Ten years of feasibility pump, and counting

Berthold, Timo; Lodi, Andrea; Salvagnin, Domenico

doi:10.1007/s13675-018-0109-7

Cited by 19 publications

(11 citation statements)

References 39 publications

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“…In addition to these strategies, there are many other primal heuristics that can be used for MINLP problems, including the center-cut algorithm [39] and feasibility pumps [6,9].…”

Section: Primal Strategy Based On Heuristicsmentioning

confidence: 99%

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The supporting hyperplane optimization toolkit for convex MINLP

2022

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In this paper, an open-source solver for mixed-integer nonlinear programming (MINLP) problems is presented. The Supporting Hyperplane Optimization Toolkit (SHOT) combines a dual strategy based on polyhedral outer approximations (POA) with primal heuristics. The POA is achieved by expressing the nonlinear feasible set of the MINLP problem with linearizations obtained with the extended supporting hyperplane (ESH) and extended cutting plane (ECP) algorithms. The dual strategy can be tightly integrated with the mixed-integer programming (MIP) subsolver in a so-called single-tree manner, i.e., only a single MIP optimization problem is solved, where the polyhedral linearizations are added as lazy constraints through callbacks in the MIP solver. This enables the MIP solver to reuse the branching tree in each iteration, in contrast to most other POA-based methods. SHOT is available as a COIN-OR open-source project, and it utilizes a flexible task-based structure making it easy to extend and modify. It is currently available in GAMS, and can be utilized in AMPL, Pyomo and JuMP as well through its ASL interface. The main functionality and solution strategies implemented in SHOT are described in this paper, and their impact on the performance are illustrated through numerical benchmarks on 406 convex MINLP problems from the MINLPLib problem library. Many of the features introduced in SHOT can be utilized in other POA-based solvers as well. To show the overall effectiveness of SHOT, it is also compared to other state-of-the-art solvers on the same benchmark set.

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“…In addition to these strategies, there are many other primal heuristics that can be used for MINLP problems, including the center-cut algorithm [39] and feasibility pumps [6,9].…”

Section: Primal Strategy Based On Heuristicsmentioning

confidence: 99%

“…Finally, in Sect. 6 we present what we call the SHOT algorithm, i.e., a detailed overview of the individual steps implemented in the SHOT solver. These sections together provide a 'recipe' for creating a solver based on the method described in the previous section.…”

Section: Shot Is Available As An Open-source Coin-or Project 1 and Is...mentioning

confidence: 99%

The supporting hyperplane optimization toolkit for convex MINLP

2022

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“…Several modifications and improvements [3][4][5][6][7][8][9][10] have been proposed for this algorithm. See the bibliography in Reference [11] for a more extensive image. The case in which the l 1 norm is used for the representation error was analyzed and a modification of the Feasibility Pump algorithm for this problem was presented in Reference [12].…”

Section: Problem Formulationmentioning

confidence: 99%

Feasibility Pump Algorithm for Sparse Representation under Gaussian Noise

Miertoiu

Dumitrescu

2020

Algorithms

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In this paper, the Feasibility Pump is adapted for the problem of sparse representations of signals affected by Gaussian noise. This adaptation is tested and then compared to Orthogonal Matching Pursuit (OMP) and the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA). The feasibility pump recovers the true support much better than the other two algorithms and, as the SNR decreases and the support size increases, it has a smaller recovery and representation error when compared with its competitors. It is observed that, in order for the algorithm to be efficient, a regularization parameter and a weight term for the error are needed.

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“…In particular, the techniques apply to optimal control problems with ordinary differential equations. The method can be also seen as an adaptation of classical feasibility pump algorithms (for an overview, see [3]) with heavy structure exploitation for mixed-integer optimal control problems.…”

Section: Introductionmentioning

confidence: 99%

Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints

et al. 2021

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We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear programming techniques. The coupling is handled using a penalty-approach. We provide an exactness result for the penalty which yields a solution approach that convergences to partial minima. We compare the quality of these dedicated points with those of other heuristics amongst an academic example and also for the optimization of electric transmission lines with switching of the network topology for flow reallocation in order to satisfy demands.

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Ten years of feasibility pump, and counting

Cited by 19 publications

References 39 publications

The supporting hyperplane optimization toolkit for convex MINLP

The supporting hyperplane optimization toolkit for convex MINLP

Feasibility Pump Algorithm for Sparse Representation under Gaussian Noise

Penalty alternating direction methods for mixed-integer optimal control with combinatorial constraints

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