Abstract
Multi-objective formulations are realistic models for many complex engineering optimization problems. In many real-life problems
considered objectives conflict with each other and optimization of one target solutions can lead to unacceptable results for other
purposes. A reasonable solution of the multi-objective problem is to study the set of solutions, each of which satisfies the objectives at
an acceptable level with no dominance of any of the solutions. The article provides a brief overview of multi-objective optimization
methods (by Pareto criteria) and their improvement.
Keywords: A fuzzy set, forecasting, risk, weakly formalized process for Pareto multi-objective optimization.
Min-based qualitative possibilistic networks are one of the effective tools for a compact representation of
decision problems under uncertainty. The exact approaches for computing decision based on possibilistic
networks are limited by the size of the possibility distributions. Generally, these approaches are based on
possibilistic propagation algorithms. An important step in the computation of the decision is the
transformation of the DAG (Direct Acyclic Graph) into a secondary structure, known as the junction trees
(JT). This transformation is known to be costly and represents a difficult problem. We propose in this paper
a new approximate approach for the computation of decision under uncertainty within possibilistic
networks. The computing of the optimal optimistic decision no longer goes through the junction tree
construction step. Instead, it is performed by calculating the degree of normalization in the moral graph
resulting from the merging of the possibilistic network codifying knowledge of the agent and that codifying
its preferences.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A comparison has been made between approximation of triangular fuzzy systems and the corresponding fuzzy triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular fuzzy numbers are also found.
Min-based qualitative possibilistic networks are one of the effective tools for a compact representation of
decision problems under uncertainty. The exact approaches for computing decision based on possibilistic
networks are limited by the size of the possibility distributions. Generally, these approaches are based on
possibilistic propagation algorithms. An important step in the computation of the decision is the
transformation of the DAG (Direct Acyclic Graph) into a secondary structure, known as the junction trees
(JT). This transformation is known to be costly and represents a difficult problem. We propose in this paper
a new approximate approach for the computation of decision under uncertainty within possibilistic
networks. The computing of the optimal optimistic decision no longer goes through the junction tree
construction step. Instead, it is performed by calculating the degree of normalization in the moral graph
resulting from the merging of the possibilistic network codifying knowledge of the agent and that codifying
its preferences.
AGGREGATION OF OPINIONS FOR SYSTEM SELECTION USING APPROXIMATIONS OF FUZZY NU...mathsjournal
In this article we assume that experts express their view points by way of approximation of Triangular fuzzy numbers. We take the help of fuzzy set theory concept to model the situation and present a method to aggregate these approximations of triangular fuzzy numbers to obtain an overall approximation of triangular fuzzy number for each system and then linear ordering done before the best system is chosen. A comparison has been made between approximation of triangular fuzzy systems and the corresponding fuzzy triangular numbers systems. The notions like fuzziness and ambiguity for the approximation of triangular fuzzy numbers are also found.
CHN and Swap Heuristic to Solve the Maximum Independent Set ProblemIJECEIAES
We describe a new approach to solve the problem to find the maximum independent set in a given Graph, known also as Max-Stable set problem (MSSP). In this paper, we show how Max-Stable problem can be reformulated into a linear problem under quadratic constraints, and then we resolve the QP result by a hybrid approach based Continuous Hopfeild Neural Network (CHN) and Local Search. In a manner that the solution given by the CHN will be the starting point of the local search. The new approach showed a good performance than the original one which executes a suite of CHN runs, at each execution a new leaner constraint is added into the resolved model. To prove the efficiency of our approach, we present some computational experiments of solving random generated problem and typical MSSP instances of real life problem.
On Continuous Approximate Solution of Ordinary Differential EquationsWaqas Tariq
In this work the problem of continuous approximate solution of the ordinary differential equations will be investigated. An approach to construct the continuous approximate solution, which is based on the discrete approximate solution and the spline interpolation, will be provided. The existence and uniqueness of such continuous approximate solution will be pointed out. Its error will be estimated and its convergence will be considered. Finally, with the aid of modern PC and nathematical software three practical computer approaches to perform above construction will be offered.
In this article, we propose a new approach to solve intuitionistic fuzzy assignment
problem. Classical assignment problem deals with deterministic cost. In practical
situations it is not easy to determine the parameters. The parameters can be modeled
to fuzzy or intuitionistic fuzzy parameters. This paper develops an approach based on
diagonal optimal algorithm to solve an intuitionistic fuzzy assignment problem. A new
ranking procedure based on combined arithmetic mean is used to order the
intuitionistic fuzzy numbers so that Diagonal optimal algorithm [22] can be applied to
solve the intuitionistic fuzzy assignment problem. To illustrate the effectiveness of the
algorithm numerical examples were given..
