Metin Turkay

Logic-based MINLP algorithms for the optimal synthesis of process networks

Abstract In this paper, the MINLP problem for the optimal synthesis of process networks is modeled as a discrete optimization problem involving logic disjunctions with nonlinear equations and pure logic relations. The logic disjunctions allow the conditional modeling of equations (e.g. if a unit is selected, apply mass/heat balances; otherwise, set the flow variables to zero). It is first shown that this framework for representing discrete optimization problems greatly simplifies the step of modeling. The outer approximation algorithm is then used as a basis to derive a new logic-based OA solution method which naturally gives rise to NLP sub-problems that avoid zero flows and a disjunctive LP master problem. The initial NLP sub-problems, that provide linearizations for all the terms in the disjunctions, are selected through a set-covering problem for which we consider both the cases of disjunctive and conjunctive normal form logic. The master problem, on the other hand, is converted to mixed-integer form using a convex-hull representation. Furthermore, based on some interesting relations of outer approximation with generalized Benders decomposition, it is also shown that it is possible to derive a logic-based method for the latter algorithm. The proposed algorithm has been tested on several structural optimization problems, including a flowsheet example showing distinct advantages in robustness and computational efficiency when compared to standard MINLP models and algorithms.

Optimization Based Tumor Classification from Microarray Gene Expression Data

Background An important use of data obtained from microarray measurements is the classification of tumor types with respect to genes that are either up or down regulated in specific cancer types. A number of algorithms have been proposed to obtain such classifications. These algorithms usually require parameter optimization to obtain accurate results depending on the type of data. Additionally, it is highly critical to find an optimal set of markers among those up or down regulated genes that can be clinically utilized to build assays for the diagnosis or to follow progression of specific cancer types. In this paper, we employ a mixed integer programming based classification algorithm named hyper-box enclosure method (HBE) for the classification of some cancer types with a minimal set of predictor genes. This optimization based method which is a user friendly and efficient classifier may allow the clinicians to diagnose and follow progression of certain cancer types. Methodology/Principal Findings We apply HBE algorithm to some well known data sets such as leukemia, prostate cancer, diffuse large B-cell lymphoma (DLBCL), small round blue cell tumors (SRBCT) to find some predictor genes that can be utilized for diagnosis and prognosis in a robust manner with a high accuracy. Our approach does not require any modification or parameter optimization for each data set. Additionally, information gain attribute evaluator, relief attribute evaluator and correlation-based feature selection methods are employed for the gene selection. The results are compared with those from other studies and biological roles of selected genes in corresponding cancer type are described. Conclusions/Significance The performance of our algorithm overall was better than the other algorithms reported in the literature and classifiers found in WEKA data-mining package. Since it does not require a parameter optimization and it performs consistently very high prediction rate on different type of data sets, HBE method is an effective and consistent tool for cancer type prediction with a small number of gene markers.

Restricted Mobility of Conserved Residues in Protein-Protein Interfaces in Molecular Simulations☆☆

Conserved residues in protein-protein interfaces correlate with residue hot-spots. To obtain insight into their roles, we have studied their mobility. We have performed 39 explicit solvent simulations of 15 complexes and their monomers, with the interfaces varying in size, shape, and function. The dynamic behavior of conserved residues in unbound monomers illustrates significantly lower flexibility as compared to their environment, suggesting that already before binding they are constrained in a boundlike configuration. To understand this behavior, we have analyzed the inter- and intrachain hydrogen-bond residence-time in the interfaces. We find that conserved residues are not involved significantly in hydrogen bonds across the interface as compared to nonconserved. However, the monomer simulations reveal that conserved residues contribute dominantly to hydrogen-bond formation before binding. Packing of conserved residues across the trajectories is significantly higher before and after the binding, rationalizing their lower mobility. Backbone torsional angle distributions show that conserved residues assume restricted regions of space and the most visited conformations in the bound and unbound trajectories are similar, suggesting that conserved residues are preorganized. Combined with previous studies, we conclude that conserved residues, hot spots, anchor, and interface-buried residues may be similar residues, fulfilling similar roles.

A mixed-integer programming approach to the clustering problem with an application in customer segmentation

Abstract This paper presents a mathematical programming based clustering approach that is applied to a digital platform company’s customer segmentation problem involving demographic and transactional attributes related to the customers. The clustering problem is formulated as a mixed-integer programming problem with the objective of minimizing the maximum cluster diameter among all clusters. In order to overcome issues related to computational complexity of the problem, we developed a heuristic approach that improves computational times dramatically without compromising from optimality in most of the cases that we tested. The performance of this approach is tested on a real problem. The analysis of our results indicates that our approach is computationally efficient and creates meaningful segmentation of data.

