branch and bound
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2031 ◽  
Vol 15 (3) ◽  
pp. 1-24
Jose Barambones ◽  
Florian Richoux ◽  
Ricardo Imbert ◽  
Katsumi Inoue

Team formation (TF) faces the problem of defining teams of agents able to accomplish a set of tasks. Resilience on TF problems aims to provide robustness and adaptability to unforeseen events involving agent deletion. However, agents are unaware of the inherent social welfare in these teams. This article tackles the problem of how teams can minimise their effort in terms of organisation and communication considering these dynamics. Our main contribution is twofold: first, we introduce the Stabilisable Team Formation (STF) as a generalisation of current resilient TF model, where a team is stabilisable if it possesses and preserves its inter-agent organisation from a graph-based perspective. Second, our experiments show that stabilisability is able to reduce the exponential execution time in several units of magnitude with the most restrictive configurations, proving that communication effort in subsequent task allocation problems are relaxed compared with current resilient teams. To do so, we developed SBB-ST, a branch-and-bound algorithm based on Distributed Constrained Optimisation Problems (DCOP) to compute teams. Results evidence that STF improves their predecessors, extends the resilience to subsequent task allocation problems represented as DCOP, and evidence how Stabilisability contributes to resilient TF problems by anticipating decisions for saving resources and minimising the effort on team organisation in dynamic scenarios.

Vahid Mahmoodian ◽  
Iman Dayarian ◽  
Payman Ghasemi Saghand ◽  
Yu Zhang ◽  
Hadi Charkhgard

This study introduces a branch-and-bound algorithm to solve mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). This class of optimization problems arises in many applications, such as finding a Nash bargaining solution (Nash social welfare optimization), capacity allocation markets, reliability optimization, etc. The proposed algorithm applies multiobjective optimization principles to solve MIBL-MMPs exploiting a special characteristic in these problems. That is, taking each multiplicative term in the objective function as a dummy objective function, the projection of an optimal solution of MIBL-MMPs is a nondominated point in the space of dummy objectives. Moreover, several enhancements are applied and adjusted to tighten the bounds and improve the performance of the algorithm. The performance of the algorithm is investigated by 400 randomly generated sample instances of MIBL-MMPs. The obtained result is compared against the outputs of the mixed-integer second order cone programming (SOCP) solver in CPLEX and a state-of-the-art algorithm in the literature for this problem. Our analysis on this comparison shows that the proposed algorithm outperforms the fastest existing method, that is, the SOCP solver, by a factor of 6.54 on average. Summary of Contribution: The scope of this paper is defined over a class of mixed-integer programs, the so-called mixed-integer bilinear maximum multiplicative programs (MIBL-MMPs). The importance of MIBL-MMPs is highlighted by the fact that they are encountered in applications, such as Nash bargaining, capacity allocation markets, reliability optimization, etc. The mission of the paper is to introduce a novel and effective criterion space branch-and-cut algorithm to solve MIBL-MMPs by solving a finite number of single-objective mixed-integer linear programs. Starting with an initial set of primal and dual bounds, our proposed approach explores the efficient set of the multiobjective problem counterpart of the MIBL-MMP through a criterion space–based branch-and-cut paradigm and iteratively improves the bounds using a branch-and-bound scheme. The bounds are obtained using novel operations developed based on Chebyshev distance and piecewise McCormick envelopes. An extensive computational study demonstrates the efficacy of the proposed algorithm.

2022 ◽  
pp. 209-220
Thomas Bläsius ◽  
Tobias Friedrich ◽  
David Stangl ◽  
Christopher Weyand

2022 ◽  
Vol 13 (2) ◽  
pp. 255-266 ◽  
Marcelo Seido Nagano ◽  
Mauricio Iwama Takano ◽  
João Vítor Silva Robazzi

In this paper it is presented an improvement of the branch and bound algorithm for the permutation flow shop problem with blocking-in-process and setup times with the objective of minimizing the total flow time and tardiness, which is known to be NP-Hard when there are two or more machines involved. With that objective in mind, a new machine-based lower bound that exploits some structural properties of the problem. A database with 27 classes of problems, varying in number of jobs (n) and number of machines (m) was used to perform the computational experiments. Results show that the algorithm can deal with most of the problems with less than 20 jobs in less than one hour. Thus, the method proposed in this work can solve the scheduling of many applications in manufacturing environments with limited buffers and separated setup times.

2021 ◽  
pp. 1-21
Chu-Min Li ◽  
Zhenxing Xu ◽  
Jordi Coll ◽  
Felip Manyà ◽  
Djamal Habet ◽  

The Maximum Satisfiability Problem, or MaxSAT, offers a suitable problem solving formalism for combinatorial optimization problems. Nevertheless, MaxSAT solvers implementing the Branch-and-Bound (BnB) scheme have not succeeded in solving challenging real-world optimization problems. It is widely believed that BnB MaxSAT solvers are only superior on random and some specific crafted instances. At the same time, SAT-based MaxSAT solvers perform particularly well on real-world instances. To overcome this shortcoming of BnB MaxSAT solvers, this paper proposes a new BnB MaxSAT solver called MaxCDCL. The main feature of MaxCDCL is the combination of clause learning of soft conflicts and an efficient bounding procedure. Moreover, the paper reports on an experimental investigation showing that MaxCDCL is competitive when compared with the best performing solvers of the 2020 MaxSAT Evaluation. MaxCDCL performs very well on real-world instances, and solves a number of instances that other solvers cannot solve. Furthermore, MaxCDCL, when combined with the best performing MaxSAT solvers, solves the highest number of instances of a collection from all the MaxSAT evaluations held so far.

Algorithms ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 365
Slim Belhaiza

When several Nash equilibria exist in the game, decision-makers need to refine their choices based on some refinement concepts. To this aim, the notion of a ϵ-proper equilibria set for polymatrix games is used to develop 0–1 mixed linear programs and compute ϵ-proper Nash equilibria. A Branch-and-Bound exact arithmetics algorithm is proposed. Experimental results are provided on polymatrix games randomly generated with different sizes and densities.

OR Spectrum ◽  
2021 ◽  
Kai Watermeyer ◽  
Jürgen Zimmermann

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.

2021 ◽  
Vol 18 (2) ◽  
pp. 188-198
D Wungguli ◽  
S S Ibrahim ◽  
L Yahya

Penelitian ini dilakukan untuk menentukan muatan barang yang akan dijual dengan menggunakan media muatan yang memiliki kapasitas terbatas dalam memperoleh keuntungan maksimum. Data yang digunakan yaitu berupa berat barang, keuntungan, dan kapasitas maksimum media muatan. Selanjutnya dilakukan perhitungan berupa berat total dan keuntungan total dari setiap barang kemudian dimodelkan kedalam bentuk matematika. Metode yang digunakan dalam penelitian ini yaitu algoritma greedy dan metode  branch and bound. Diperoleh beberapa solusi optimal dalam menggunakan algoritma greedy yaitu greedy by weight, greedy by profit, dan greedy by density. Hasil penilitian menunjukkan bahwa dengan menggunakan algoritma greedy diperoleh hasil yang maksimal pada perhitungan greedy by profit dengan keuntungan yaitu Rp13952000  dan berat total 15319Kg Sedangkan menggunakan metode branch and bound diperoleh keuntungan Rp141689000 dengan berat total 15599Kg.

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