Multi‐Objective Optimization of a Batch Copoly(ethylene‐polyoxyethylene terephthalate) Reactor Using Different Adaptations of Nondominated Sorting Genetic Algorithm

Summary: A multi‐objective optimization is carried out for a copoly(ethylene‐polyoxyethylene terephthalate) (CEPT) batch reactor using different adaptations of the elitist nondominated sorting genetic algorithm (NSGA‐II). Several two objective function problems are formulated and solved. One objective is to minimize the total copolymerization time and other objective is to minimize the formation of total undesirable side products, namely, acid end group, vinyl ester end group, diethylene glycol ester end group of polyethylene terephthalate, and diethylene glycol. End‐point constraint is incorporated to obtain the specified number‐average degree of copolymerization. The operating temperature history of batch CEPT reactor is the only important decision variable for first optimization problem, whereas operating temperature history and molar ratio of feed to the reactor are taken as decision variables for the second optimization problem. Optimal Pareto frontiers are obtained for both the problems studied. In order to operate the polymerization reactor optimally, it is found that higher isothermal temperature history is needed for short copolymerization time, whereas lower nonisothermal temperature history is required for higher copolymerization time. The results of NSGA‐II technique are analyzed and compared with the jumping gene (JG) and adapted jumping gene (aJG) operator in NSGA‐II separately. It is found that NSGA‐II‐JG is superior to NSGA‐II and NSGA‐II‐aJG.

Optimization of a batch copoly(ethylene‐polyoxyethylene terephthalate) reactor.     

Multiobjective Optimization of Industrial Petroleum Processing Units Using Genetic Algorithms

For many years most of refining processes were optimized using single objective approach, but practically such complex processes must be optimized with several objectives. Multiobjective optimization allows taking all of desired objectives directly and provide search of optimal solution with respect to all of them. Genetic algorithms proved themselves as a powerful and robust tool for multi-objective optimization. In this article, the review for a last decade of multi-objective optimization cases is provided. Most popular genetic algorithms and techniques are mentioned. From a practical point it is shown which objectives are usually chosen for optimization, what constraint and limitations might impose multi-objective optimization problem formulation. Different types of petroleum refining processes are considered such as catalytic and thermal.     

A fast annealing evolutionary algorithm for global optimization

By combining the aspect of population in genetic algorithms (GAs) and the simulated annealing algorithm (SAA), a novel algorithm, called fast annealing evolutionary algorithm (FAEA), is proposed. The algorithm is similar to the annealing evolutionary algorithm (AEA), and a very fast annealing technique is adopted for the annealing procedure. By an application of the algorithm to the optimization of test functions and a comparison of the algorithm with other stochastic optimization methods, it is shown that the algorithm is a highly efficient optimization method. It was also applied in optimization of Lennard-Jones clusters and compared with other methods in this study. The results indicate that the algorithm is a good tool for the energy minimization problem.     

Multiobjective optimization of a free radical bulk polymerization reactor using genetic algorithm

A multiobjective optimization technique has been developed for free radical bulk polymerization reactors using genetic algorithm. The polymerization of methyl methacrylate in a batch reactor has been studied as an example. The two objective functions which are minimized are the total reaction time and the polydispersity index of the polymer product. Simultaneously, end‐point constraints are incorporated to attain desired values of the monomer conversion (x_m) and the number average chain length (μ_n). A nondominated sorting genetic algorithm (NSGA) has been adapted to obtain the optimal control variable (temperature) history. It has been shown that the optimal solution converges to a unique point and no Pareto set is obtained. It has been observed that the optimal solution obtained using the NSGA for multiobjective function optimization compares very well with the solution obtained using the simple genetic algorithm (SGA) for a single objective function optimization problem, in which only the total reaction time is minimized and the two end‐point constraints on x_m and μ_n are satisfied.     

Evolutionary-algorithm-based strategy for computer-assisted structure elucidation

An evolutionary algorithm (EA) using a graph-based data structure to explore the molecular constitution space is presented. The EA implementation proves to be a promising alternative to deterministic approaches to the problem of computer-assisted structure elucidation (CASE). While not relying on any external database, the EA-guided CASE program SENECA is able to find correct solutions within calculation times comparable to that of other CASE expert systems. The implementation presented here significantly expands the size limit of constitutional optimization problems treatable with evolutionary algorithms by introducing novel efficient graph-based genetic operators. The new EA-based search strategy is discussed including the underlying data structures, component design, parameter optimization, and evolution process control. Typical structure elucidation examples are given to demonstrate the algorithm's performance.     

