithm, Technical Report 103, Computer Engineering and Communication Networks Lab (TIK), Swiss Federal Institute of Technology (ETH) Zurich (2001) [http://www.tik.ee.ethz.ch/publications/?db=publications&form=report_single_publication&publication_id=1319]</ref> and multiobjective [[differential evolution]] variants have become standard approaches, although some schemes based on [[Particle swarm optimization#Variants|particle swarm optimization]] and [[simulated annealing]]<ref>{{cite journal|first1=B.|last1=Suman|first2=P.|last2=Kumar|title=A survey of simulated annealing as a tool for single and multiobjective optimization|journal=Journal of the Operational Research Society|volume=57|issue=10|pages=1143–1160|year=2006|doi=10.1057/palgrave.jors.2602068|s2cid=18916703}}</ref> are significant. The main advantage of evolutionary algorithms, when applied to solve multi-objective optimization problems, is the fact that they typically generate sets of solutions, allowing computation of an approximation of the entire Pareto front. The main disadvantage of evolutionary algorithms is their lower speed and the Pareto optimality of the solutions cannot be guaranteed; it is only known that none of the generated solutions is dominated by another.

Another paradigm for multi-objective optimization based on novelty using evolutionary algorithms was recently improved upon.<ref name=vargas2015>Danilo Vasconcellos Vargas, Junichi Murata, Hirotaka Takano, Alexandre Claudio Botazzo Delbem (2015), "[https://arxiv.org/abs/1901.00266 General Subpopulation Framework and Taming the Conflict Inside Populations]", Evolutionary computation 23 (1), 1-36.</ref> This paradigm searches for novel solutions in objective space (i.e., novelty search<ref>Lehman, Joel, and Kenneth O. Stanley. "Abandoning objectives: Evolution through the search for novelty alone." Evolutionary computation 19.2 (2011): 189-223.</ref> on objective space) in addition to the search for non-dominated solutions. Novelty search is like stepping stones guiding the search to previously unexplored places. It is especially useful in overcoming bias and plateaus as well as guiding the search in many-objective optimization problems.