decision problems
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Author(s):  
Hamza Abubakar ◽  
Abdullahi Muhammad ◽  
Smaiala Bello

The Boolean Satisfiability Problem (BSAT) is one of the most important decision problems in mathematical logic and computational sciences for determining whether or not a solution to a Boolean formula.. Hopfield neural network (HNN) is one of the major type artificial neural network (NN) popularly known for it used in solving various optimization and decision problems based on its energy minimization machinism. The existing models that incorporate standalone network projected non-versatile framework as fundamental Hopfield type of neural network (HNN) employs random search in its training stages and sometimes get trapped at local optimal solution. In this study, Ants Colony Optimzation Algorithm (ACO) as a novel variant of probabilistic metaheuristic algorithm (MA) inspired by the behavior of real Ants, has been incorporated in the training phase of Hopfield types of the neural network (HNN) to accelerate the training process for Random Boolean kSatisfiability reverse analysis (RANkSATRA) based for logic mining. The proposed hybrid model has been evaluated according to robustness and accuracy of the induced logic obtained based on the agricultural soil fertility data set (ASFDS). Based on the experimental simulation results, it reveals that the ACO can effectively work with the Hopfield type of neural network (HNN) for Random 3 Satisfiability Reverse Analysis with 87.5 % classification accuracy


2022 ◽  
Vol 183 (1-2) ◽  
pp. 125-167
Author(s):  
Ronny Tredup

For a fixed type of Petri nets τ, τ-SYNTHESIS is the task of finding for a given transition system A a Petri net N of type τ(τ-net, for short) whose reachability graph is isomorphic to A if there is one. The decision version of this search problem is called τ-SOLVABILITY. If an input A allows a positive decision, then it is called τ-solvable and a sought net N τ-solves A. As a well known fact, A is τ-solvable if and only if it has the so-called τ-event state separation property (τ-ESSP, for short) and the τ-state separation property (τ-SSP, for short). The question whether A has the τ-ESSP or the τ-SSP defines also decision problems. In this paper, for all b ∈ ℕ, we completely characterize the computational complexity of τ-SOLVABILITY, τ-ESSP and τ-SSP for the types of pure b-bounded Place/Transition-nets, the b-bounded Place/Transitionnets and their corresponding ℤb+1-extensions.


2022 ◽  
pp. 1491-1509
Author(s):  
Steven Walczak

Artificial neural networks (ANNs) have proven to be efficacious for modeling decision problems in medicine, including diagnosis, prognosis, resource allocation, and cost reduction problems. Research using ANNs to solve medical domain problems has been increasing regularly and is continuing to grow dramatically. This chapter examines recent trends and advances in ANNs and provides references to a large portion of recent research, as well as looking at the future direction of research for ANN in medicine.


2022 ◽  
Vol 14 (1) ◽  
pp. 0-0

With the fast growing of data-rich systems, dealing with complex decision problems with skewed input data sets and respective outliers is unavoidable. Generally, data skewness refers to a non-uniform distribution in a dataset, i.e. a dataset which contains asymmetries and/or outliers. Normalization is the first step of most multi-criteria decision making (MCDM) problems to obtain dimensionless data, from heterogeneous input data sets, that enable aggregation of criteria and thereby ranking of alternatives. Therefore, when in presence of outliers in criteria datasets, finding a suitable normalization technique is of utmost importance. As such, in this work, we compare seven normalization techniques (Max, Max-Min, Vector, Sum, Logarithmic, Target-based, and Fuzzification) on criteria datasets, which contain outliers to analyse their results for MCDM problems. A numerical example illustrates the behaviour of the chosen normalization techniques and an (ongoing) evaluation assessment framework is used to recommend the best normalization technique for this type of criteria.


2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Nancy M. Arratia-Martinez ◽  
Nelly M. Hernandez-Gonzalez ◽  
Fernando Lopez-Irarragorri

A project portfolio can be defined as a set of project proposals that are selected according to one or more criteria by a decision-maker (individual or group). Regularly, the portfolio selection involves different decision problems, among those evaluation, selection, scheduling, and resource allocation. In published scientific literature, these problems have been addressed mainly separately giving as a result suboptimal solutions (portfolios). In addition, elements as partial allocation and project representation through tasks constitute relevant characteristics in practice that remain unaddressed in depth. The proposal of this research is to integrate the project selection and project scheduling, incorporating all relevant elements of both decision problems through the scheduling of tasks allowing to determine when the task will be funded and executed. The main impact of precedence rules at the task level in the portfolio is also studied. In this work, Project Portfolio Selection and Scheduling Problem (PPSS) is studied and solved through a new mixed-integer linear programming (MILP) model. The model incorporates renewable and nonrenewable resource allocation, along with partial and total funding policies, project divisibility, and interdependences. Scheduling is integrated into the model, both at the project level and at the project task level, which allows scheduling in noncontiguous periods. Small instances (up to 64 projects) and medium instances (up to 128 projects) were solved optimally in very short times. The relationship between the quality of near-optimal solutions and the solution computing time by modifying the parameters of the solver employed was researched. No significant change in the solution’s quality was perceived, but a significant reduction in solution computing time was achieved. Furthermore, the main effects of precedence rules on solution times and portfolio impact were studied. Results show that even if few precedence rules were introduced, the resource allocation of tasks changed significantly, even though the portfolio impact or the number of projects of the selected portfolios remains the same.