Pareto optimization in computational protein design with multiple objectives

The optimization for function in computational design requires the treatment of, often competing, multiple objectives. Current algorithms reduce the problem to a single objective optimization problem, with the consequent loss of relevant solutions. We present a procedure, based on a variant of a Pareto algorithm, to optimize various competing objectives in protein design that allows reducing in several orders of magnitude the search of the solution space. Our methodology maintains the diversity of solutions and provides an iterative way to incorporate automatic design methods in the design of functional proteins. We have applied our systematic procedure to design enzymes optimized for both catalysis and stability. However, this methodology can be applied to any computational chemistry application requiring multi-objective combinatorial optimization techniques.     

Optimizing fitting parameters in thermogravimetry

This study presents an alternative to simple estimation of parametric fitting models used in thermal analysis. The addressed problem consists in performing an alternative optimization method to fit thermal analysis curves, specifically TG curves and their first derivatives. This proposal consists in estimating the optimal parameters corresponding to fitting kinetic models applied to thermogravimetric (TG) curves, using evolutionary algorithms: differential evolution (DE), simulated annealing and covariance matrix adapting evolutionary strategy. This procedure does not need to include a vector with the initial values of the parameters, as is currently required. Despite their potential benefits, the application of these methods is by no means usual in the context of thermal analysis curve’s estimation. Simulated TG curves are obtained and fitted using a generalized logistic mixture model, where each logistic component represents a thermal degradation process. The simulation of TG curves in four different scenarios taking into account the extent of processes overlapping allows us to evaluate the final results and thus to validate the proposed procedure: two degradation processes non-overlapped simulated using two generalized logistics, two processes overlapped, four processes non-overlapped and four processes overlapped two by two. The mean square error function is chosen as objective function and the above algorithms have been applied separately and together, i.e., taking the final solution of the DE algorithm is the initial solution of the remaining. The results show that the evolutionary algorithms provide a good solution for adjusting simulated TG curves, better than that provided by traditional methods.     

Multi-objective dynamic optimization of semi-batch polymerization processes

An improved evolutionary algorithm is proposed to perform multi-objective dynamic optimization of a semi-batch styrene polymerization process. The target is to determine the optimal feeding trajectories and the reactor operating temperature, which maximize the monomer conversion rate and minimize the initiator residue concentration in the final product. The optimization problem has been formulated as a multi-objective mixed-integer nonlinear problem (MOMINLP). The proposed approach allows the effective computation of the optimal operating strategies for the production of polymers with the average molecular weight and the polydispersity index required.     

Optimization strategy based on genetic algorithms and neural networks applied to a polymerization process

The article presents a simple and general methodology, especially destined to the optimization of complex, strongly nonlinear systems, for which no extensive knowledge or precise models are available. The optimization problem is solved by means of a simple genetic algorithm, and the results are interpreted both from the mathematical point of view (the minimization of the objective function) and technological (the estimation of the achievement of individual objectives in multiobjective optimization). The use of a scalar objective function is supported by the fact that the genetic algorithm also computes the weights attached to the individual objectives along with the optimal values of the decision variables. The optimization strategy is accomplished in three stages: (1) the design and training of the neural model by a new method based on a genetic algorithm where information about the network is coded into the chromosomes; (2) the actual optimization based on genetic algorithms, which implies testing different values for parameters and different variants of the algorithm, computing the weights of the individual objectives and determining the optimal values for the decision variables; (3) the user's decision, who chooses a solution based on technological criteria. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

On the suitability of different representations of solid catalysts for combinatorial library design by genetic algorithms

Genetic algorithms are widely used to solve and optimize combinatorial problems and are more often applied for library design in combinatorial chemistry. Because of their flexibility, however, their implementation can be challenging. In this study, the influence of the representation of solid catalysts on the performance of genetic algorithms was systematically investigated on the basis of a new, constrained, multiobjective, combinatorial test problem with properties common to problems in combinatorial materials science. Constraints were satisfied by penalty functions, repair algorithms, or special representations. The tests were performed using three state-of-the-art evolutionary multiobjective algorithms by performing 100 optimization runs for each algorithm and test case. Experimental data obtained during the optimization of a noble metal-free solid catalyst system active in the selective catalytic reduction of nitric oxide with propene was used to build up a predictive model to validate the results of the theoretical test problem. A significant influence of the representation on the optimization performance was observed. Binary encodings were found to be the preferred encoding in most of the cases, and depending on the experimental test unit, repair algorithms or penalty functions performed best.     

