Exploring relaxation induced neighborhoods to improve MIP solutions

Danna, Emilie; Rothberg, Edward; Pape, Claude Le

doi:10.1007/s10107-004-0518-7

Cited by 421 publications

(245 citation statements)

References 21 publications

Supporting

Mentioning

233

Contrasting

Unclassified

Order By: Relevance

“…Danna et al [10] present an approach called Relaxation Induced Neighborhood Search (RINS) in order to explore the neighborhoods of promising MIP solutions more intensively. The main idea is to occasionally devise a sub-MIP at a node of the B&B tree that corresponds to a certain neighborhood of an incumbent solution: First, variables having the same values in the incumbent and in the current solution of the LP-relaxation are fixed.…”

Section: Metaheuristics For Strategic Guidance Of Exact Search Frencmentioning

confidence: 99%

Combining Metaheuristics and Exact Algorithms in Combinatorial Optimization: A Survey and Classification

Puchinger

Raidl

2005

Artificial Intelligence and Knowledge Engineering Applications: A Bioinspired Approach

216

118

View full text Add to dashboard Cite

Abstract. In this survey we discuss different state-of-the-art approaches of combining exact algorithms and metaheuristics to solve combinatorial optimization problems. Some of these hybrids mainly aim at providing optimal solutions in shorter time, while others primarily focus on getting better heuristic solutions. The two main categories in which we divide the approaches are collaborative versus integrative combinations. We further classify the different techniques in a hierarchical way. Altogether, the surveyed work on combinations of exact algorithms and metaheuristics documents the usefulness and strong potential of this research direction.

show abstract

Section: Metaheuristics For Strategic Guidance Of Exact Search Frencmentioning

confidence: 99%

Combining Metaheuristics and Exact Algorithms in Combinatorial Optimization: A Survey and Classification

Puchinger

Raidl

2005

Artificial Intelligence and Knowledge Engineering Applications: A Bioinspired Approach

216

118

View full text Add to dashboard Cite

show abstract

“…Another fixing method is based on the idea of Relaxation Induced Neighborhood Search (RINS) [9]. Let ν 2 and ν 3 be positive numbers which are smaller but close to 1 and ν 2 < ν 1 (e.g., ν 2 = 0.94 and ν 3 = 0.91).…”

Section: Primal Heuristicsmentioning

confidence: 99%

Algorithmic Cost Allocation Games: Theory and Applications

Hoàng

2012

Operations Research Proceedings

View full text Add to dashboard Cite

Due to economy of scale, it is suggested that individual users, in order to save costs, should join a cooperation rather than acting on their own. However, a challenge for individuals when cooperating with others is that every member of the cooperation has to agree on how to allocate the common costs among members, otherwise the cooperation cannot be realised. Taken this issue into account, we set the objective of our thesis in investigating the issue of fair allocations of common costs among users in a cooperation. This thesis combines cooperative game theory and state-ofthe-art algorithms from linear and integer programming in order to define fair cost allocations and calculate them numerically for large real-world applications. Our approaches outclasse traditional cost allocation methods in terms of fairness and users' satisfaction.Cooperative game theory analyzes the possible grouping of individuals to form their coalitions. It provides mathematical tools to understand fair prices in the sense that a fair price prevents the collapse of the grand coalition and increases the stability of the cooperation. The current definition of cost allocation game does not allow us to restrict the set of possible coalitions of players and to set conditions on the output prices, which often occur in real-world applications. Our generalization bring the cost allocation game model a step closer to practice. Based on our definition, we present and discuss in the thesis several mathematical concepts, which model fairness.This thesis also considers the question of whether there exists a "best" cost allocation, which people naturally like to have. It is well-known that multicriteria optimization problems often do not have "the optimal solution" that simultaneously optimizes each objective to its optimal value. There is also no "perfect" voting-system which can satisfy all the five simple, essential social choice procedures presented in the book "Mathematics and Politics. Strategy, Voting, Power and Proof" of Taylor et al. Similarly, the cost allocation problem is shown to experience the same problem. In i particular, there is no cost allocation which can satisfy all of our desired properties, which are coherent and seem to be reasonable or even indispensable. Our game theoretical concepts try to minimize the degree of axiomatic violation while the validity of some most important properties is kept.From the complexity point of view, it is NP-hard to calculate the allocations which are based on the considered game theoretical concepts. The hardest challenge is that we must take into account the exponential number of the possible coalitions. However, this difficulty can be overcome by using constraint generation approaches. Several primal and dual heuristics are constructed in order to decrease the solving time of the separation problem. Based on these techniques, we are able to solve our applications, whose sizes vary from small with 4 players, to medium with 18 players, and even large with 85 players and 2 85 − 1 possible c...

show abstract

“…Alternative heuristic techniques for ILP problems have been presented in the scientific literature: see for instance the relaxation induced neighborhood search technique illustrated by (Danna et al 2005); like all local search techniques it requires to be initialized with a feasible integer solution. Compared to other possible heuristic methods (greedy constructive algorithms, local search algorithms, meta-heuristics,...), our method based on iterated rounding does not require any initialization and it allows to solve to proven optimality small instances (when the ILP model is solvable in reasonable time) or to obtain estimates on the achieved approximation error for larger instances.…”

Section: Cordone Et Al: Optimization Of Multi-skill Call Centers Conmentioning

confidence: 99%

Optimization of Multi-skill Call Centers Contracts and Work-shifts

Cordone

Piselli²,

Ravizza³

et al. 2011

Service Science

View full text Add to dashboard Cite

all centers are complex systems in which it is essential to optimize the trade-off between the service level provided to the customers and the cost for the personnel. In this paper we describe a quantitative approach to choose the most suitable contracts to hire the call center operators. The aim is to organize their work-shifts and their rest periods, including lunch-breaks, in such a way that the mix of skills obtained in each time slot is as close as possible to a desired level, estimated according to demand forecasts. The approach here proposed is based on a heuristic method which exploits a general purpose linear programming solver.

show abstract

Exploring relaxation induced neighborhoods to improve MIP solutions

Cited by 421 publications

References 21 publications

Combining Metaheuristics and Exact Algorithms in Combinatorial Optimization: A Survey and Classification

Combining Metaheuristics and Exact Algorithms in Combinatorial Optimization: A Survey and Classification

Algorithmic Cost Allocation Games: Theory and Applications

Optimization of Multi-skill Call Centers Contracts and Work-shifts

Contact Info

Product

Resources

About