2021 ◽  
Vol 127 (25) ◽  
Author(s):  
Dorian Bouchet ◽  
Lukas M. Rachbauer ◽  
Stefan Rotter ◽  
Allard P. Mosk ◽  
Emmanuel Bossy

Author(s):  
Cyrille Chenavier ◽  
Benjamin Dupont ◽  
Philippe Malbos

Abstract Convergent rewriting systems on algebraic structures give methods to solve decision problems, to prove coherence results, and to compute homological invariants. These methods are based on higher-dimensional extensions of the critical branching lemma that proves local confluence from confluence of the critical branchings. The analysis of local confluence of rewriting systems on algebraic structures, such as groups or linear algebras, is complicated because of the underlying algebraic axioms. This article introduces the structure of algebraic polygraph modulo that formalizes the interaction between the rules of an algebraic rewriting system and the inherent algebraic axioms, and we show a critical branching lemma for algebraic polygraphs. We deduce a critical branching lemma for rewriting systems on algebraic models whose axioms are specified by convergent modulo rewriting systems. We illustrate our constructions for string, linear, and group rewriting systems.


2021 ◽  
pp. 1-19
Author(s):  
Cristóvão Sousa ◽  
Daniel Teixeira ◽  
Davide Carneiro ◽  
Diogo Nunes ◽  
Paulo Novais

As the availability of computational power and communication technologies increases, Humans and systems are able to tackle increasingly challenging decision problems. Taking decisions over incomplete visions of a situation is particularly challenging and calls for a set of intertwined skills that must be put into place under a clear rationale. This work addresses how to deliver autonomous decisions for the management of a public street lighting network, to optimize energy consumption without compromising light quality patterns. Our approach is grounded in an holistic methodology, combining semantic and Artificial Intelligence principles to define methods and artefacts for supporting decisions to be taken in the context of an incomplete domain. That is, a domain with absence of data and of explicit domain assertions.


Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3179
Author(s):  
David Ruiz Bargueño ◽  
Valerio Antonio Pamplona Salomon ◽  
Fernando Augusto Silva Marins ◽  
Pedro Palominos ◽  
Luis Armando Marrone

Cultural, economical, political, and social developments, added to population increases, favored the consolidation of cities. However, rapid city growth in the last decades has contrasted with the slowness in which states and municipalities responded to the new reality. In this sense, the analytic hierarchy process (AHP), a leading multiple criteria decision-making (MCDM) method, can be applied in the solution of common demands among municipalities, evaluating alternative plans for urban mobility. Since AHP has been applied to these specific decision problems, our research question is: How has AHP been applied to solve decision problems regarding urban mobility? The objective of this work is to identify the state of the art of AHP applications to urban mobility. To answer the research question, this paper presents a literature review (LR). State of the art review (SAR) is an LR approach expected to deliver results with medium comprehensiveness and results closer to exhaustive. With the support of graphical software, three clusters were identified, in the keywords network: AHP, Innovation & Public Management, and Urban Mobility. In the AHP cluster, research is driven by methodological subjects; on Innovation & Public Management, there is an open discussion on local versus national coordination; and the urban mobility cluster has hybrid or non-AHP applications of MCDM.


Author(s):  
Murat Levent Demircan ◽  
Berkay Özcan

AbstractLogistics processes have been analyzed as one of the most critical expense items for companies. Companies that failed to manage their logistics processes well could not reach the desired growth rates, and some even disappeared. Logistics management without process optimizations can be time and money consuming for the companies. Logistics processes significantly influence organizations' efficiency. Logistic professionals should keep the process flow quality at a certain level, and some decision problems should be analyzed and answered well. Location selection of a warehouse is one of the most crucial decision problems of supply chain and logistics management. Alternatives are evaluated in quantitative and qualitative criteria to decide the best location alternative using scientific MCDM techniques. Different scientific methods have been developed and used to solve this problem. As for this study, the aim is to investigate the warehouse location selection of third-party cold chain logistics suppliers. The importance of keeping perishable products under the right conditions increased, since it is realized that cold chain warehousing and transportation prevent the product spoiled. Organizations can save their funds and time by having effective cold chain management. This study's main scope is to give a new scientific perspective for warehouse selection in cold chain logistics. MCDM technique of Interval-Valued Neutrosophic Fuzzy (IVNF) EDAS method has been used to evaluate essential criteria and choose the best option. Critical cities of Gulf Region countries have been considered alternatives in a numerical illustration.


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