Submitted:
07 July 2026
Posted:
08 July 2026
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Abstract

Keywords:
1. Introduction
- (a)
- Experimental screening of candidate solvents for the system,
- (b)
- Database screening based on physical, chemical, and related properties, and
- (c)
- Computer-aided molecular design (CAMD) to generate optimal solvents.
2. The Solvent Selection Problem
- Distribution coefficient is the ratio of the desired solute’s concentration in the solvent phase to its concentration in the original mixture.
- Solvent selectivity measures how effectively a solvent attracts the desired solute relative to undesired components.
2.1. Computer-Aided Molecular Design
- N1: the total number of functional groups
- N2(i): the index of each group (i = 1,…,N1)
2.2. Group Contribution Method: UNIFAC
| (2b), | (2c), | (2d) |
| (2e), | (2f) |
2.3. Solvent Selection Optimization Problem
3. Algorithmic Framework
3.1. Ant-Colony Optimization
3.2. Simulated Annealing
3.3. Hammersley Sequence Sampling
3.4. Efficient Ant-Colony Optimization (EACO)
3.5. Efficient Simulated Annealing (ESA)
4. Results and Discussions
4.1. Candidate Solvents Using ACO and SA
4.2. Candidate Solvents Using EACO and ESA
5. Conclusion
References
- Kim K-J, Diwekar UM, Joback KG. Greener solvent selection under uncertainty. ACS Symposium Series, vol. 819, Washington, DC; American Chemical Society; 1999; 2002, p. 224–37.
- Kim KJ, Diwekar UM. Efficient combinatorial optimization under uncertainty. 2. Application to stochastic solvent selection. Ind Eng Chem Res 2002;41:1285–96. [CrossRef]
- Papadimitriou C, Steiglitz K. Combinatorial Optimization: Algorithms and Complexity. vol. 32. New York: DOVER PUBLICATIONS, INC.; 1982. [CrossRef]
- Blum C. Ant colony optimization: Introduction and recent trends. Phys Life Rev 2005;2:353–73. [CrossRef]
- Nistala VS, Bhartiya S, Juvekar V, Diwekar UM. Designing Solvents to Extract Nutraceuticals from Multicomponent Sugar Cane Wax Using a Computer-Aided Molecular Design (CAMD) Approach. Ind Eng Chem Res 2026;65:11655–70. [CrossRef]
- Food and Agriculture Organization of the United Nations. Food and Agriculture Organization of the United Nations (2025) – with major processing by Our World in Data. “Sugar cane production – UN FAO” 2026.
- Sharma R, Matsuzaka T, Kaushik MK, Sugasawa T, Ohno H, Wang Y, et al. Octacosanol and policosanol prevent high-fat diet-induced obesity and metabolic disorders by activating brown adipose tissue and improving liver metabolism. Sci Rep 2019;9. [CrossRef]
- Shen J, Luo F, Lin Q. Policosanol: Extraction and biological functions. J Funct Foods 2019;57:351–60. [CrossRef]
- Marinangeli CPF, Jones PJH, Kassis AN, Eskin MNA. Policosanols as nutraceuticals: Fact or fiction. Crit Rev Food Sci Nutr 2010;50:259–67. [CrossRef]
- Asikin Y, Takahashi M, Hirose N, Hou DX, Takara K, Wada K. Wax, policosanol, and long-chain aldehydes of different sugarcane (Saccharum officinarum L.) cultivars. European Journal of Lipid Science and Technology 2012;114:583–91. [CrossRef]
- Kamchonemenukool S, Ho CT, Boonnoun P, Li S, Pan MH, Klangpetch W, et al. High Levels of Policosanols and Phytosterols from Sugar Mill Waste by Subcritical Liquefied Dimethyl Ether. Foods 2022;11. [CrossRef]
- Irmak S, Dunford NT, Milligan J. Policosanol contents of beeswax, sugar cane and wheat extracts. Food Chem 2006;95:312–8. [CrossRef]
- Attard TM, McElroy CR, Rezende CA, Polikarpov I, Clark JH, Hunt AJ. Sugarcane waste as a valuable source of lipophilic molecules. Ind Crops Prod 2015;76:95–103. [CrossRef]
- Cignitti S, Rodriguez-Donis I, Abildskov J, You X, Shcherbakova N, Gerbaud V. CAMD for entrainer screening of extractive distillation process based on new thermodynamic criteria. Chemical Engineering Research and Design 2019;147:721–33. [CrossRef]
- Salazar J, Diwekar U, Joback K, Berger AH, Bhown AS. Solvent selection for post-combustion CO2 capture. Energy Procedia 2013;37:257–64. [CrossRef]
- Trevizo C, Daniel D, Nirmalakhandan N. Screening alternative degreasing solvents using multivariate analysis. Environ Sci Technol 2000;34:2587–95. [CrossRef]
- Kim KJ, Diwekar UM. Integrated solvent selection and recycling for continuous processes. Ind Eng Chem Res 2002;41:4479–88. [CrossRef]
- Button A, Merk D, Hiss JA, Schneider G. Automated de novo molecular design by hybrid machine intelligence and rule-driven chemical synthesis. Nat Mach Intell 2019;1:307–15. [CrossRef]
- Fredenslund A, Gmehling J, Rasmussen P. Vapor-liquid equilibria using UNIFAC : a group contribution method. 1st ed. Amsterdam: Elsevier Scientific Pub. Co.; 1977.
