This paper is concerned with the multi-floor, cross-dock door assignment problem (MCDAP) to minimize the total material handling costs. We present a novel mixed-integer nonlinear programming model and a classic linear...
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This paper is concerned with the multi-floor, cross-dock door assignment problem (MCDAP) to minimize the total material handling costs. We present a novel mixed-integer nonlinear programming model and a classic linearization form for the MCDAP. We use a combination of multi-start, genetic random-key, and very-large-scale neighborhood search (VLSN) as the diversification strategies for the solution perturbation method embedded within the critical event Tabu search to solve MCDAP. We will test the proposed algorithms on a set of 60 very-large sized instances with 150-300 loading doors, and 100-300 unloading doors that raise size of cost matrix up to 90,000 by 90,000.
The transformer manufacturing cost minimisation (TMCM), also known as transformer design optimisation, is a complex constrained mixed-integer non-linear programming problem with discontinuous objective function. This ...
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The transformer manufacturing cost minimisation (TMCM), also known as transformer design optimisation, is a complex constrained mixed-integer non-linear programming problem with discontinuous objective function. This paper proposes an innovative method combining genetic algorithm (GA) and finite element method (FEM) for the solution of TMCM problem. The main contributions of the proposed method are: (a) introduction of an innovative recursive GA with a novel external elitism strategy associated with variable crossover and mutation rates resulting in an improved GA, (b) adoption of two particular finite element models of increased accuracy and high computational speed for the validation of the optimal design by computing the no-load loss and impedance and (c) combination of the innovative recursive GA with the two particular finite element models resulting in a proposed GA-FEM model that finds the global optimum, as concluded after several tests on actual transformer designs, while other existing methods provided suboptimal solutions that are 3.1-5.8% more expensive than the optimal solution.
Pre-control is a quality tool for quick set-up approvals, especially used in short-run processes. It is based on specifications instead of the natural variability of the process and uses cumulative counts in order to ...
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Pre-control is a quality tool for quick set-up approvals, especially used in short-run processes. It is based on specifications instead of the natural variability of the process and uses cumulative counts in order to yield a conclusion. Its main drawbacks are a high false alarm rate and a low power to detect process deviations, under certain circumstances. These issues can be addressed by making the technique more flexible, as shown in previous works. In this paper, we introduce a Mathematical programming approach in order to optimally determine the value of the pre-control parameters, so that it can meet the user's requirements while minimizing the sample size of the technique as much as possible. We propose and develop a mathematical model for optimal pre-control and perform some numerical experiments in order to show its effectiveness. Copyright (c) 2015John Wiley & Sons, Ltd.
Scheduling of crude oil operations is an important component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. The mathematical modeling of blending different crud...
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Scheduling of crude oil operations is an important component of overall refinery operations, because crude oil costs account for about 80% of the refinery turnover. The mathematical modeling of blending different crudes in storage tanks results in many bilinear terms, which transform the problem into a challenging, nonconvex, mixed-integer nonlinear programming (MINLP) optimization model. In practice, uncertainties are unavoidable and include demand fluctuations, ship arrival delays, equipment malfunction, and tank unavailability. In the presence of these uncertainties, an optimal schedule generated using nominal parameter values may often be suboptimal or even become infeasible. In this article, the robust optimization framework proposed by Lin et al. and Janak et al. is extended to develop a deterministic robust counterpart optimization model for demand uncertainty. The recently proposed branch and bound global optimization algorithm with piecewise-linear underestimation of bilinear terms by Li et al. is also extended to solve the nonconvex MINLP deterministic robust counterpart optimization model and generate robust schedules. Two examples are used to illustrate the capability of the proposed robust optimization approach, and the extended branch and bound global optimization algorithm for demand uncertainty. The computational results demonstrate that the obtained schedules are robust in the presence of demand uncertainty. (C) 2011 American Institute of Chemical Engineers AIChE J, 58: 23732396, 2012
We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO probl...
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We consider strategies for integrated design and control through the robust and efficient solution of a mixed-integer dynamic optimization (MIDO) problem. The algorithm is based on the transformation of the MIDO problem into a mixed-integer nonlinear programming (MINLP) program. In this approach, both the manipulated and controlled variables are discretized using a simultaneous dynamic optimization approach. We also develop three MINLP formulations based on a nonconvex formulation, the conventional Big.-M formulation and generalized disjunctive programming (GDP). In addition, we compare the outer approximation and NLP branch and bound algorithms on these formulations. This problem is applied to a system of two series connected continuous stirred tank reactors where a first-order reaction takes place. Our results demonstrate that the simultaneous MIDO approach is able to efficiently address the solution of the integrated design and control problem in a systematic way. (c) 2006 Elsevier Ltd. All rights reserved.
An outer-approximation algorithm is presented for solving mixed-integer nonlinear programming problems of a particular class. Linearity of the integer (or discrete) variables, and convexity of the nonlinear functions ...
