In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The pr...
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In this paper, we introduce a new generalized multiperiod scheduling version of the pooling problem to represent time varying blending systems. A general nonconvex MINLP formulation of the problem is presented. The primary difficulties in solving this optimization problem are the presence of bilinear terms, as well as binary decision variables required to impose operational constraints. An illustrative example is presented to provide unique insight into the difficulties faced by conventional MINLP approaches to this problem, specifically in finding feasible solutions. Based on recent work, a new radix-based discretization scheme is developed with which the problem can be reformulated approximately as an MILP, which is incorporated in a heuristic procedure and in two rigorous global optimization methods, and requires much less computational time than existing global optimization solvers. Detailed computational results of each approach are presented on a set of examples, including a comparison with other global optimization solvers. (C) 2013 Elsevier Ltd. All rights reserved.
An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed-integer dynamic opti...
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An efficient decomposition method to solve the integrated problem of scheduling and dynamic optimization for sequential batch processes is proposed. The integrated problem is formulated as a mixed-integer dynamic optimization problem or a large-scale mixed-integer nonlinear programming (MINLP) problem by discretizing the dynamic models. To reduce the computational complexity, we first decompose all dynamic models from the integrated problem, which is then approximated by a scheduling problem based on the flexible recipe. The recipe candidates are expressed by Pareto frontiers, which are determined offline by using multiobjective dynamic optimization to minimize the processing cost and processing time. The operational recipe is then optimized simultaneously with the scheduling decisions online. Because the dynamic models are encapsulated by the Pareto frontiers, the online problem is a mixed-integerprogramming problem which is much more computationally efficient than the original MINLP problem, and allows the online implementation to deal with uncertainties. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 2379-2406, 2013
We introduce a generalized orienteering problem (OP) where, as usual, a vehicle is routed from a prescribed start node, through a directed network, to a prescribed destination node, collecting rewards at each node vis...
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We introduce a generalized orienteering problem (OP) where, as usual, a vehicle is routed from a prescribed start node, through a directed network, to a prescribed destination node, collecting rewards at each node visited, to maximize the total reward along the path. In our generalization, transit on arcs in the network and reward collection at nodes both consume a variable amount of the same limited resource. We exploit this resource trade-off through a specialized branch-and-bound algorithm that relies on partial path relaxation problems that often yield tight bounds and lead to substantial pruning in the enumeration tree. We present the smuggler search problem (SSP) as an important real-world application of our generalized OP. Numerical results show that our algorithm applied to the SSP outperforms standard mixed-integer nonlinear programming solvers for moderate to large problem instances. We demonstrate model enhancements that allow practitioners to represent realistic search planning scenarios by accounting for multiple heterogeneous searchers and complex smuggler motion. (c) 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013
The short-term unit commitment (UC) problem of hydrothermal generation systems is a mixed-integer nonlinear programming (MINLP), which is difficult to solve efficiently, especially for large-scale instances. The persp...
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The short-term unit commitment (UC) problem of hydrothermal generation systems is a mixed-integer nonlinear programming (MINLP), which is difficult to solve efficiently, especially for large-scale instances. The perspective relaxation (PR) is an effective approach to constructing tight approximations to MINLP with semi-continuous variables. In this paper, the PR of UC problem is formulated as a mixedinteger second-order cone programming (SOCP) model because the quadratic polynomial cost function of the UC problem is SOCP-representable. The proposed model is implemented by using the commercial optimization software IBM CPLEX 12.4. Extensive numerical studies have been conducted to verify the advantages of our proposed method. Instances of the test system vary from 10 to 1000 units. Our results indicate that the proposed method performs better than the existing methods in terms of production cost savings and faster computational times, especially for large systems. (C) 2013 Elsevier Ltd. All rights reserved.
Over the last years, psychological research has increasingly used computer-supported tests, especially in the analysis of complex human decision making and problem solving. The approach is to use computerbased test sc...