- Stodola P, Michenka K, Nohel J, Rybanský M. Hybrid algorithm based on ant colony optimization and simulated annealing applied to the dynamic traveling salesman problem. Entropy 2020;22. [CrossRef]
- Wu Y, Wang H, Li M, Tan H, Wang D, Sheng M. The Adaptive Two-Stage Ant Colony Simulated Annealing Algorithm for Solving The Traveling Salesman Problem. RAIRO - Operations Research 2025;59:1199–213. [CrossRef]
- Anggraeni DAF, Dianutami VR, Tyasnurita R. Investigation of Simulated Annealing and Ant Colony optimization to Solve Delivery Routing Problem in Surabaya, Indonesia. Procedia Comput. Sci., vol. 234, Elsevier B.V.; 2024, p. 592–601. [CrossRef]
- Dorigo M, Stu¨tzle T. Ant Colony Optimization. The MIT Press; 2004.
- Diwekar U, Gebreslassie B. Efficient ant colony optimization (EACO) algorithm for deterministic optimization. International Journal of Swarm Intelligence and Evolutionary Computation 2016;1. [CrossRef]
- Socha K, Dorigo M. Ant colony optimization for continuous domains. Eur J Oper Res 2008;185:1155–73. [CrossRef]
- Aarts E, Korst J. Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing. Essex, Great Britain: John Wiley & Sons Ltd.; 1989.
- Kim KJ, Diwekar UM. Hammersley stochastic annealing: Efficiency improvement for combinatorial optimization under uncertainty. IIE Transactions (Institute of Industrial Engineers) 2002;34:761–77. [CrossRef]
- van Laarhoven P, Aarts E. Simulated Annealing: Theory and Applications. Springer-Science+ Business Media, B. V. ; 1992.
- Gebreslassie BH, Diwekar UM. Efficient ant colony optimization for computer aided molecular design: Case study solvent selection problem. Comput Chem Eng 2015;78:1–9. [CrossRef]
- Kalagnanam JR, Diwekar UM. An efficient sampling technique for off-line quality control. Technometrics 1997;39:308–19. [CrossRef]
- Szu H, Hartley R. Fast simulated annealing. Phys Lett A 1987;122:157–62. [CrossRef]
- Azizi N, Zolfaghari S, Liang M. Hybrid simulated annealing with memory: An evolution-based diversification approach. Int J Prod Res 2010;48:5455–80. [CrossRef]
