We propose a new deterministic global optimization algorithm for solving mixed-integer bilinear programs. It relies on a two-stage decomposition strategy featuring mixed-integer linear programming relaxations to compu...
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We propose a new deterministic global optimization algorithm for solving mixed-integer bilinear programs. It relies on a two-stage decomposition strategy featuring mixed-integer linear programming relaxations to compute estimates of the global optimum, and constrained non-linear versions of the original non-convex mixed-integernonlinear program to find feasible solutions. As an alternative to spatial branch-and-bound with bilinear envelopes, we use extensively piecewise relaxations for computing estimates and reducing variable domain through optimality-based bound tightening. The novelty is that the number of partitions, a critical tuning parameter affecting the quality of the relaxation and computational time, increases and decreases dynamically based on the computational requirements of the previous iteration. Specifically, the algorithm alternates between piecewise McCormick and normalized multiparametric disaggregation. When solving ten benchmark problems from the literature, we obtain the same or better optimality gaps than two commercial global optimization solvers.
We propose a new medical evacuation (MEDEVAC) model with endogenous uncertainty in the casualty delivery times. The goal is to provide timely evacuation and medical treatment to injured soldiers. The model enforces th...
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We propose a new medical evacuation (MEDEVAC) model with endogenous uncertainty in the casualty delivery times. The goal is to provide timely evacuation and medical treatment to injured soldiers. The model enforces the "Golden Hour" evacuation doctrine, attempts to maximize the expected number of severely injured soldiers evacuated within one hour without delay, and represents the availability of air ambulances as an endogenous source of uncertainty. The MEDEVAC model is a mixed-integer nonlinear programming problem whose continuous relaxation is in general nonconvex and for which we develop an algorithmic method articulated around (i) new bounding techniques obtained through the solution of restriction and relaxation problems and (ii) a spatial branch-and-bound algorithm solving conic mixed-integer programs at each node. The computational study, based on data from Operation Enduring Freedom, reveals that the bounding problems can be quickly solved regardless of problem size, the bounds are tight, and the spatial branch-and-bound dominates the CPLEX and BARON solvers in terms of computational time and robustness. Compared to the MEDEVAC myopic policy, our approach increases the number of casualties treated timely and can contribute to reducing the number of deaths on the battlefield. The benefits increase as the MEDEVAC resources become tighter and the combats intensify. The model can be used at the strategic level to design an efficient MEDEVAC system and at the tactical level for intelligent tasking and dispatching.
We consider the risk-averse uncapacitated facility location problem under stochastic disruptions. By the Conditional-value-at-risk, we control the risks at each individual customer, while previous works usually contro...
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We consider the risk-averse uncapacitated facility location problem under stochastic disruptions. By the Conditional-value-at-risk, we control the risks at each individual customer, while previous works usually control the entire networks. We show that our model provides more reliable solutions than previous ones. The resulting formulation is a mixed-integer nonlinear programming. In response, we develop a multi-dual decomposition algorithm based on the augmented Lagrangian and classic penalty function. A class of decomposed unconstrained subproblems are then solved by an iterative approach not relying on Lagrange multipliers and differentiability. Our experiments show that the algorithm performs well even for some larger problems.
We study a service network design problem in which the network operator wishes to determine facility locations and sizes in order to satisfy the demand of the customers while balancing the cost of the system with a me...
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We study a service network design problem in which the network operator wishes to determine facility locations and sizes in order to satisfy the demand of the customers while balancing the cost of the system with a measure of quality-of-service faced by the customers. We assume customers choose the facilities that meet demand, in order to minimize their total cost, including costs associated with traveling and waiting. When having demand served at a facility, customers face a service delay that depends on the total usage (congestion) of the facility. The total cost of meeting a customer's demand at a facility includes a facility-specific unit travel cost and a function of the service delay. When customers all minimize their own costs, the resulting distribution of customer demand to facilities is modeled as an equilibrium. This problem is motivated by several applications, including supplier selection in supply chain planning, preventive healthcare services planning, and shelter location-allocation in disaster management. We model the problem as a mixed-integer bilevel program that can be reformulated as a nonconvex mixed-integernonlinear program. The reformulated problem is difficult to solve by general-purpose solvers. Hence, we propose a Lagrangian relaxation approach that finds a candidate feasible solution along with a lower bound that can be used to validate the solution quality. The computational results indicate that the method can efficiently find feasible solutions, along with bounds on their optimality gap, even for large instances.
An alternative method for chemical process synthesis using a block-based superstructure representation is proposed. The block-based superstructure is a collection of blocks arranged in a two-dimensional grid. The assi...
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An alternative method for chemical process synthesis using a block-based superstructure representation is proposed. The block-based superstructure is a collection of blocks arranged in a two-dimensional grid. The assignment of different equipment on blocks and the determination of their connectivity are performed using a mixed-integernonlinear formulation for automated flowsheet generation and optimization-based process synthesis. Based on the special structure of the block representation, an efficient strategy is proposed to generate and successively refine feasible and optimized process flowsheets. Our approach is demonstrated using two process synthesis case studies adapted from the literature and one new process synthesis problem for methanol production from biogas (C) 2018 American Institute of Chemical Engineers
Although ionic liquids (ILs) have been widely explored as solvents for extractive desulfurization (EDS) of fuel oils, systematic studying of the optimal design of ILs for this process is still scarce. The UNIFAC-IL mo...