Over the past decade or so, Particle Swarm Optimization (PSO) has emerged to be one of most useful methodologies to address complex high dimensional optimization problems - it’s popularity can be attributed to its ease of implementation, and fast convergence prop- erty (compared to other population based algorithms). However, a premature stagnation of candidate solutions has been long standing in the way of its wider application, particularly to constrained single-objective problems. This issue becomes all the more pronounced in the case of optimization problems that involve a mixture of continuous and discrete de- sign variables. In this paper, a modification of the standard Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints and deal with mixed-discrete variables. Continuous optimization, as in conventional PSO, is imple- mented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest vertex approximation criterion. This approach is expected to avoid the undesirable discrepancy in the rate of evolution of discrete and continuous vari- ables. To address the issue of premature convergence, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each it- eration. The estimated diversity measure is then used to apply (i) a dynamic repulsion towards the globally best solution in the case of continuous variables, and (ii) a stochas- tic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is successfully applied to a wide variety of standard test problems: (i) a set of 9 unconstrained problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) problems.
Multi objective optimization and Benchmark functions resultPiyush Agarwal
Implemented Strength Pareto Evolutionary Algorithm (SPEA 2) and Non Dominated Sorting Genetic Algorithm (NSGA II) in MATLAB, Guide Assistant Prof. Divy Kumar, MNNIT Allahabad.
The two algorithms are use to solve multiobjective functions. Tested the algorithms on all the benchmark functions.
Applied both the algorithms to solve Portfolio Optimization satisfying different types of constraints to derive the optimal portfolio.
CHN and Swap Heuristic to Solve the Maximum Independent Set ProblemIJECEIAES
We describe a new approach to solve the problem to find the maximum independent set in a given Graph, known also as Max-Stable set problem (MSSP). In this paper, we show how Max-Stable problem can be reformulated into a linear problem under quadratic constraints, and then we resolve the QP result by a hybrid approach based Continuous Hopfeild Neural Network (CHN) and Local Search. In a manner that the solution given by the CHN will be the starting point of the local search. The new approach showed a good performance than the original one which executes a suite of CHN runs, at each execution a new leaner constraint is added into the resolved model. To prove the efficiency of our approach, we present some computational experiments of solving random generated problem and typical MSSP instances of real life problem.
On Continuous Approximate Solution of Ordinary Differential EquationsWaqas Tariq
In this work the problem of continuous approximate solution of the ordinary differential equations will be investigated. An approach to construct the continuous approximate solution, which is based on the discrete approximate solution and the spline interpolation, will be provided. The existence and uniqueness of such continuous approximate solution will be pointed out. Its error will be estimated and its convergence will be considered. Finally, with the aid of modern PC and nathematical software three practical computer approaches to perform above construction will be offered.
In this article, we propose a new approach to solve intuitionistic fuzzy assignment
problem. Classical assignment problem deals with deterministic cost. In practical
situations it is not easy to determine the parameters. The parameters can be modeled
to fuzzy or intuitionistic fuzzy parameters. This paper develops an approach based on
diagonal optimal algorithm to solve an intuitionistic fuzzy assignment problem. A new
ranking procedure based on combined arithmetic mean is used to order the
intuitionistic fuzzy numbers so that Diagonal optimal algorithm [22] can be applied to
solve the intuitionistic fuzzy assignment problem. To illustrate the effectiveness of the
algorithm numerical examples were given..
Over the past decade or so, Particle Swarm Optimization (PSO) has emerged to be one of most useful methodologies to address complex high dimensional optimization problems - it’s popularity can be attributed to its ease of implementation, and fast convergence prop- erty (compared to other population based algorithms). However, a premature stagnation of candidate solutions has been long standing in the way of its wider application, particularly to constrained single-objective problems. This issue becomes all the more pronounced in the case of optimization problems that involve a mixture of continuous and discrete de- sign variables. In this paper, a modification of the standard Particle Swarm Optimization (PSO) algorithm is presented, which can adequately address system constraints and deal with mixed-discrete variables. Continuous optimization, as in conventional PSO, is imple- mented as the primary search strategy; subsequently, the discrete variables are updated using a deterministic nearest vertex approximation criterion. This approach is expected to avoid the undesirable discrepancy in the rate of evolution of discrete and continuous vari- ables. To address the issue of premature convergence, a new adaptive diversity-preservation technique is developed. This technique characterizes the population diversity at each it- eration. The estimated diversity measure is then used to apply (i) a dynamic repulsion towards the globally best solution in the case of continuous variables, and (ii) a stochas- tic update of the discrete variables. For performance validation, the Mixed-Discrete PSO algorithm is successfully applied to a wide variety of standard test problems: (i) a set of 9 unconstrained problems, and (ii) a comprehensive set of 98 Mixed-Integer Nonlinear Programming (MINLP) problems.