- Yu X, Liu Z, Wu X, Wang X. A hybrid differential evolution and simulated annealing algorithm for global optimization. Journal of Intelligent and Fuzzy Systems 2021;41:1375–91. [CrossRef]









| 1 | CH3– | 2 | CH2< | 3 | –CH< | 4 | >C< | 5 | H2O |
| 6 | CH2=CH– | 7 | –CH=CH– | 8 | –CH=C< | 9 | CH2=C< | 10 | –OH |
| 11 | ACH | 12 | AC | 13 | ACCH3 | 14 | ACCH2 | 15 | ACCH |
| 16 | ACOH | 17 | CH3–CO– | 18 | –CH2–CO– | 19 | –CHO | 20 | –COOH |
| Sno. | UNIFAC groups in the candidate solvent | ||
| 1 | 2 CH3 | 529.49 | 1.69 |
| 2 | 1 CH3, 1 CHO | 168.32 | 7.29 |
| 3 | 1 CH3, 1 CH2, 1 CHO | 64.58 | 5.41 |
| 4 | 2 CH3, 1 CH, 1 CHO | 30.89 | 4.34 |
| 5 | 1 CH3, 2 CH2, 1 CHO | 30.71 | 4.34 |
| 6 | 2 CH3, 1 CH2, 1 CH, 1 CHO | 17.43 | 3.65 |
| 7 | 1 CH3, 3 CH2, 1 CHO | 17.36 | 3.65 |
| 8 | 3 CH3, 1 C, 1 CHO | 15.71 | 3.67 |
| 9 | 3 CH3, 1 CH2, 1 C, 1 CHO | 10.35 | 3.20 |
| 10 | 2 CH3, 1 CH=C, 1 CHO | 4.03 | 3.17 |
| 11 | 2 CH3, 1 CH, 1 COOH | 3.408 | 3.11 |
| 12 | 1 CH3, 2 CH2, 1 COOH | 3.401 | 3.11 |
| 13 | 1 CH3, 1 CH2, 1 COOH | 3.07 | 4.29 |
| 14 | 2 CH3, 1 CH2, 1 CH, 1 COOH | 3.03 | 2.43 |
| 15 | 1 CH3, 3 CH2, 1 COOH | 3.03 | 2.43 |
| 16 | 3 CH3, 1 C, 1 COOH | 2.84 | 2.42 |
| 17 | 2 CH3, 2 CH2, 1 CH, 1 COOH | 2.57 | 2.03 |
| 18 | 3 CH3, 1 CH2, 3 CH, 1 CHO, 1 COOH | 2.45 | 3.54 |
| 19 | 1 CH3, 3 CH2, 1 CH, 1 CHO, 1 COOH | 2.23 | 4.38 |
| 20 | 4 CH3, 1 CH2, 2 CH, 1 CH=C, 2 CHO | 1.48 | 2.97 |
| Sno. | UNIFAC groups in the candidate solvent | ||
| 1 | 2 CH3 | 529.49 | 1.69 |
| 2 | 1 CH3, 1 CHO | 168.32 | 7.29 |
| 3 | 1 CH3, 1 CH2, 1 CHO | 64.58 | 5.41 |
| 4 | 2 CH3, 1 CH, 1 CHO | 30.89 | 4.34 |
| 5 | 1 CH3, 2 CH2, 1 CHO | 30.71 | 4.34 |
| 6 | 2 CH3, 1 CH2, 1 CH, 1 CHO | 17.43 | 3.65 |
| 7 | 1 CH3, 3 CH2, 1 CHO | 17.36 | 3.65 |
| 8 | 3 CH3, 1 C, 1 CHO | 15.71 | 3.67 |
| 9 | 3 CH3, 2 CH, 1 CHO | 11.19 | 3.18 |
| 10 | 2 CH3, 2 CH2, 1 CH, 1 CHO | 11.15 | 3.18 |
| 11 | 1 CH3, 4 CH2, 1 CHO | 11.12 | 3.18 |
| 12 | 3 CH3, 1 CH2, 1 C, 1 CHO | 10.35 | 3.20 |
| 13 | 3 CH3, 1 CH2, 2 CH, 1 CHO | 7.84 | 2.83 |
| 14 | 2 CH3, 3 CH2, 1 CH, 1 CHO | 7.82 | 2.83 |
| 15 | 1 CH3, 5 CH2, 1 CHO | 7.80 | 2.83 |
| 16 | 2 CH3, 1 CH=C, 1 CHO | 4.03 | 3.17 |
