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Integer programming approaches for minimum stabbing problems

Breno Piva, Cid C. de Souza, Yuri Frota, Luidi Simonetti (2014)

RAIRO - Operations Research - Recherche Opérationnelle

The problem of finding structures with minimum stabbing number has received considerable attention from researchers. Particularly, [10] study the minimum stabbing number of perfect matchings (mspm), spanning trees (msst) and triangulations (mstr) associated to set of points in the plane. The complexity of the mstr remains open whilst the other two are known to be 𝓝𝓟-hard. This paper presents integer programming (ip) formulations for these three problems, that allowed us to...

Learnheuristics: hybridizing metaheuristics with machine learning for optimization with dynamic inputs

Laura Calvet, Jésica de Armas, David Masip, Angel A. Juan (2017)

Open Mathematics

This paper reviews the existing literature on the combination of metaheuristics with machine learning methods and then introduces the concept of learnheuristics, a novel type of hybrid algorithms. Learnheuristics can be used to solve combinatorial optimization problems with dynamic inputs (COPDIs). In these COPDIs, the problem inputs (elements either located in the objective function or in the constraints set) are not fixed in advance as usual. On the contrary, they might vary in a predictable (non-random)...

MEMOTS: a memetic algorithm integrating tabu search for combinatorial multiobjective optimization

Thibaut Lust, Jacques Teghem (2008)

RAIRO - Operations Research

We present in this paper a new multiobjective memetic algorithm scheme called MEMOX. In current multiobjective memetic algorithms, the parents used for recombination are randomly selected. We improve this approach by using a dynamic hypergrid which allows to select a parent located in a region of minimal density. The second parent selected is a solution close, in the objective space, to the first parent. A local search is then applied to the offspring. We experiment this scheme with a new multiobjective...

Metaheuristics based on Bin Packing for the line balancing problem

Michel Gourgand, Nathalie Grangeon, Sylvie Norre (2007)

RAIRO - Operations Research

The line balancing problem consits in assigning tasks to stations in order to respect precedence constraints and cycle time constraints. In this paper, the cycle time is fixed and the objective is to minimize the number of stations. We propose to use metaheuristics based on simulated annealing by exploiting the link between the line balancing problem and the bin packing problem. The principle of the method lies in the combination between a metaheuristic and a bin packing heuristic. Two representations of...

MIP-based heuristics for multi-item capacitated lot-sizing problem with setup times and shortage costs

Nabil Absi, Safia Kedad-Sidhoum (2007)

RAIRO - Operations Research

We address a multi-item capacitated lot-sizing problem with setup times that arises in real-world production planning contexts. Demand cannot be backlogged, but can be totally or partially lost. Safety stock is an objective to reach rather than an industrial constraint to respect. The problem is NP-hard. We propose mixed integer programming heuristics based on a planning horizon decomposition strategy to find a feasible solution. The planning horizon is partitioned into several sub-horizons over...

New algorithms for coupled tasks scheduling – a survey

Jacek Blazewicz, Grzegorz Pawlak, Michal Tanas, Wojciech Wojciechowicz (2012)

RAIRO - Operations Research - Recherche Opérationnelle

The coupled tasks scheduling problem is a class of scheduling problems introduced for beam steering software of sophisticated radar devices, called phased arrays. Due to increasing popularity of such radars, the importance of coupled tasks scheduling is constantly growing. Unfortunately, most of the coupled tasks problems are NP-hard, and only a few practically usable algorithms for such problems were found. This paper provides a survey of already known complexity results of various variants of...

Niching mechanisms in evolutionary computations

Zdzisław Kowalczuk, Tomasz Białaszewski (2006)

International Journal of Applied Mathematics and Computer Science

Different types of niching can be used in genetic algorithms (GAs) or evolutionary computations (ECs) to sustain the diversity of the sought optimal solutions and to increase the effectiveness of evolutionary multi-objective optimization solvers. In this paper four schemes of niching are proposed, which are also considered in two versions with respect to the method of invoking: a continuous realization and a periodic one. The characteristics of these mechanisms are discussed, while as their performance...

Non-parametric approximation of non-anticipativity constraints in scenario-based multistage stochastic programming

Jean-Sébastien Roy, Arnaud Lenoir (2008)

Kybernetika

We propose two methods to solve multistage stochastic programs when only a (large) finite set of scenarios is available. The usual scenario tree construction to represent non-anticipativity constraints is replaced by alternative discretization schemes coming from non-parametric estimation ideas. In the first method, a penalty term is added to the objective so as to enforce the closeness between decision variables and the Nadaraya–Watson estimation of their conditional expectation. A numerical application...

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