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Solving Optimisation Problems with Catamorphisms
, 1992
"... . This paper contributes to an ongoing effort to construct a calculus for deriving programs for optimisation problems. The calculus is built around the notion of initial data types and catamorphisms which are homomorphisms on initial data types. It is shown how certain optimisation problems, which a ..."
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Cited by 12 (3 self)
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. This paper contributes to an ongoing effort to construct a calculus for deriving programs for optimisation problems. The calculus is built around the notion of initial data types and catamorphisms which are homomorphisms on initial data types. It is shown how certain optimisation problems, which
Some optimisation problems revisited
"... We consider some simple optimisation problems and employ a nontraditional method to solve them. We try to model both the problem and solution domains as algebraic structures, attempting to characterise the join operations on these domains. In each of the examples chosen, these structures turn out t ..."
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We consider some simple optimisation problems and employ a nontraditional method to solve them. We try to model both the problem and solution domains as algebraic structures, attempting to characterise the join operations on these domains. In each of the examples chosen, these structures turn out
On the Hardness of Decision and Optimisation Problems
, 1998
"... . Recent work on phase transition has detected apparently interesting phenomena in the distribution of hard optimisation problems (find, on some measure, the least m such that the given instance x has a solution of value m) and their corresponding decision problems (determine, for a given bound m wh ..."
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Cited by 10 (5 self)
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. Recent work on phase transition has detected apparently interesting phenomena in the distribution of hard optimisation problems (find, on some measure, the least m such that the given instance x has a solution of value m) and their corresponding decision problems (determine, for a given bound m
Multilevel Refinement for Combinatorial Optimisation Problems
 SE10 9LS
, 2001
"... Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found (some ..."
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Cited by 57 (5 self)
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Abstract. We consider the multilevel paradigm and its potential to aid the solution of combinatorial optimisation problems. The multilevel paradigm is a simple one, which involves recursive coarsening to create a hierarchy of approximations to the original problem. An initial solution is found
Logspace Optimisation Problems and their Approximation Properties
 Electronic Colloquium on Computational Complexity
, 2003
"... Abstract This paper introduces logspace optimisation problems as analogues of the wellstudied polynomialtime optimisation problems. Similarly to them, logspace optimisation problems can have vastly different approximation properties, even though the underlying existence and budget problems have t ..."
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Cited by 1 (0 self)
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Abstract This paper introduces logspace optimisation problems as analogues of the wellstudied polynomialtime optimisation problems. Similarly to them, logspace optimisation problems can have vastly different approximation properties, even though the underlying existence and budget problems have
Uncertain Constraint Optimisation Problems
"... Abstract Data uncertainties are inherent in the real world. The uncertain CSP (UCSP) is an extension of classical CSP that models incomplete and erroneous data by coefficients in the constraints whose values are unknown but bounded, for instance by an interval. It resolution is a closure, a set of p ..."
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Cited by 1 (1 self)
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of potential solutions. This paper extends the UCSP model to account for optimisation criteria, by defining the uncertain CSOP. The challenge is to combine optimisation (preferences over individual solutions) with a closure of a certain type (preference over sets of solutions) to a UCSOP. Unlike traditional
in dose optimisation problems.
"... Advantages of combining gamma scanning techniques and 3D dose simulation ..."
Portfolio Optimisation Problems
, 1996
"... . More generally there may be simple lower and upper bounds # i # x i # u i i = 1, . . . , n (1.1) on the weights (e.g. the fraction of the portfolio in property must be between 5% and 20%), and general linear constraints # n+i # a T i x # u n+i i = 1, . . . , m. (e.g. the total fractio ..."
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. More generally there may be simple lower and upper bounds # i # x i # u i i = 1, . . . , n (1.1) on the weights (e.g. the fraction of the portfolio in property must be between 5% and 20%), and general linear constraints # n+i # a T i x # u n+i i = 1, . . . , m. (e.g. the total fraction of the portfolio allocated to all international assets must not exceed 40%). Writing the constant vectors a i # R n as the rows of the matrix A # R mn defined by A T = [a 1 am ] the linear constraints are # # # x Ax # # u, (1.2) where # #<F11.
A Unified Model of Optimisation Problems
"... In this work, a conceptual software model of optimisation problems is developed. Problemspecific aspects are clearly identified as such. To achieve the desired separation between problems and solvers, the details of the problem are encapsulated, and mechanisms capable of supporting the optimisation ..."
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Cited by 1 (0 self)
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In this work, a conceptual software model of optimisation problems is developed. Problemspecific aspects are clearly identified as such. To achieve the desired separation between problems and solvers, the details of the problem are encapsulated, and mechanisms capable of supporting
On the use of CBR in optimisation problems such as the TSP
, 1995
"... The particular strength of CBR is normally considered to be its use in weak theory domains where solution quality is compiled into cases and is reusable. In this paper we explore an alternative use of CBR in optimisation problems where cases represent highly optimised structures in a huge highly ..."
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Cited by 5 (2 self)
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The particular strength of CBR is normally considered to be its use in weak theory domains where solution quality is compiled into cases and is reusable. In this paper we explore an alternative use of CBR in optimisation problems where cases represent highly optimised structures in a huge highly
Results 1  10
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