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Over the last years, psychological research has increasingly used computer-supported tests, especially in the analysis of complex human decision making and problem solving. The approach is to use computerbased test scenarios and to evaluate the performance of participants and correlate it to certain attributes, such as the participant's capacity to regulate emotions. However, two important questions can only be answered with the help of modern optimization methodology. The first one considers an analysis of the exact situations and decisions that led to a bad or good overall performance of test persons. The second important question concerns performance, as the choices made by humans can only be compared to one another, but not to the optimal solution, as it is unknown in general. Additionally, these test-scenarios have usually been defined on a trial-and-error basis, until certain characteristics became apparent. The more complex models become, the more likely it is that unforeseen and unwanted characteristics emerge in studies. To overcome this important problem, we propose to use mathematical optimization methodology not only as an analysis and training tool, but also in the design stage of the complex problem scenario. We present a novel test scenario, the IWR Tailorshop, with functional relations and model parameters that have been formulated based on optimization results. We also present a tailored decomposition approach to solve the resulting mixed-integernonlinear programs with nonconvex relaxations and show some promising results of this approach. (C) 2012 Elsevier B.V. All rights reserved.
The distributed generation (DG) of combined heat and power (CHP) for commercial buildings is gaining increased interest, yet real-world installations remain limited. This lack of implementation is due, in part, to the...
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The distributed generation (DG) of combined heat and power (CHP) for commercial buildings is gaining increased interest, yet real-world installations remain limited. This lack of implementation is due, in part, to the challenging economics associated with volatile utility pricing and potentially high system capital costs. Energy technology application analyses are also faced with insufficient knowledge regarding how to appropriately design (i.e., configure and size) and dispatch (i.e., operate) an integrated CHP system. Existing research efforts to determine a minimum-cost-system design and dispatch do not consider many dynamic performance characteristics of generation and storage technologies. Consequently, we present a mixed-integer nonlinear programming (MINLP) model that prescribes a globally minimum cost system design and dispatch, and that includes off-design hardware performance characteristics for CHP and energy storage that are simplified or not considered in other models. Specifically, we model the maximum turn-down, start up, ramping, and part-load efficiency of power generation technologies, and the time-varying temperature of thermal storage technologies. The consideration of these characteristics can be important in applications for which system capacity, building demand, and/or utility guidelines dictate that the dispatch schedule of the devices varies over time. We demonstrate the impact of neglecting system dynamics by comparing the solution prescribed by a simpler, linear model with that of our MINLP for a case study consisting of a large hotel, located in southern Wisconsin, retrofitted with solid-oxide fuel cells (SOFCs) and a hot water storage tank. The simpler model overestimates the SOFC operational costs and, consequently, underestimates the optimal SOFC capacity by 15%. Published by Elsevier Ltd.
It is crucial nowadays for shipping companies to reduce bunker consumption while maintaining a certain level of shipping service in view of the high bunker price and concerned shipping emissions. After introducing the...
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It is crucial nowadays for shipping companies to reduce bunker consumption while maintaining a certain level of shipping service in view of the high bunker price and concerned shipping emissions. After introducing the three bunker consumption optimization contexts: minimization of total operating cost, minimization of emission and collaborative mechanisms between port operators and shipping companies, this paper presents a critical and timely literature review on mathematical solution methods for bunker consumption optimization problems. Several novel bunker consumption optimization methods are subsequently proposed. The applicability, optimality, and efficiency of the existing and newly proposed methods are also analyzed. This paper provides technical guidelines and insights for researchers and practitioners dealing with the bunker consumption issues. (C) 2013 Elsevier Ltd. All rights reserved.
The superstructure optimization of algae-based hydrocarbon biorefinery with sequestration of CO2 from power plant flue gas is proposed. The major processing steps include carbon capture, algae growth, dewatering, lipi...
