scholarly journals A partition-based branch-and-bound algorithm for the project duration problem with partially renewable resources and general temporal constraints

OR Spectrum ◽  
2021 ◽  
Author(s):  
Kai Watermeyer ◽  
Jürgen Zimmermann
Keyword(s):  
Exact Solution ◽  
Branch And Bound ◽  
Renewable Resources ◽  
State Of The Art ◽  
Branch And Bound Algorithm ◽  
Time Lags ◽  
Temporal Constraints ◽  
New Approach ◽  
Project Duration ◽  
Partially Renewable Resources

AbstractThe concept of partially renewable resources provides a general modeling framework that can be used for a wide range of different real-life applications. In this paper, we consider a resource-constrained project duration problem with partially renewable resources, where the temporal constraints between the activities are given by minimum and maximum time lags. We present a new branch-and-bound algorithm for this problem, which is based on a stepwise decomposition of the possible resource consumptions by the activities of the project. It is shown that the new approach results in a polynomially bounded depth of the enumeration tree, which is obtained by kind of a binary search. In a comprehensive experimental performance analysis, we compare our exact solution procedure with all branch-and-bound algorithms and state-of-the-art heuristics from the literature on different benchmark sets. The results of the performance study reveal that our branch-and-bound algorithm clearly outperforms all exact solution procedures. Furthermore, it is shown that our new approach dominates the state-of-the-art heuristics on well known benchmark instances.

scholarly journals Branch and bound algorithm for solving the total weighted tardiness criterion for the permutation flowshop scheduling problem with time lags

2021 ◽  
pp. 23-23
Author(s):  
Fatmah Almathkour ◽  
Omar Belgacem ◽  
Said Toumi ◽  
Bassem Jarboui
Keyword(s):  
Branch And Bound ◽  
Branch And Bound Algorithm ◽  
Total Weighted Tardiness ◽  
Time Lags ◽  
Scheduling Problem ◽  
Flowshop Scheduling ◽  
Permutation Flowshop ◽  
Weighted Tardiness ◽  
Time Requirements ◽  
Flowshop Scheduling Problem

This paper deals with the permutation flowshop scheduling problem with time lags constraints to minimize the total weighted tardiness criterion by using the Branch and Bound algorithm. A new lower bound was developed for the flowshop scheduling problem. The computational experiments indicate that the proposed algorithm provides good solution in terms of quality and time requirements.

Probabilistic Temporal Network for Numeric and Symbolic Time Information

2011 ◽  
pp. 67-86
Author(s):  
Malek Mouhoub ◽  
Jia Liu
Keyword(s):  
Branch And Bound ◽  
Real World ◽  
Possible Worlds ◽  
Constraint Satisfaction Problem ◽  
Constraint Propagation ◽  
Branch And Bound Algorithm ◽  
Temporal Constraints ◽  
Robust Solution ◽  
The Real ◽  
Interval Algebra

We propose a probabilistic extension of Allen’s Interval Algebra for managing uncertain temporal relations. Although previous work on various uncertain forms of quantitative and qualitative temporal networks have been proposed in the literature, little has been addressed to the most obvious type of uncertainty, namely the probabilistic one. More precisely, our model adapts the probabilistic Constraint Satisfaction Problem (CSP) framework in order to handle uncertain symbolic and numeric temporal constraints. In a probabilistic CSP, each constraint C is given a probability of its existence in the real world. There is thus more than one CSP to solve as opposed to the traditional CSP where no such uncertainties exist. In a probabilistic temporal CSP, since we use the Interval Algebra where a constraint is a disjunction of Allen primitives, the probability is assigned to each of these Allen primitives rather than to the temporal constraint. This means that a probabilistic temporal CSP involves many possible temporal CSPs, each with a probability of its existence. Solving a probabilistic temporal CSP consists of finding a scenario that has the highest probability to be the solution for the real world. This is an optimization problem that we solve using a branch and bound algorithm we propose and involving constraint propagation. Experimental study conducted on randomly generated temporal problems demonstrates the efficiency in time of our solving method. In the case of uncertain numeric constraints, our TemPro framework for handling numeric and symbolic temporal constraints is extended to handle uncertain domains. An algorithm for dividing domains into non-overlapping areas is proposed. This algorithm guarantees that the generated possible worlds do not intersect. Probable worlds are then constructed by combining these areas. A new branch and bound algorithm, we propose, is finally applied to find the most robust solution.

Vertex Selection Heuristics in Branch-and-Bound Algorithms for the Maximum k-Plex Problem

2019 ◽  
Vol 28 (05) ◽  
pp. 1950015
Author(s):  
Kuixian Wu ◽  
Jian Gao ◽  
Rong Chen ◽  
Xianji Cui
Keyword(s):  
Social Networks ◽  
Graph Theory ◽  
Branch And Bound ◽  
State Of The Art ◽  
The State ◽  
Branch And Bound Algorithm ◽  
Sparse Graphs ◽  
Historical Information ◽  
Branch And Bound Algorithms ◽  
Heuristic Strategies

As a relaxation of clique in graph theory, k-plex is a powerful tool for analyzing social networks and identifying cohesive structures in graphs. Recently, more and more researchers have concentrated on the algorithms for the maximum k-plex problem. Among those algorithms, a branch-and-bound algorithm proposed very recently shows a good performance on solving large sparse graphs, but does not work well on social networks. In this paper, we propose two novel vertex selection heuristic strategies for branching. The first one employs historical information of vertex reduction, and the second one is a combination of the first heuristic and the degree-based approach. Intensive experiments on Facebook benchmark show that the algorithm combining our heuristics outperforms the state-of-the-art algorithms.

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