Multi objective optimization and Benchmark functions resultPiyush Agarwal
Implemented Strength Pareto Evolutionary Algorithm (SPEA 2) and Non Dominated Sorting Genetic Algorithm (NSGA II) in MATLAB, Guide Assistant Prof. Divy Kumar, MNNIT Allahabad.
The two algorithms are use to solve multiobjective functions. Tested the algorithms on all the benchmark functions.
Applied both the algorithms to solve Portfolio Optimization satisfying different types of constraints to derive the optimal portfolio.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
A Study of Some Systems of Linear and Nonlinear Partial Differential Equation...inventionjournals
In this paper, we introduce the solution of systems of linear and nonlinear partial differential equations subject to the initial conditions by using reduced differential transformation method. The proposed method was applied to three systems of linear and nonlinear partial differential equations, leading to series solutions with components easily computable. The results obtained are indicators of the simplicity and effectiveness of the method
Quantum inspired evolutionary algorithm for solving multiple travelling sales...eSAT Publishing House
IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
applications.
Robust Fuzzy Data Clustering In An Ordinal Scale Based On A Similarity MeasureIJRES Journal
This paper is devoted to processing data given in an ordinal scale. A new objective function of a
special type is introduced. A group of robust fuzzy clustering algorithms based on the similarity measure is
introduced.
EFFICIENT KNOWLEDGE BASE MANAGEMENT IN DCSP ijasuc
DCSP (Distributed Constraint Satisfaction Problem) has been a very important research area in AI
(Artificial Intelligence). There are many application problems in distributed AI that can be formalized as
DSCPs. With the increasing complexity and problem size of the application problems in AI, the required
storage place in searching and the average searching time are increasing too. Thus, to use a limited
storage place efficiently in solving DCSP becomes a very important problem, and it can help to reduce
searching time as well. This paper provides an efficient knowledge base management approach based on
general usage of hyper-resolution-rule in consistence algorithm. The approach minimizes the increasing of
the knowledge base by eliminate sufficient constraint and false nogood. These eliminations do not change
the completeness of the original knowledge base increased. The proofs are given as well. The example
shows that this approach decrease both the new nogoods generated and the knowledge base greatly. Thus
it decreases the required storage place and simplify the searching process.
The numerical solution of helmholtz equation via multivariate padé approximationeSAT Journals
Abstract
In this study, we consider the numerical solution of the Helmholtz equation, arising from numerous physical phenomena and
engineering applications including energy systems. We make use of a Padé Approximation method for the solution of the
Helmholtz equation. Firstly, Helmholtz partial differential equation had been converted to power series by two-dimensional
differential transformation, then the numerical solution of the equation was put into Padé series form for accelerating
convergence and decreasing computational time. Hereby, we obtained numerical solution of Helmholtz type partial differential
equation.
Key Words: Helmholtz equation, Two-dimensional differential transformation, Multivariate Padé approximation,
power series
A wide variety of combinatorial problems can be viewed as Weighted Constraint Satisfaction Problems (WCSPs). All resolution methods have an exponential time complexity for big instances. Moreover, they combine several techniques, use a wide variety of concepts and notations that are difficult to understand and implement. In this paper, we model this problem in terms of an original 0-1 quadratic programming subject to linear constraints. This model is validated by the proposed and demonstrated theorem. View its performance, we use the Hopfield neural network to solve the obtained model basing on original energy function. To validate our model, we solve several instances of benchmarking WCSP. Our approach has the same memory complexity as the HNN and the same time complexity as Euler-Cauchy method. In this regard, our approach recognizes the optimal solution of the said instances.
