Operational algorithms for solving the inverse problem for the graph model for conflict resolution are presented for the case of two decision makers (DMs) under a variety of solution concepts, including Nash stability...
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Operational algorithms for solving the inverse problem for the graph model for conflict resolution are presented for the case of two decision makers (DMs) under a variety of solution concepts, including Nash stability (Nash), general metarationality (GMR), symmetric metarationality (SMR), and sequential stability (SEQ). The algorithms based on integer programming enable a DM, an analyst, or a mediator to obtain all of the preferences required to make a specified state to be an equilibrium or resolution. For the cases of Nash, GMR, and SMR, the respective inverse algorithm for the focal DM is formulated as a 0-1 integer linear programming problem even when both DMs' preferences are unknown. For the situation of SEQ, when both DMs' preferences are unknown, the focal DM's algorithm is a 0-1 integer nonlinear programming problem while, under the condition that the opponent's preferences are known, the focal DM's 0-1 integer programming problem is linear. The usefulness of the algorithms developed is demonstrated by applying them to an illustrative dispute.
One of the recent challenging but vital tasks in graph theory and network analysis, especially when dealing with graphs equipped with a set of nodal attributes, is to discover subgraphs consisting of highly interactin...
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ISBN:
(数字)9788396242396
ISBN:
(纸本)9788396242396
One of the recent challenging but vital tasks in graph theory and network analysis, especially when dealing with graphs equipped with a set of nodal attributes, is to discover subgraphs consisting of highly interacting nodes with respect to the number of edges and the attributes' similarities. This paper proposes an approach based on integer programming modeling and the graph neural network message-passing manner for efficiently extracting these subgraphs. The experiments illustrate the proposed method's privilege over some alternative algorithms known so far, utilizing several well-known instances.
As e-waste consists of hazardous components, developing a cost-effective method at the user level is essential. This paper presents a binary integer programming (BIP) model designed to affordably manage e-waste by min...
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We propose a new perspective for solving the trace-reconstruction problem. In this problem, multiple traces (or subsequences) are independently sampled from an unknown integer sequence. The goal is to find the shortes...
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ISBN:
(数字)9798350399981
ISBN:
(纸本)9798350399981
We propose a new perspective for solving the trace-reconstruction problem. In this problem, multiple traces (or subsequences) are independently sampled from an unknown integer sequence. The goal is to find the shortest sequence that agrees with all traces. Our primary result is that this problem can be efficiently solved with an integer programming model under some mild assumptions. We introduced two sets of valid inequalities to further speed up the optimization process. We also compare our algorithm with classic depth-first searching. Through the experimental results, our algorithm shows a dramatic speed and efficiency advantage over DFS.
The process of sectorization aims at dividing a dataset into smaller sectors according to certain criteria, such as equilibrium and compactness. Sectorization problems appear in several different contexts, such as pol...
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ISBN:
(纸本)9783030781705;9783030781699
The process of sectorization aims at dividing a dataset into smaller sectors according to certain criteria, such as equilibrium and compactness. Sectorization problems appear in several different contexts, such as political districting, sales territory design, healthcare districting problems and waste collection, to name a few. Solution methods vary from application to application, either being exact, heuristics or a combination of both. In this paper, we propose two quadratic integer programming models to obtain a sectorization: one with compactness as the main criterion and equilibrium constraints, and the other considering equilibrium as the objective and compactness bounded in the constraints. These two models are also compared to ascertain the relationship between the criteria.
Even though it is well known that for most relevant computational problems, different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best ...
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Even though it is well known that for most relevant computational problems, different algorithms may perform better on different classes of problem instances, most researchers still focus on determining a single best algorithmic configuration based on aggregate results such as the average. In this paper, we propose integer programming-based approaches to build decision trees for the algorithm selection problem. These techniques allow the automation of three crucial decisions: (a) discerning the most important problem features to determine problem classes, (b) grouping the problems into classes, and (c) selecting the best algorithm configuration for each class. To evaluate this new approach, extensive computational experiments were executed using the linear programming algorithms implemented in the COIN-OR branch-and-cut solver across a comprehensive set of instances, including all MIPLIB benchmark instances. The results exceeded our expectations. While selecting the single best parameter setting across all instances decreased the total running time by 22%, our approach decreased the total running time by 40% on average across 10-fold cross-validation experiments. These results indicate that our method generalizes quite well and does not overfit.
In this article, an exact method is proposed to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP). This kind of problems arises whenever two associated decisio...
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In this article, an exact method is proposed to optimize two preference functions over the efficient set of a multiobjective integer linear program (MOILP). This kind of problems arises whenever two associated decision-makers have to optimize their respective preference functions over many efficient solutions. For this purpose, we develop a branch-and-cut algorithm based on linear programming, for finding efficient solutions in terms of both preference functions and MOILP problem, without explicitly enumerating all efficient solutions of MOILP problem. The branch and bound process, strengthened by efficient cuts and tests, allows us to prune a large number of nodes in the tree to avoid many solutions. An illustrative example and an experimental study are reported.
Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the da...
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Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. Our approach can also handle numerical features via thresholding. We show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.
We present here classes of integer programming problems that are solvable efficiently and with combinatorial flow algorithms. The problems are characterized by constraints that have either at most two variables per in...
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We present here classes of integer programming problems that are solvable efficiently and with combinatorial flow algorithms. The problems are characterized by constraints that have either at most two variables per inequality that appear with opposite sign coefficients, or have in addition a third variable that appears only in one constraint. Such integer programs, referred to here as monotone IP2 or IP3, are shown to be solvable in polynomial time for polynomially bounded variables. This article demonstrates the vast applicability of IP2 and IP3 as models for integer programs in multiple scenarios. Since the problems are easily recognized, the knowledge of their structure enables one to determine easily that they are efficiently solvable. The variety of applications, that previously were not known to be solved as efficiently, underlies the importance of recognizing this structure and, if appropriate, formulating problems as monotone IP2 or IP3. Additionally, if there is flexibility in the modeling of an integer programming problem, the formulation choice as monotone IP2 or IP3 leads to efficient algorithms, whereas slightly different modeling choices would lead to NP-hard problems.
Decision diagrams have been successfully used to help solve several classes of discrete optimization problems. We explore an approach to incorporate them into integer programming solvers, motivated by the wide adoptio...
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Decision diagrams have been successfully used to help solve several classes of discrete optimization problems. We explore an approach to incorporate them into integer programming solvers, motivated by the wide adoption of integer programming technology in practice. The main challenge is to map generic integer programming models to a recursive structure that is suitable for decision diagram compilation. We propose a framework that opportunistically constructs decision diagrams for suitable substructures, if present. In particular, we explore the use of a prevalent substructure in integer programming solvers known as the conflict graph, which we show to be amenable to decision diagrams. We use Lagrangian relaxation and constraint propagation to consider constraints that are not represented directly by the substructure. We use the decision diagrams to generate dual and primal bounds to improve the pruning process of the branch-and-bound tree of the solver. Computational results on the independent set problem with side constraints indicate that our approach can provide substantial speedups when conflict graphs are present.
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