The use of duality to increase the effectiveness of the branch and bound method when solving the knapsack problem

Alekseyev, A. O.; Alekseyev, O. G.; Anisimov, Vladimir; Anisimov, E. G.

doi:10.1016/0041-5553(85)90008-4

Cited by 9 publications

(4 citation statements)

References 3 publications

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“…Conventionally determined models allow obtaining acceptable damage estimates with a short period of retrospection and small amounts of information, and stochastic models with significantly large amounts. In order to increase the objectivity of forecasts due to minimization of subjective information used in modeling, uncertainty relief in building both conditionally determined and stochastic models is based on the "maximum uncertainty" principle formalized in the form of maximum entropy [5][6][7]. 3 Results of the study…”

Section: Methodsmentioning

confidence: 99%

“…In general, the presented ratios (1) -(4), (8), (9), (13), (14) are a conditionally determined model for forecasting in the interests of the energy management of economic damage during technological accidents at energy facilities and in power supply systems enterprises under assumptions (6), (7).…”

Section: Methodical Approach To the Construction Of Conditionally Detmentioning

confidence: 99%

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Models for predicting damage due to accidents at energy objects and in energy systems of enterprises

et al. 2019

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Achieving energy security by preventing and timely eliminating the consequences of accidents at energy facilities and in energy supply systems of enterprises is one of the important tasks of energy management. The basis for planning appropriate energy security measures is the prediction of damage from these accidents. The purpose of forecasting is to assess the possibility of an accident occurring at some point in time and leading to a particular damage, and to assess the magnitude of this damage. The article proposed methodological approaches to the construction of mathematical models of such prediction. In this case, as an indicator of damage, the economic losses caused by these accidents are taken. The simulation is based on the representation of this indicator in the form of a step change function of the magnitude of losses in the event of an accident. Depending on the amount of information available in the period prior to forecasting, the mathematical representation of the forecasting problem is reduced to the construction of conditionally determined or stochastic models. Conditionally determined models allow obtaining acceptable damage estimates with a short period of retrospection and small amounts of information, and stochastic models with significantly large amounts. At the same time, the principle of “maximum uncertainty” formalized in the form of maximum entropy is the basis for removing uncertainty in the construction of both conditionally determined and stochastic models. Its use has allowed increasing the objectivity of forecasts by minimizing the subjective information used in modeling. The proposed approaches to the construction of mathematical models for predicting accidents at energy facilities and power supply systems of enterprises are the basis for creating specific techniques for solving relevant energy management tasks both at the micro level at the scale of individual enterprises and at the macro level at the scale of industries, regions and the state as a whole.

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Section: Methodsmentioning

confidence: 99%

Section: Methodical Approach To the Construction Of Conditionally Detmentioning

confidence: 99%

Models for predicting damage due to accidents at energy objects and in energy systems of enterprises

et al. 2019

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“…Problem (7) -(13) belongs to the non-linear problems of distributing discrete on-uniform resources in the random network. It is NPa complex problem of discrete programming [4][5][6]. Precise methods of solving problems of such class have been offered for the first time in [7][8].…”

Section: Cc-tesc2018mentioning

confidence: 99%

Digital transformation and optimization models in the sphere of logistics

Anisimov

Saurenko

et al. 2018

SHS Web of Conf.

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The efficiency, optimization, speed and time limits have always been of crucial importance for the logistics system, while saving of speed and time in the real-time mode are the key factors with transition to digital technologies and establishment of Industry 4.0 since they become the competitive advantages. The innovative use of technologies in such fields as data analysis, Internet of things and cloud calculations significantly change the logistical and transportation systems as a result of mating digital and existing supply chains becoming the catalyst of transition to “Logistika 4.0”. This work offers a model and method of shaping an optimal plan of fulfilling a complex of interrelated logistical operations for such changing conditions.The model is based on the presentation of optimization procedure as a non-linear task of discrete programming consisting in minimization of time of fulfilling the above complex of operations by a limited number of contractors partially interchangeable under conditions of limited budgeting. A model obtained thereat for establishing an optimal plan will belong to the class of nonpolynimially challenging tasks. In order to solve these tasks, a method has been suggested supported by a procedure of branches and boundaries. Thealgorithmisbasedon dichotomous branchingdiagram. Itsapplicationprovidesforreceivingboth quasi-optimalandoptimallogisticsplansfor the finite number of steps. Atthat, theassessmentofaccuracy is provided for quasi-optimal plans. The proposed model and method help solve a wide spectrum of practical tasks of logistical planning under conditions of digital transformation.

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“…Within this framework, one of the most important categories is the optimal distribution of discrete resources [1][2][3][4][5]. For the realtime mode AIMS the allocation of resources present a multistaged process [6,7].…”

Section: Introductionmentioning

confidence: 99%

Mathematical Simulation Of Adaptive Allocation Of Discrete Resources

Anisimov¹,

Anisimov²,

Sonkin³

2016

Proceedings of the 2016 Conference on Information Technologies in Science, Management, Social Sphere and Medicine

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-The dynamic and uncertainty of management system generate and complicate the problem of providing appropriate quality management solutions. Optimization and adaptive approach to the process of taking a management decision is one the most effective. Practically, it can be implemented by modeling adaptive distribution of discrete resources. So, the results of this article include the methods of forming mathematical models of distribution of discrete resources, based on the principle of optimization and adaptive approach to the process of taking a management decision in automated information management systems in the real-time mode (AIMS). The implementation of considered methods help to scrutinize such aspects of a real management system as dynamics and uncertainty of situations, but at the same time to operate with simple mathematical models of static optimization for taking a decision about the distribution of resources.

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The use of duality to increase the effectiveness of the branch and bound method when solving the knapsack problem

Cited by 9 publications

References 3 publications

Models for predicting damage due to accidents at energy objects and in energy systems of enterprises

Models for predicting damage due to accidents at energy objects and in energy systems of enterprises

Digital transformation and optimization models in the sphere of logistics

Mathematical Simulation Of Adaptive Allocation Of Discrete Resources

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