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Although ionic liquids (ILs) have been widely explored as solvents for extractive desulfurization (EDS) of fuel oils, systematic studying of the optimal design of ILs for this process is still scarce. The UNIFAC-IL model is extended first to describe the EDS system based on exhaustive experimental data. Then, based on the obtained UNIFAC-IL model and group contribution models for predicting the melting point and viscosity of ILs, a mixed-integer nonlinear programming (MINLP) problem is formulated for the purpose of computer-aided ionic liquid design (CAILD). The MINLP problem is solved to optimize the liquid-liquid extraction performance of ILs in a given multicomponent model EDS system, under consideration of constraints regarding the IL structure, thermodynamic and physical properties. The top five IL candidates preidentified from CAILD are further evaluated by means of process simulation using ASPEN Plus. Thereby, [C5MPy][C(CN)(3)] is identified as the most suitable solvent for EDS. (c) 2017 American Institute of Chemical Engineers
Work and heat exchanger networks have recently drawn increasing attention due to their paramount importance in achieving energy savings. In this work, we introduce a new optimization model for the cost-effective synth...
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Work and heat exchanger networks have recently drawn increasing attention due to their paramount importance in achieving energy savings. In this work, we introduce a new optimization model for the cost-effective synthesis and energy integration of work and heat exchanger networks considering unclassified process streams (ie., streams whose classification as hot or cold streams cannot be defined a priori). Our innovative modelling approach combines mathematical programming techniques and the pinch location method to obtain an optimal network design with minimal cost, while adjusting pressure and temperature levels of unclassified streams. We propose disjunctive operators for the selection of pressure manipulation equipment, and streams identity classification depending on energy requirements and process operating conditions. In addition, our approach addresses previous shortcomings by eliminating the need for: (i) assigning a specific route of pressure manipulation;and, (ii) classifying streams as low or high-pressure streams;which provides further flexibility to the system. Our methodology is also able to effectively deal with variable inlet and outlet streams temperatures to reach specific optimization goals. The model is solved to global optimality through the minimization of the process total annualized cost. Besides improved computational performance, results from energy analyses reveal that streams classification during process optimization can be greatly advantageous for both subambient and above-ambient applications. In the liquefied natural gas process, it reduces up to 89% the energy demand when compared to literature records.
This paper is on the problem of short-term hydro scheduling, particularly concerning a head-sensitive hydro chain. A novel mixed-integer nonlinear programming approach is proposed for optimizing power generation effic...
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This paper is on the problem of short-term hydro scheduling, particularly concerning a head-sensitive hydro chain. A novel mixed-integer nonlinear programming approach is proposed for optimizing power generation efficiency. The proposed approach considers not only the nonlinear dependence between power generation, water discharge and head, but also start-up costs for the hydro units and discontinuous operating regions, in order to obtain more realistic and feasible results. Numerical results based on one of the main Portuguese cascaded hydro systems illustrate the proficiency of the proposed approach.
This paper presents a mixed-integer quadratically constrained programming (MIQCP) formulation for B-spline constraints. The formulation can be used to obtain an exact MIQCP reformulation of any spline-constrained opti...
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This paper presents a mixed-integer quadratically constrained programming (MIQCP) formulation for B-spline constraints. The formulation can be used to obtain an exact MIQCP reformulation of any spline-constrained optimization problem problem, provided that the polynomial spline functions are continuous. This reformulation allows practitioners to use a general-purpose MIQCP solver, instead of a special-purpose spline solver, when solving B-spline constrained problems. B-splines are a powerful and widely used modeling tool, previously restricted from optimization due to lack of solver support. This contribution may encourage practitioners to use B-splines to model constraint functions. However, as the numerical study suggests, there is still a large gap between the solve times of the general-purpose solvers using the proposed formulation, and the special-purpose spline solver CENSO, the latter being significantly lower.
The objective of this paper is to jointly optimize supplier selection, pipeline and safety stock inventories, and production-sales policies for new products over multiple planning horizons such that the total" pr...
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The objective of this paper is to jointly optimize supplier selection, pipeline and safety stock inventories, and production-sales policies for new products over multiple planning horizons such that the total" profit over the product's life-cycle is maximized. A mixed-integer nonlinear programming model is proposed that not only allows for adjusting the level of pipeline and safety stocks at different supply chain stages, but also for switching suppliers and/or modifying their demand allocations in different planning horizons in response to changes in the new product's demand. A representative supply chain network for computer assembly is then used to illustrate the applicability of the model. The findings from our numerical experiments with the model can potentially have important implications for future research and practice. In contrast to the traditional understanding of flexibility, the results indicate that the total profit may not necessarily be an increasing function of the number of planning horizons. The performance of commonly used heuristic policies for supplier selection as well as different myopic and build-up production-sales policies are also compared with the model's prescribed solutions in order to provide insight on when such heuristic policies and combinations thereof can be effective. The interdependency between supplier switching cost and the number of build-up periods is also illustrated.
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