Globally convergent trust-region methods for self-consistent field electronic structure calculations

As far as more complex systems are being accessible for quantum chemical calculations, the reliability of the algorithms used becomes increasingly important. Trust-region strategies comprise a large family of optimization algorithms that incorporates both robustness and applicability for a great variety of problems. The objective of this work is to provide a basic algorithm and an adequate theoretical framework for the application of globally convergent trust-region methods to electronic structure calculations. Closed shell restricted Hartree-Fock calculations are addressed as finite-dimensional nonlinear programming problems with weighted orthogonality constraints. A Levenberg-Marquardt-like modification of a trust-region algorithm for constrained optimization is developed for solving this problem. It is proved that this algorithm is globally convergent. The subproblems that ensure global convergence are easy-to-compute projections and are dependent only on the structure of the constraints, thus being extendable to other problems. Numerical experiments are presented, which confirm the theoretical predictions. The structure of the algorithm is such that accelerations can be easily associated without affecting the convergence properties.     

Chemical reaction optimization for solving shortest common supersequence problem

Shortest common supersequence (SCS) is a classical NP-hard problem, where a string to be constructed that is the supersequence of a given string set. The SCS problem has an enormous application of data compression, query optimization in the database and different bioinformatics activities. Due to NP-hardness, the exact algorithms fail to compute SCS for larger instances. Many heuristics and meta-heuristics approaches were proposed to solve this problem. In this paper, we propose a meta-heuristics approach based on chemical reaction optimization, CRO_SCS that is designed inspired by the nature of the chemical reactions. For different optimization problems like 0-1 knapsack, quadratic assignment, global numeric optimization problems CRO algorithm shows very good performance. We have redesigned the reaction operators and a new reform function to solve the SCS problem. The outcomes of the proposed CRO_SCS algorithm are compared with those of the enhanced beam search (IBS_SCS), deposition and reduction (DR), ant colony optimization (ACO) and artificial bee colony (ABC) algorithms. The length of supersequence, execution time and standard deviation of all related algorithms show that CRO_SCS gives better results on the average than all other algorithms.     

Predicting equilibrium structures in freezing processes

We propose genetic algorithms as a new tool that is able to predict all possible solid candidate structures into which a simple fluid can freeze. In contrast to the conventional approach where the equilibrium structures of the solid phases are chosen from a preselected set of candidates, genetic algorithms perform a parameter-free, unbiased, and unrestricted search in the entire search space, i.e., among all possible candidate structures. We apply the algorithm to recalculate the zero-temperature phase diagrams of neutral star polymers and of charged microgels over a large density range. The power of genetic algorithms and their advantages over conventional approaches is demonstrated by the fact that new and unexpected equilibrium structures for the solid phases are discovered. Improvements of the algorithm that lead to a more rapid convergence are proposed and the role of various parameters of the method is critically assessed.     

Graph-based molecular Pareto optimisation

Computer-assisted design of small molecules has experienced a resurgence in academic and industrial interest due to the widespread use of data-driven techniques such as deep generative models. While the ability to generate molecules that fulfil required chemical properties is encouraging, the use of deep learning models requires significant, if not prohibitive, amounts of data and computational power. At the same time, open-sourcing of more traditional techniques such as graph-based genetic algorithms for molecular optimisation [Jensen, Chem. Sci., 2019, 12, 3567–3572] has shown that simple and training-free algorithms can be efficient and robust alternatives. Further research alleviated the common genetic algorithm issue of evolutionary stagnation by enforcing molecular diversity during optimisation [Van den Abeele, Chem. Sci., 2020, 42, 11485–11491]. The crucial lesson distilled from the simultaneous development of deep generative models and advanced genetic algorithms has been the importance of chemical space exploration [Aspuru-Guzik, Chem. Sci., 2021, 12, 7079–7090]. For single-objective optimisation problems, chemical space exploration had to be discovered as a useable resource but in multi-objective optimisation problems, an exploration of trade-offs between conflicting objectives is inherently present. In this paper we provide state-of-the-art and open-source implementations of two generations of graph-based non-dominated sorting genetic algorithms (NSGA-II, NSGA-III) for molecular multi-objective optimisation. We provide the results of a series of benchmarks for the inverse design of small molecule drugs for both the NSGA-II and NSGA-III algorithms. In addition, we introduce the dominated hypervolume and extended fingerprint based internal similarity as novel metrics for these benchmarks. By design, NSGA-II, and NSGA-III outperform a single optimisation method baseline in terms of dominated hypervolume, but remarkably our results show they do so without relying on a greater internal chemical diversity.

Chemical diversity in Pareto optimization is sufficiently ensured by the structure of the algorithms, and outperforms an explicit quality-diversity approach.     

