The Experts below are selected from a list of 96162 Experts worldwide ranked by ideXlab platform
Ruth Misener - One of the best experts on this subject based on the ideXlab platform.
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using functional programming to recognize Named Structure in an optimization problem application to pooling
2016Co-Authors: Francesco Ceccon, Georgia Kouyialis, Ruth MisenerAbstract:Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting Named special Structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling Structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network Structures; we show that we can additionally detect nonlinear pooling patterns. Finding Named Structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the Named Structure. To demonstrate the recognition algorithm, we use the recognized Structure to apply primal heuristics to a test set of standard pooling problems. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3085–3095, 2016
Misener R - One of the best experts on this subject based on the ideXlab platform.
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Using functional programming to recognize Named Structure in an optimization problem: Application to pooling
2016Co-Authors: Ceccon F, Misener RAbstract:The pooling problem is a nonconvex nonlinear optimization problem with applications including [1]: crude oil scheduling [2] , water networks [3], natural gas production [4] , fixed-charge transportation with product blending [5], hybrid energy systems [6] , and multi-period blend scheduling [7]. It is possible to integrate additional complexity into the pooling problem, e.g., allowing mutable topological decisions [8] or nonlinear blending rules [9]. A wide variety of pooling variants with generic process networks applications can be found in MINLPLib. In solving process networks optimization problems there is a common theme: it is much easier to solve large-scale instantiations of the standard, archetypal pooling problem than it is to solve variants including mutable topology, nonlinear blending, or temporal aspects. For example, a recent primal heuristic performs consistently well on the order of 10k variables and constraints [10] , but the approach exploits the standard pooling network Structure and does not apply to pooling variants. Previous work in mixed-integer linear optimization (MILP) has found that using network Structure can significantly help generate strong cutting planes [11]. Automatically identifying these embedded networks in large-scale optimization models is NP-hard [12] , but there exist several polynomial time approximation algorithms to find good networks [13]. State-of-the-art MILP solver software, such as CPLEX uses preprocessing heuristics to automatically find these network patterns. More recent work has considered detecting more complex Structures such as multi-commodity flow [14] . This manuscript proposes automatically recognizing pooling Structure within a mixed integer nonlinear optimization problem (MINLP). The pooling Structure inside of a generic process optimization problem is a subset of the entire problem, so specialized, pooling-specific, cutting planes will also be valid bounds for the entire process networks problem. We also show that primal heuristic solutions to the standard pooling problem would be a good starting point for primal heuristics for the entire optimization problem. Identifying pooling problem Structure hinges on pattern matching. Patterns are defined by which variables and coefficients are expected in a constraint and by constraint bounds. The implementation is in F#, a strongly typed functional programming language targeting the .NET runtime environment. Pattern matching, one of the most distinctive F# features, has many uses, from decomposing data to control flow. The core concept is defining how data is expected to look and acting accordingly. We tested the implementation on 3 sets of input OSiL files: the 70 large-scale standard pooling Dey and Gupte [10] examples, the 16 standard and extended Misener et al. [15] examples, and the 1342 MINLPLib test cases. For each test set, we read in a flat optimization problem and try to produce a pooling network. The implementation successfully deduces the original network Structure for all 70 Dey and Gupte [10] examples, i.e., large-scale, standard pooling problems with up to 40 input, 30 pool, and 50 output nodes. Running our implementation on the 1342 test cases in MINLPLib2, 3 produce complete pooling problems and 78 more produce a pooling-like network. We also show that, after detecting the pooling problem in the flat MINLP, we can apply a good heuristic approach to get a good approximation solution
Francesco Ceccon - One of the best experts on this subject based on the ideXlab platform.
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using functional programming to recognize Named Structure in an optimization problem application to pooling
2016Co-Authors: Francesco Ceccon, Georgia Kouyialis, Ruth MisenerAbstract:Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting Named special Structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling Structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network Structures; we show that we can additionally detect nonlinear pooling patterns. Finding Named Structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the Named Structure. To demonstrate the recognition algorithm, we use the recognized Structure to apply primal heuristics to a test set of standard pooling problems. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3085–3095, 2016
Ceccon F - One of the best experts on this subject based on the ideXlab platform.
