Inverse Mixed Integer Optimization: Polyhedral Insights and Trust Region Methods

Inverse optimization—determining parameters of an optimization problem that render a given solution optimal—has received increasing attention in recent years. Although significant inverse optimization literature exists for convex optimization problems, there have been few advances for discrete problems, despite the ubiquity of applications that fundamentally rely on discrete decision making. In this paper, we present a new set of theoretical insights and algorithms for the general class of inverse mixed integer linear optimization problems. Specifically, a general characterization of optimality conditions is established and leveraged to design new cutting plane solution algorithms. Through an extensive set of computational experiments, we show that our methods provide substantial improvements over existing methods in solving the largest and most difficult instances to date.

COMTOP: Protein Residue–Residue Contact Prediction through Mixed Integer Linear Optimization

Protein contact prediction helps reconstruct the tertiary structure that greatly determines a protein’s function; therefore, contact prediction from the sequence is an important problem. Recently there has been exciting progress on this problem, but many of the existing methods are still low quality of prediction accuracy. In this paper, we present a new mixed integer linear programming (MILP)-based consensus method: a Consensus scheme based On a Mixed integer linear opTimization method for prOtein contact Prediction (COMTOP). The MILP-based consensus method combines the strengths of seven selected protein contact prediction methods, including CCMpred, EVfold, DeepCov, NNcon, PconsC4, plmDCA, and PSICOV, by optimizing the number of correctly predicted contacts and achieving a better prediction accuracy. The proposed hybrid protein residue–residue contact prediction scheme was tested in four independent test sets. For 239 highly non-redundant proteins, the method showed a prediction accuracy of 59.68%, 70.79%, 78.86%, 89.04%, 94.51%, and 97.35% for top-5L, top-3L, top-2L, top-L, top-L/2, and top-L/5 contacts, respectively. When tested on the CASP13 and CASP14 test sets, the proposed method obtained accuracies of 75.91% and 77.49% for top-L/5 predictions, respectively. COMTOP was further tested on 57 non-redundant ɑ-helical transmembrane proteins and achieved prediction accuracies of 64.34% and 73.91% for top-L/2 and top-L/5 predictions, respectively. For all test datasets, the improvement of COMTOP in accuracy over the seven individual methods increased with the increasing number of predicted contacts. For example, COMTOP performed much better for large number of contact predictions (such as top-5L and top-3L) than for small number of contact predictions such as top-L/2 and top-L/5. The results and analysis demonstrate that COMTOP can significantly improve the performance of the individual methods; therefore, COMTOP is more robust against different types of test sets. COMTOP also showed better/comparable predictions when compared with the state-of-the-art predictors.

Portfolio-Wide Optimization of Pharmaceutical R&D Activities Using Mathematical Programming

The research and development (R&D) management in any major research pharmaceutical company is constantly faced with the need to make complicated activity scheduling and resource allocation decisions, as they carry out scientific work to develop new therapeutic products. This paper describes how we develop a decision support tool that allows practitioners to determine portfolio-wide optimal schedules in a systematic, quantitative, and largely automated fashion. Our tool is based on a novel mixed-integer linear optimization model that extends archetypal multimode resource-constrained project scheduling models in order to accommodate multiple rich features that are pertinent to the Chemistry, Manufacturing, and Controls (CMC) activities carried out within the pharmaceutical R&D setting. The tool addresses this problem at the operational level, determining schedules that are optimal in light of chosen business objectives under activity sequencing, resource availability, and deadline constraints. Applying the tool on current workload data demonstrates its tractability for practical adoption. We further illustrate how, by utilizing the tool under different input instances, one may conduct various tactical analyses to assess the system’s ability to cope with sudden changes or react to shifting management priorities.

Design and optimization of a soybean supply chain network under uncertainty

Demands of foods have been increased in recent years for human and animal nutrition. Food supply chain management has been required to administer series of products and services in efficient ways for agriculture and food production to achieve customer satisfaction at the lowest cost. Agricultural systems have been changed during recent years, and have caused improvements in consumption and production patterns. However, there is not much research on supply chains of seeds (e.g., soybean) which have been produced in Canada. In this research, we propose a mixed-integer linear optimization formulation for a soybean supply chain network. The profit is maximized in the objective function. The mathematical formulation consists of multiple products, growers, potential farm company facilities, potential locations of distributers, and customers. Then, the mathematical model is extended by possibilistic approach to include uncertain parameters. In addition, the results are discussed and analyzed for the soybean supply chain network.

Design and optimization of a soybean supply chain network under uncertainty

Demands of foods have been increased in recent years for human and animal nutrition. Food supply chain management has been required to administer series of products and services in efficient ways for agriculture and food production to achieve customer satisfaction at the lowest cost. Agricultural systems have been changed during recent years, and have caused improvements in consumption and production patterns. However, there is not much research on supply chains of seeds (e.g., soybean) which have been produced in Canada. In this research, we propose a mixed-integer linear optimization formulation for a soybean supply chain network. The profit is maximized in the objective function. The mathematical formulation consists of multiple products, growers, potential farm company facilities, potential locations of distributers, and customers. Then, the mathematical model is extended by possibilistic approach to include uncertain parameters. In addition, the results are discussed and analyzed for the soybean supply chain network.

Scheduling of electrical vehicle charging for a charging facility with single charger or multiple chargers

Merchant-owned charging stations will replace gasoline stations in the near future. As charging times of electric vehicles (EV) may be significant, without optimization, customers will wait to get charged without knowing the actual period of charging. In this thesis, two optimal scheduling methods for charging electric vehicles were developed for merchant-owned charging facilities, the first with a single charger and the second with multiple chargers. In the mathematical model for the single merchant-owned charging station, the problem is formulated as a hybrid nonlinear optimization model and solved using a backward recursive algorithm with nonlinear optimization solvers. As for a single charger, a hybrid system framework was used to capture the tradeoff between demand charges and speed of charging. For the merchant-owned multiple chargers case, the problem is formulated as a mixed integer linear optimization challenge with three-dimensional matrices characterizing the solution space and was solved using the MOSEK optimization toolbox in MATLAB. The proposed algorithms have been analyzed for different penalty factors which were imposed on total waiting time of each EV. Final results are analyzed and discussed.

Scheduling of electrical vehicle charging for a charging facility with single charger or multiple chargers

Merchant-owned charging stations will replace gasoline stations in the near future. As charging times of electric vehicles (EV) may be significant, without optimization, customers will wait to get charged without knowing the actual period of charging. In this thesis, two optimal scheduling methods for charging electric vehicles were developed for merchant-owned charging facilities, the first with a single charger and the second with multiple chargers. In the mathematical model for the single merchant-owned charging station, the problem is formulated as a hybrid nonlinear optimization model and solved using a backward recursive algorithm with nonlinear optimization solvers. As for a single charger, a hybrid system framework was used to capture the tradeoff between demand charges and speed of charging. For the merchant-owned multiple chargers case, the problem is formulated as a mixed integer linear optimization challenge with three-dimensional matrices characterizing the solution space and was solved using the MOSEK optimization toolbox in MATLAB. The proposed algorithms have been analyzed for different penalty factors which were imposed on total waiting time of each EV. Final results are analyzed and discussed.