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An outer-approximation algorithm is presented for solving mixed-integer nonlinear programming problems of a particular class. Linearity of the integer (or discrete) variables, and convexity of the nonlinear functions involving continuous variables are the main features in the underlying mathematical structure. Based on principles of decomposition, outer-approximation and relaxation, the proposed algorithm effectively exploits the structure of the problems, and consists of solving an alternating finite sequence of nonlinearprogramming subproblems and relaxed versions of a mixed-integer linear master program. Convergence and optimality properties of the algorithm are presented, as well as a general discussion on its implementation. Numerical results are reported for several example problems to illustrate the potential of the proposed algorithm for programs in the class addressed in this paper. Finally, a theoretical comparison with generalized Benders decomposition is presented on the lower bounds predicted by the relaxed master programs.
Gasoline is one of the most valuable products in an oil refinery and can account for as much as 60-70% of total profit. Optimal integrated scheduling of gasoline blending and order delivery operations can significantl...
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Gasoline is one of the most valuable products in an oil refinery and can account for as much as 60-70% of total profit. Optimal integrated scheduling of gasoline blending and order delivery operations can significantly increase profit by avoiding ship demurrage, improving customer satisfaction, minimizing quality give-aways, reducing costly transitions and slop generation, exploiting low-quality cuts, and reducing inventory costs. In this article, we first introduce a new unit-specific event-based continuous-time formulation for the integrated treatment of recipes, blending, and scheduling of gasoline blending and order delivery operations. Many operational features are included such as nonidentical parallel blenders, constant blending rate, minimum blend length and amount, blender transition times, multipurpose product tanks, changeovers, and piecewise constant profiles for blend component qualities and feed rates. To address the non-convexities arising from forcing constant blending rates during a run, we propose a hybrid global optimization approach incorporating a schedule adjustment procedure, iteratively via a mixed-integerprogramming and nonlinearprogramming scheme, and a rigorous deterministic global optimization approach. The computational results demonstrate that our proposed formulation does improve the mixed-integer linear programming relaxation of Li and Karimi, Ind. Eng. Chem. Res., 2011, 50, 9156-9174. All examples are solved to be 1%-global optimality with modest computational effort. (C) 2016 American Institute of Chemical Engineers
A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-t...
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A recent series of papers has examined the extension of disjunctive-programming techniques to mixed-integer second-order-cone programming. For example, it has been shown-by several authors using different techniques-that the convex hull of the intersection of an ellipsoid, , and a split disjunction, with , equals the intersection of with an additional second-order-cone representable (SOCr) set. In this paper, we study more general intersections of the form and , where is a SOCr cone, is a nonconvex cone defined by a single homogeneous quadratic, and H is an affine hyperplane. Under several easy-to-verify conditions, we derive simple, computable convex relaxations and , where is a SOCr cone. Under further conditions, we prove that these two sets capture precisely the corresponding conic/convex hulls. Our approach unifies and extends previous results, and we illustrate its applicability and generality with many examples.
This paper presents a model for loading margin calculation integrated with transmission line switching. A mixed-integernonlinear optimization model is developed which maximizes the loading margin of the system subjec...
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This paper presents a model for loading margin calculation integrated with transmission line switching. A mixed-integernonlinear optimization model is developed which maximizes the loading margin of the system subject to various operational system constraints. An iterative algorithm, based on the Benders decomposition method, is used to solve the problem. The proposed method is tested on medium and large scale test systems and optimization results are compared with that of a non-decomposed method to show the efficacy of the proposed approach. (C) 2014 Elsevier Ltd. All rights reserved.
This paper proposes an open-source distributed solver for solving Sparse Convex Optimization (SCO) problems over computational networks. Motivated by past algorithmic advances in mixed-integer optimization, the Sparse...
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This paper proposes an open-source distributed solver for solving Sparse Convex Optimization (SCO) problems over computational networks. Motivated by past algorithmic advances in mixed-integer optimization, the Sparse Convex Optimization Toolkit (SCOT) adopts a mixed-integer approach to find exact solutions to SCO problems. In particular, SCOT combines various techniques to transform the original SCO problem into an equivalent convex mixed-integer nonlinear programming (MINLP) problem that can benefit from high-performance and parallel computing platforms. To solve the equivalent mixed-integer problem, we present the Distributed Hybrid Outer Approximation (DiHOA) algorithm that builds upon the LP/NLP-based branch-and-bound and is tailored for this specific problem structure. The DiHOA algorithm combines the so-called single- and multi-tree outer approximation, naturally integrates a decentralized algorithm for distributed convex nonlinear subproblems, and employs enhancement techniques such as quadratic cuts. Finally, we present detailed computational experiments that show the benefit of our solver through numerical benchmarks on 140 SCO problems with distributed datasets. To show the overall efficiency of SCOT we also provide solution profiles comparing SCOT to other state-of-the-art MINLP solvers.
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