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Using functional programming to recognize Named Structure in an optimization problem: Application to pooling
2016Co-Authors: Ceccon F, Misener RAbstract:The pooling problem is a nonconvex nonlinear optimization problem with applications including [1]: crude oil scheduling [2] , water networks [3], natural gas production [4] , fixed-charge transportation with product blending [5], hybrid energy systems [6] , and multi-period blend scheduling [7]. It is possible to integrate additional complexity into the pooling problem, e.g., allowing mutable topological decisions [8] or nonlinear blending rules [9]. A wide variety of pooling variants with generic process networks applications can be found in MINLPLib. In solving process networks optimization problems there is a common theme: it is much easier to solve large-scale instantiations of the standard, archetypal pooling problem than it is to solve variants including mutable topology, nonlinear blending, or temporal aspects. For example, a recent primal heuristic performs consistently well on the order of 10k variables and constraints [10] , but the approach exploits the standard pooling network Structure and does not apply to pooling variants. Previous work in mixed-integer linear optimization (MILP) has found that using network Structure can significantly help generate strong cutting planes [11]. Automatically identifying these embedded networks in large-scale optimization models is NP-hard [12] , but there exist several polynomial time approximation algorithms to find good networks [13]. State-of-the-art MILP solver software, such as CPLEX uses preprocessing heuristics to automatically find these network patterns. More recent work has considered detecting more complex Structures such as multi-commodity flow [14] . This manuscript proposes automatically recognizing pooling Structure within a mixed integer nonlinear optimization problem (MINLP). The pooling Structure inside of a generic process optimization problem is a subset of the entire problem, so specialized, pooling-specific, cutting planes will also be valid bounds for the entire process networks problem. We also show that primal heuristic solutions to the standard pooling problem would be a good starting point for primal heuristics for the entire optimization problem. Identifying pooling problem Structure hinges on pattern matching. Patterns are defined by which variables and coefficients are expected in a constraint and by constraint bounds. The implementation is in F#, a strongly typed functional programming language targeting the .NET runtime environment. Pattern matching, one of the most distinctive F# features, has many uses, from decomposing data to control flow. The core concept is defining how data is expected to look and acting accordingly. We tested the implementation on 3 sets of input OSiL files: the 70 large-scale standard pooling Dey and Gupte [10] examples, the 16 standard and extended Misener et al. [15] examples, and the 1342 MINLPLib test cases. For each test set, we read in a flat optimization problem and try to produce a pooling network. The implementation successfully deduces the original network Structure for all 70 Dey and Gupte [10] examples, i.e., large-scale, standard pooling problems with up to 40 input, 30 pool, and 50 output nodes. Running our implementation on the 1342 test cases in MINLPLib2, 3 produce complete pooling problems and 78 more produce a pooling-like network. We also show that, after detecting the pooling problem in the flat MINLP, we can apply a good heuristic approach to get a good approximation solution
Georgia Kouyialis - One of the best experts on this subject based on the ideXlab platform.
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using functional programming to recognize Named Structure in an optimization problem application to pooling
2016Co-Authors: Francesco Ceccon, Georgia Kouyialis, Ruth MisenerAbstract:Branch-and-cut optimization solvers typically apply generic algorithms, e.g., cutting planes or primal heuristics, to expedite performance for many mathematical optimization problems. But solver software receives an input optimization problem as vectors of equations and constraints containing no structural information. This article proposes automatically detecting Named special Structure using the pattern matching features of functional programming. Specifically, we deduce the industrially-relevant nonconvex nonlinear Pooling Problem within a mixed-integer nonlinear optimization problem and show that we can uncover pooling Structure in optimization problems which are not pooling problems. Previous work has shown that preprocessing heuristics can find network Structures; we show that we can additionally detect nonlinear pooling patterns. Finding Named Structures allows us to apply, to generic optimization problems, cutting planes or primal heuristics developed for the Named Structure. To demonstrate the recognition algorithm, we use the recognized Structure to apply primal heuristics to a test set of standard pooling problems. © 2016 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 62: 3085–3095, 2016
