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12,755
Heuristics From Nature For Hard Combinatorial Optimization Problems
, 1996
"... In this paper we try to describe the main characters of Heuristics "derived" from Nature, a border area between Operations Research and Artificial Intelligence, with applications to graph optimization problems. These algorithms take inspiration from physics, biology, social sciences, and u ..."
Abstract
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Cited by 33 (0 self)
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. The paper is then composed of six review sections: each of them concerns a heuristic and its application to an NP-hard combinatorial optimization problem. We consider the following topics: genetic algorithms with timetable problems, simulated annealing with dial-a-ride problems, sampling & clustering
Efficiently Solvable Special Cases of Hard Combinatorial Optimization Problems
, 1997
"... We survey some recent advances in the field of polynomially solvable special cases of hard combinatorial optimization problems like the travelling salesman problem, quadratic assignment problems and Steiner tree problems. Such special cases can be found by considering special cost structures, the ge ..."
Abstract
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Cited by 3 (0 self)
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We survey some recent advances in the field of polynomially solvable special cases of hard combinatorial optimization problems like the travelling salesman problem, quadratic assignment problems and Steiner tree problems. Such special cases can be found by considering special cost structures
Towards Grid Implementations of Metaheuristics for Hard Combinatorial Optimization Problems
"... Metaheuristics are approximation algorithms that nd very good solutions to hard combinatorial optimization problems at the expense of large computational requirements. They do, however, offer a wide range of possibilities for implementations of effective robust parallel algorithms which run in much ..."
Abstract
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Metaheuristics are approximation algorithms that nd very good solutions to hard combinatorial optimization problems at the expense of large computational requirements. They do, however, offer a wide range of possibilities for implementations of effective robust parallel algorithms which run in much
Distributed Collective Adaptation Applied to a Hard Combinatorial Optimization Problem
"... We utilize collective memory to integrate weak and strong search heuristics to find cliques in FC, a family of graphs. We construct FC such that pruning of partial solutions will be ineffective. Each weak heuristic maintains a local cache of the collective memory. We examine the impact on the distri ..."
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To solve hard combinatorial optimization problems we can use parallel and distributed versions of serial search heuristics, which can either reduce the time taken to find the optimal solution or allow for the scaling up of problem complexity. We can add a collective memory (either centralized
TOWARDS HYBRID METHODS FOR SOLVING HARD COMBINATORIAL OPTIMIZATION PROBLEMS
, 2006
"... in my opinion, it ..."
Abstract—Everyone having used Constraint Programming
"... (CP) to solve hard combinatorial optimization problems with ..."
Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization
- SIAM Journal on Optimization
, 1993
"... We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to S ..."
Abstract
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Cited by 547 (12 self)
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mechanical way to algorithms for SDP with proofs of convergence and polynomial time complexity also carrying over in a similar fashion. Finally we study the significance of these results in a variety of combinatorial optimization problems including the general 0-1 integer programs, the maximum clique
The Ant System: Optimization by a colony of cooperating agents
- IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS-PART B
, 1996
"... An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call Ant System. We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation ..."
Abstract
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Cited by 1300 (46 self)
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An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call Ant System. We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed
Constrained model predictive control: Stability and optimality
- AUTOMATICA
, 2000
"... Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence and t ..."
Abstract
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Cited by 738 (16 self)
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Model predictive control is a form of control in which the current control action is obtained by solving, at each sampling instant, a finite horizon open-loop optimal control problem, using the current state of the plant as the initial state; the optimization yields an optimal control sequence
Optimally sparse representation in general (non-orthogonal) dictionaries via ℓ¹ minimization
- PROC. NATL ACAD. SCI. USA 100 2197–202
, 2002
"... Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work considered ..."
Abstract
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Cited by 633 (38 self)
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Given a ‘dictionary’ D = {dk} of vectors dk, we seek to represent a signal S as a linear combination S = ∑ k γ(k)dk, with scalar coefficients γ(k). In particular, we aim for the sparsest representation possible. In general, this requires a combinatorial optimization process. Previous work
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