SODOCK: swarm optimization for highly flexible protein-ligand docking

Protein-ligand docking can be formulated as a parameter optimization problem associated with an accurate scoring function, which aims to identify the translation, orientation, and conformation of a docked ligand with the lowest energy. The parameter optimization problem for highly flexible ligands with many rotatable bonds is more difficult than that for less flexible ligands using genetic algorithm (GA)-based approaches, due to the large numbers of parameters and high correlations among these parameters. This investigation presents a novel optimization algorithm SODOCK based on particle swarm optimization (PSO) for solving flexible protein-ligand docking problems. To improve efficiency and robustness of PSO, an efficient local search strategy is incorporated into SODOCK. The implementation of SODOCK adopts the environment and energy function of AutoDock 3.05. Computer simulation results reveal that SODOCK is superior to the Lamarckian genetic algorithm (LGA) of AutoDock, in terms of convergence performance, robustness, and obtained energy, especially for highly flexible ligands. The results also reveal that PSO is more suitable than the conventional GA in dealing with flexible docking problems with high correlations among parameters. This investigation also compared SODOCK with four state-of-the-art docking methods, namely GOLD 1.2, DOCK 4.0, FlexX 1.8, and LGA of AutoDock 3.05. SODOCK obtained the smallest RMSD in 19 of 37 cases. The average 2.29 A of the 37 RMSD values of SODOCK was better than those of other docking programs, which were all above 3.0 A.     

Global cluster geometry optimization by a phenotype algorithm with Niches: Location of elusive minima,and low-order scaling with cluster size

The problem of global geometry optimization of clusters is addressed with a phenotype variant of the method of genetic algorithms, with several novel performance enhancements. The resulting algorithm is applied to Lennard–Jones clusters as benchmark system, with up to 150 atoms. The well-known, difficult cases involving nonicosahedral global minima can be treated reliably using the concept of niches. The scaling of computer time with cluster size is approximately cubic, which is crucial for future applications to much larger clusters. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 1752–1759, 1999     

Application of the combined CFD and swarm intelligence for optimization of baffles number in a mixer-settler

Process optimization in a mixer-settler is of great importance. Optimization algorithm of particle swarm optimization is one of the evolutionary algorithms to solve optimization problem which is used in many fields. In this study, the optimal condition is calculated in finite volume method in terms of the number of baffles, inlet velocity of fluid, and impeller speed in a mixer-settler with a specific dimension that can be extended to industrial dimensions using the PSO algorithm and the numerical solution of Navier-Stokes equations and k-ε standard.     

Fast and high precision algorithms for optimization in large-scale genomic problems

There are several very difficult problems related to genetic or genomic analysis that belong to the field of discrete optimization in a set of all possible orders. With n elements (points, markers, clones, sequences, etc.), the number of all possible orders is n!/2 and only one of these is considered to be the true order. A classical formulation of a similar mathematical problem is the well-known traveling salesperson problem model (TSP). Genetic analogues of this problem include: ordering in multilocus genetic mapping, evolutionary tree reconstruction, building physical maps (contig assembling for overlapping clones and radiation hybrid mapping), and others. A novel, fast and reliable hybrid algorithm based on evolution strategy and guided local search discrete optimization was developed for TSP formulation of the multilocus mapping problems. High performance and high precision of the employed algorithm named guided evolution strategy (GES) allows verification of the obtained multilocus orders based on different computing-intensive approaches (e.g., bootstrap or jackknife) for detection and removing unreliable marker loci, hence, stabilizing the resulting paths. The efficiency of the proposed algorithm is demonstrated on standard TSP problems and on simulated data of multilocus genetic maps up to 1000 points per linkage group.     

Protein structure prediction from inaccurate and sparse NMR data using an enhanced genetic algorithm

Nuclear Magnetic Resonance Spectroscopy (most commonly known as NMR Spectroscopy) is used to generate approximate and partial distances between pairs of atoms of the native structure of a protein. To predict protein structure from these partial distances by solving the Euclidean distance geometry problem from the partial distances obtained from NMR Spectroscopy, we can predict three-dimensional (3D) structure of a protein. In this paper, a new genetic algorithm is proposed to efficiently address the Euclidean distance geometry problem towards building 3D structure of a given protein applying NMR's sparse data. Our genetic algorithm uses (i) a greedy mutation and crossover operator to intensify the search; (ii) a twin removal technique for diversification in the population; (iii) a random restart method to recover from stagnation; and (iv) a compaction factor to reduce the search space. Reducing the search space drastically, our approach improves the quality of the search. We tested our algorithms on a set of standard benchmarks. Experimentally, we show that our enhanced genetic algorithms significantly outperforms the traditional genetic algorithms and a previously proposed state-of-the-art method. Our method is capable of producing structures that are very close to the native structures and hence, the experimental biologists could adopt it to determine more accurate protein structures from NMR data.