The Branch-And-Reduce Optimization Navigator (BARON) is a computational system for facilitating the solution of nonconvex optimization problems to global optimality. We provide a brief description of the algorithms us...
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The Branch-And-Reduce Optimization Navigator (BARON) is a computational system for facilitating the solution of nonconvex optimization problems to global optimality. We provide a brief description of the algorithms used by the software, describe the types of problems that can be currently solved and summarize our recent computational experience. BARON is available by anonymous ftp from ***.
This paper presents valid inequalities and range contraction techniques that can be used to reduce the size of the search space of global optimization problems. To demonstrate the algorithmic usefulness of these techn...
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This paper presents valid inequalities and range contraction techniques that can be used to reduce the size of the search space of global optimization problems. To demonstrate the algorithmic usefulness of these techniques, we incorporate them within the branch-and-bound framework. This results in a branch-and-reduce global optimization algorithm. A detailed discussion of the algorithm components and theoretical properties are provided. Specialized algorithms for polynomial and multiplicative programs are developed. Extensive computational results are presented for engineering design problems, standard global optimization test problems, univariate polynomial programs, linear multiplicative programs, mixed-integernonlinear programs and concave quadratic programs. For the problems solved, the computer implementation of the proposed algorithm provides very accurate solutions in modest computational time.
This paper deals with the synthesis and optimization of an isothermal CSTR-network for the industrially widespread cyclohexane oxidation process. Generally the mathematical representation of synthesis and optimization...
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This paper deals with the synthesis and optimization of an isothermal CSTR-network for the industrially widespread cyclohexane oxidation process. Generally the mathematical representation of synthesis and optimization problems is attained by a superstructure, which considers all reasonable process topologies with respect to feasible connectivity options and alternative unit operations. integer variables indicating the selection of process units from the superstructure and nonlinear process constraints arising from the unit models and thermodynamic calculations lead to a mixed-integer nonlinear programming (MINLP) optimization problem. Here a new approach is introduced, where the corresponding MINLP optimization problem is handled by a commercial equation-oriented flowsheeting package in combination with a mixed-integer Linear programming (MILP) routine.
According to the operation characteristics of such plants, on the basis of Mauderli-Wellons's research, the mathematical models of operation optimization are modified which consider the campaign formation and prod...
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According to the operation characteristics of such plants, on the basis of Mauderli-Wellons's research, the mathematical models of operation optimization are modified which consider the campaign formation and production plan problem respectively. A new heuristics is advanced to search for the dominant production campaigns. Comparing the heuristics with Mauderli's algorithm, it ensures that parallel items in-phase have the same batch and that each production line operates with optimized batch, therefore the plant has a larger processing rate. This heuristics can effectively relieve the bottlenecks, and avoid the complexity resulting from the nonconvexity of the model. Within the resource alocated, the mixed-integer algorithm is used to maximize the profit.
An extended version of Kelley's cutting plane method is introduced in the present paper. The extended method can be applied for the solution of convex MINLP (mixed-integer non-linear programming) problems, while K...
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An extended version of Kelley's cutting plane method is introduced in the present paper. The extended method can be applied for the solution of convex MINLP (mixed-integer non-linear programming) problems, while Kelley's cutting plane method was originally introduced for the solution of convex NLP (non-linear programming) problems only. The method is suitable for solving large convex MINLP problems with a moderate degree of nonlinearity. The convergence properties of the method are given in the present paper and an example is provided to illustrate the numerical procedure.
The package planning (chip layout and compaction) problem can be stated in terms of an optimization problem. The goal is to find the relative placement and shapes of the chips in a way that minimizes the total chip ar...
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The package planning (chip layout and compaction) problem can be stated in terms of an optimization problem. The goal is to find the relative placement and shapes of the chips in a way that minimizes the total chip area subject to linear and nonlinear constraints. The constraints arise from geometric design rules, distance and connectivity requirements between various components, area and communication costs and other designer-specified requirements. The problem has been addressed in various settings. It is of unusual computational difficulty due to the nonconvexities involved. This paper presents a new mixed-integer nonlinear programming formulation for simultaneous chip layout and two-dimensional compaction. Global optimization algorithms are developed for this model as well as for an existing formulation for the chip compaction problem. These algorithms are implemented with the global optimization software BARON and illustrated by solving several example problems.
This paper deals with designing of cryogenic distillation systems for the separation of hydrogen isotopes in a thermonuclear fusion process. The design must minimize the tritium inventory in the distillation columns a...
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This paper deals with designing of cryogenic distillation systems for the separation of hydrogen isotopes in a thermonuclear fusion process. The design must minimize the tritium inventory in the distillation columns and satisfy the separation requirements. This induces the optimization of both the structure and the operating conditions of the columns. Such a problem is solved by use of a mixed-integer nonlinear programming (MINLP) tool coupled to a process simulator. The MINLP procedure is based on the iterative and alternative treatment of two subproblems : a NLP problem which is solved by a reduced-gradient method, and a MILP problem, solved with a Branch and Bound method coupled to a simplexe. The formulation of the problem and the choice of an appropriate superstructure are here detailed, and results are finally presented, concerning the optimal design of a specific isotope separation system.
Overall strategy for capacity expansion of a plant has been found by investigating basic expansion methods for each major process item of a plant (BikiC et al., 1991). There are two different ways to providing capacit...
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Overall strategy for capacity expansion of a plant has been found by investigating basic expansion methods for each major process item of a plant (BikiC et al., 1991). There are two different ways to providing capacity for future expansions: overdesign and debottlenecking. To decide between these mutually exclusive design alternatives, we used mixed-integer non-linear programming (MINLP). MINLP formulation of design for future expansions is presented. The use of the proposed method is demonstrated in an example. Savings from ''optimal'' expansion strategy may amount up to 1O% of total fixed capital costs.
In parallel to the increase of computer sophistication, optimization techniques are finding wide applications in chemical process design. The chemical process synthesis problem can be stated as a mixed-integer nonline...
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In parallel to the increase of computer sophistication, optimization techniques are finding wide applications in chemical process design. The chemical process synthesis problem can be stated as a mixed-integer nonlinear programming problem, where the integer variables represent the process structure and the continuous variables refer to operating conditions of the process units. The formulation of a classical chemical engineering problem is presented in the first part on the paper. Three mathematical programming methods (GRG - branch and bound - and mixed-integer nonlinear programming) with increasing degree of sophistication are used to solve this problem, and the results are then compared. From this example, the mixed-integer nonlinear programming method appears to be the most powerful tool for solving chemical process synthesis problems, even though the branch and bound procedure is a well suitable approach for solving the particular problem of choosing configurations for a process. Finally it is shown that the introduction into the initial objective function of an outer penalty term on the number of process links may avoid equivalent process structures to be obtained.
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.
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