| 17 | 2 CH3, 1 CH2, 1 CH=C, 1 CHO | 3.73 | 2.81 |
| 18 | 2 CH3, 1 CH, 1 COOH | 3.408 | 3.11 |
| 19 | 1 CH3, 2 CH2, 1 COOH | 3.401 | 3.11 |
| 20 | 1 CH3, 1 CH2, 1 COOH | 3.07 | 4.29 |
| Sno. | UNIFAC groups in the candidate solvent | ||
| 1 | 2 CH3 | 529.49 | 1.69 |
| 2 | 1 CH3, 1 CHO | 168.32 | 7.29 |
| 3 | 1 CH3, 1 CH2, 1 CHO | 64.58 | 5.41 |
| 4 | 2 CH3, 1 CH, 1 CHO | 30.89 | 4.34 |
| 5 | 1 CH3, 2 CH2, 1 CHO | 30.71 | 4.34 |
| 6 | 2 CH3, 1 CH2, 1 CH, 1 CHO | 17.43 | 3.65 |
| 7 | 1 CH3, 3 CH2, 1 CHO | 17.36 | 3.65 |
| 8 | 3 CH3, 1 C, 1 CHO | 15.71 | 3.67 |
| 9 | 3 CH3, 1 CH2, 1 C, 1 CHO | 10.35 | 3.20 |
| 10 | 2 CH3, 1 CH=C, 1 CHO | 4.03 | 3.17 |
| 11 | 2 CH3, 1 CH, 1 COOH | 3.408 | 3.11 |
| 12 | 1 CH3, 2 CH2, 1 COOH | 3.401 | 3.11 |
| 13 | 2 CH3, 2 CH2, 2 CH, 2 CHO | 3.07 | 3.78 |
| 14 | 1 CH3, 1 CH2, 1 COOH | 3.07 | 4.29 |
| 15 | 2 CH3, 1 CH2, 1 CH, 1 COOH | 3.03 | 2.43 |
| 16 | 1 CH3, 3 CH2, 1 COOH | 3.03 | 2.43 |
| 17 | 2 CH3, 1 CH2, 2 CH, 2 CHO | 3.02 | 4.08 |
| 18 | 3 CH3, 1 C, 1 COOH | 2.84 | 2.42 |
| 19 | 2 CH3, 1 CH2, 1 C, 2 CHO | 2.75 | 4.51 |
| 20 | 3 CH3, 2 CH, 1 COOH | 2.57 | 2.03 |
| Sno. | UNIFAC groups in the candidate solvent | ||
| 1 | 2 CH3 | 529.49 | 1.69 |
| 2 | 1 CH3, 1 CHO | 168.32 | 7.29 |
| 3 | 1 CH3, 1 CH2, 1 CHO | 64.58 | 5.41 |
| 4 | 2 CH3, 1 CH, 1 CHO | 30.89 | 4.34 |
| 5 | 1 CH3, 2 CH2, 1 CHO | 30.71 | 4.34 |
| 6 | 2 CH3, 1 CH2, 1 CH, 1 CHO | 17.43 | 3.65 |
| 7 | 1 CH3, 3 CH2, 1 CHO | 17.36 | 3.65 |
| 8 | 3 CH3, 1 C, 1 CHO | 15.71 | 3.67 |
| 9 | 3 CH3, 2 CH, 1 CHO | 11.19 | 3.18 |
| 10 | 2 CH3, 2 CH2, 1 CH, 1 CHO | 11.15 | 3.18 |
| 11 | 1 CH3, 4 CH2, 1 CHO | 11.12 | 3.18 |
| 12 | 3 CH3, 1 CH2, 1 C, 1 CHO | 10.35 | 3.20 |
| 13 | 3 CH3, 1 CH2, 2 CH, 1 CHO | 7.84 | 2.83 |
| 14 | 2 CH3, 3 CH2, 1 CH, 1 CHO | 7.82 | 2.83 |
| 15 | 1 CH3, 5 CH2, 1 CHO | 7.80 | 2.83 |
| 16 | 4 CH3, 2 CH2, 1 C, 1 CHO | 7.42 | 2.85 |
| 17 | 3 CH3, 2 CH2, 1 C, 1 CHO | 7.39 | 2.85 |
| 18 | 4 CH3, 3 CH, 1 CHO | 5.88 | 2.57 |
| 19 | 3 CH3, 2 CH2, 2 CH, 1 CHO | 5.87 | 2.57 |
| 20 | 2 CH3, 4 CH2, 1 CH, 1 CHO | 5.86 | 2.57 |
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