Synergy analysis of collaborative supply chain management in energy systems using multi-period MILP

Energy, a fundamental entity of modern life, is usually produced using fossil fuels as the primary raw material. A consequence of burning fossil fuels is the emission of environmentally harmful substances. Energy production systems generate steam and electricity that are served to different customers to satisfy their energy requirement. The improvement of economical and environmental performance of energy production systems is a major issue due to central role of energy in every industrial activity. A systematic approach to identify the synergy among different energy systems is addressed in this paper. The multi-period and discrete-continuous nature of the energy production systems including investment costs are modeled using MILP. The proposed approach is applied on two examples that are simplified versions of an industrial problem. It is shown that the approach presented in this paper is very effective in identifying the synergy among different companies to improve their economical and environmental performance significantly.

Multi-company collaborative supply chain management with economical and environmental considerations

Process systems must interact with other systems for a better production performance. The interaction among process systems is usually established when these systems exchange materials such as steam and electricity. Integrated analysis of different process systems can provide valuable insight and also identify improvements in the financial and environmental performance of industrial supply chain systems. A systematic approach to identify the synergy among different process systems has been developed. The proposed approach uses three steps; the generation of standardized models for process units, integration of process unit models for the supply chain system and solution of the model and analysis of the results. The developed approach is illustrated with an example that is a simplified version of a real problem and tested on an industrial problem. It is shown that important improvements in the cost and release of environmentally harmful emissions can be accomplished by integration of different process systems.

Relationships Between Amino Acid Sequence and Backbone Torsion Angle Preferences

Statistical averages and correlations for backbone torsion angles of chymotrypsin inhibitor 2 are calculated by using the Rotational Isomeric States model of chain statistics. Statistical weights of torsional states of ϕψ pairs, needed for the statistics of the full chain, are obtained in two different ways: 1) by using knowledge‐based pairwise dependent ϕψ energy maps from Protein Data Bank (PDB) and 2) by collecting torsion angle data from a large number of random coil configurations of an all‐atom protein model with volume exclusion. Results obtained by using PDB data show strong correlations between adjacent torsion angle pairs belonging to both the same and different residues. These correlations favor the choice of the native‐state torsion angles, and they are strongly context dependent, determined by the specific amino acid sequence of the protein. Excluded volume or steric clashes, only, do not introduce context‐dependent ϕψ correlations into the chain that would affect the choice of native‐state torsional angles. Proteins 2004;55:000–000.

EOQ Revisited with Sustainability Considerations

Abstract The economic order quantity (EOQ) model is a pure economic model in classical inventory control theory. The model is designed to find the order quantity so as to minimize total cost under a deterministic setting. In this study, we revise the standard EOQ model to incorporate sustainability considerations that include environmental and social criteria in addition to the conventional economic considerations. We propose models for a number of different policies and analyze these revised models. Based on our analysis, we show how the triple bottom line considerations of sustainability be appended to traditional cost accounting in EOQ model. We also provide a number of useful insights for decision and policy making practices.

Structural flowsheet optimization with complex investment cost functions

The optimization of process systems with complex investment cost functions, defined over several intervals of equipment sizes, operating pressures and temperatures, is addressed in this paper. The discontinuities with respect to these variables are modeled with disjunctions that are converted into tight mixed-integer constraints with the convex hull formulation for each disjunction. The efficiency of the resulting MINLP model for fixed structures is shown on a flowsheet optimization problem and compared with the big-M formulation. To address the structural optimization of process flowsheets, we propose a generalized disjunctive programming algorithm (GDP) in which the complex investment cost functions are formulated as embedded disjunctions. The GDP algorithm consists of MINLP subproblems for the optimization of fixed flowsheet structures and MILP master problems to predict new flowsheets to be optimized. The proposed algorithm is tested on the synthesis of a process network with nine units, and the synthesis of a vinyl chloride monomer production process consisting of 32 process units. It is shown that the proposed GDP algorithm is rigorous for handling discontinuities in complex cost functions, and is robust and efficient for structural flowsheet optimization problems.

Classification of cytochrome P450 inhibitors with respect to binding free energy and pIC50 using common molecular descriptors.

Virtual screening of chemical libraries following experimental assays of drug candidates is a common procedure in structure based drug discovery. However, the relationship between binding free energies and biological activities (pIC50) of drug candidates is still an unsolved issue that limits the efficiency and speed of drug development processes. In this study, the relationship between them is investigated based on a common molecular descriptor set for human cytochrome P450 enzymes (CYPs). CYPs play an important role in drug-drug interactions, drug metabolism, and toxicity. Therefore, in silico prediction of CYP inhibition by drug candidates is one of the major considerations in drug discovery. The combination of partial least-squares regression (PLSR) and a variety of classification algorithms were employed by considering this relationship as a classification problem. Our results indicate that PLSR with classification is a powerful tool to predict more than one output such as binding free energy and pIC50 simultaneously. PLSR with mixed-integer linear programming based hyperboxes predicts the binding free energy and pIC50 with a mean accuracy of 87.18% (min: 81.67% max: 97.05%) and 88.09% (min: 79.83% max: 92.90%), respectively, for the cytochrome p450 superfamily using the common 6 molecular descriptors with a 10-fold cross-validation.