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The superstructure optimization of algae-based hydrocarbon biorefinery with sequestration of CO2 from power plant flue gas is proposed. The major processing steps include carbon capture, algae growth, dewatering, lipid extraction and power generation, and algal biorefinery. We propose a multiobjective mixed-integer nonlinear programming (MINLP) model that simultaneously maximizes the net present value (NPV) and minimizes the global warming potential (GWP) subject to technology selection constraints, mass balance constraints, energy balance constraints, technoeconomic analysis constraints, and environmental impact constraints. The model simultaneously determines the optimal decisions that include production capacity, size of each processing unit, mass flow rates at each stage of the process, utility consumption, economic, and environmental performances. We propose a two-stage heuristic solution algorithm to solve the non-convex MINLP model. Finally, the bicriteria optimization problem is solved with e-constraint method, and the resulting Pareto-optimal curve reveals the trade-off between the economic and environmental criteria. The results show that for maximum NPV, the optimal process design uses direct flue gas, a tubular photobioreactor for algae growth, a filtration dewatering unit, and a hydroprocessing pathway leading to 47.1 MM gallons of green diesel production per year at $6.33/gal corresponding to GWP of 108.7 kg CO2-eq per gallon. (C) 2013 American Institute of Chemical Engineers AIChE J, 59: 1599-1621, 2013
Energy management systems (EMS) are vital supervisory control tools used to optimally operate and schedule Microgrids (MG). In this paper, an EMS algorithm based on mixed-integer nonlinear programming (MINLP) is prese...
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Energy management systems (EMS) are vital supervisory control tools used to optimally operate and schedule Microgrids (MG). In this paper, an EMS algorithm based on mixed-integer nonlinear programming (MINLP) is presented for MG in islanding mode considering different scenarios. A local energy market (LEM) is also proposed with in this EMS to obtain the cheapest price, maximizing the utilization of distributed energy resources. The proposed energy management is based on LEM and allows scheduling the MG generation with minimum information shared sent by generation units. Load demand management is carried out by demand response concept to improve reliability and efficiency as well as to reduce the total cost of energy (COE). Simulations are performed with real data to test the performance and accuracy of the proposed algorithm. The proposed algorithm is experimentally tested to evaluate processing speed as well as to validate the results obtained from the simulation setup on a real MG Testbed. The results of the EMS-MINLP based on LEM are compared with a conventional EMS based on LEM. Simulation and experimental results show the effectiveness of the proposed algorithm which provides a reduction of 15% in COE, in comparison with conventional EMS. (C) 2013 Elsevier Ltd. All rights reserved.
This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road net...
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This paper addresses the discrete network design problem (DNDP) with multiple capacity levels, or multi-capacity DNDP for short, which determines the optimal number of lanes to add to each candidate link in a road network. We formulate the problem as a bi-level programming model, where the upper level aims to minimize the total travel time via adding new lanes to candidate links and the lower level is a traditional Wardrop user equilibrium (UE) problem. We propose two global optimization methods by taking advantage of the relationship between UE and system optimal (SO) traffic assignment principles. The first method, termed as SO-relaxation, exploits the property that an optimal network design solution under SO principle can be a good approximate solution under UE principle, and successively sorts the solutions in the order of increasing total travel time under SO principle. Optimality is guaranteed when the lower bound of the total travel time of the unexplored solutions under UE principle is not less than the total travel time of a known solution under UE principle. The second method, termed as UE-reduction, adds the objective function of the Beckmann-McGuire-Winsten transformation of UE traffic assignment to the constraints of the SO-relaxation formulation of the multi-capacity DNDP. This constraint is convex and strengthens the SO-relaxation formulation. We also develop a dynamic outer-approximation scheme to make use of the state-of-the-art mixed-integer linear programming solvers to solve the SO-relaxation formulation. Numerical experiments based on a two-link network and the Sioux-Falls network are conducted. (C) 2013 Elsevier Ltd. All rights reserved.
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