A Mathematical Programming Approach for Selection of Variables in Cluster Ana...IJRES Journal
Data clustering is a common technique for statistical data analysis; it is defined as a class of
statistical techniques for classifying a set of observations into completely different groups. Cluster analysis
seeks to minimize group variance and maximize between group variance. In this study we formulate a
mathematical programming model that chooses the most important variables in cluster analysis. A nonlinear
binary model is suggested to select the most important variables in clustering a set of data. The idea of the
suggested model depends on clustering data by minimizing the distance between observations within groups.
Indicator variables are used to select the most important variables in the cluster analysis.
Similar to Method of solving multi objective optimization problem in the presence of uncertainty (20)
Mechanical properties of hybrid fiber reinforced concrete for pavementseSAT Journals
Abstract
The effect of addition of mono fibers and hybrid fibers on the mechanical properties of concrete mixture is studied in the present
investigation. Steel fibers of 1% and polypropylene fibers 0.036% were added individually to the concrete mixture as mono fibers and
then they were added together to form a hybrid fiber reinforced concrete. Mechanical properties such as compressive, split tensile and
flexural strength were determined. The results show that hybrid fibers improve the compressive strength marginally as compared to
mono fibers. Whereas, hybridization improves split tensile strength and flexural strength noticeably.
Keywords:-Hybridization, mono fibers, steel fiber, polypropylene fiber, Improvement in mechanical properties.
Material management in construction – a case studyeSAT Journals
Abstract
The objective of the present study is to understand about all the problems occurring in the company because of improper application
of material management. In construction project operation, often there is a project cost variance in terms of the material, equipments,
manpower, subcontractor, overhead cost, and general condition. Material is the main component in construction projects. Therefore,
if the material management is not properly managed it will create a project cost variance. Project cost can be controlled by taking
corrective actions towards the cost variance. Therefore a methodology is used to diagnose and evaluate the procurement process
involved in material management and launch a continuous improvement was developed and applied. A thorough study was carried
out along with study of cases, surveys and interviews to professionals involved in this area. As a result, a methodology for diagnosis
and improvement was proposed and tested in selected projects. The results obtained show that the main problem of procurement is
related to schedule delays and lack of specified quality for the project. To prevent this situation it is often necessary to dedicate
important resources like money, personnel, time, etc. To monitor and control the process. A great potential for improvement was
detected if state of the art technologies such as, electronic mail, electronic data interchange (EDI), and analysis were applied to the
procurement process. These helped to eliminate the root causes for many types of problems that were detected.
Managing drought short term strategies in semi arid regions a case studyeSAT Journals
Abstract
Drought management needs multidisciplinary action. Interdisciplinary efforts among the experts in various fields of the droughts
prone areas are helpful to achieve tangible and permanent solution for this recurring problem. The Gulbarga district having the total
area around 16, 240 sq.km, and accounts 8.45 per cent of the Karnataka state area. The district has been situated with latitude 17º 19'
60" North and longitude of 76 º 49' 60" east. The district is situated entirely on the Deccan plateau positioned at a height of 300 to
750 m above MSL. Sub-tropical, semi-arid type is one among the drought prone districts of Karnataka State. The drought
management is very important for a district like Gulbarga. In this paper various short term strategies are discussed to mitigate the
drought condition in the district.
Keywords: Drought, South-West monsoon, Semi-Arid, Rainfall, Strategies etc.
Life cycle cost analysis of overlay for an urban road in bangaloreeSAT Journals
Abstract
Pavements are subjected to severe condition of stresses and weathering effects from the day they are constructed and opened to traffic
mainly due to its fatigue behavior and environmental effects. Therefore, pavement rehabilitation is one of the most important
components of entire road systems. This paper highlights the design of concrete pavement with added mono fibers like polypropylene,
steel and hybrid fibres for a widened portion of existing concrete pavement and various overlay alternatives for an existing
bituminous pavement in an urban road in Bangalore. Along with this, Life cycle cost analyses at these sections are done by Net
Present Value (NPV) method to identify the most feasible option. The results show that though the initial cost of construction of
concrete overlay is high, over a period of time it prove to be better than the bituminous overlay considering the whole life cycle cost.
The economic analysis also indicates that, out of the three fibre options, hybrid reinforced concrete would be economical without
compromising the performance of the pavement.
Keywords: - Fatigue, Life cycle cost analysis, Net Present Value method, Overlay, Rehabilitation
Laboratory studies of dense bituminous mixes ii with reclaimed asphalt materialseSAT Journals
Abstract
The issue of growing demand on our nation’s roadways over that past couple of decades, decreasing budgetary funds, and the need to
provide a safe, efficient, and cost effective roadway system has led to a dramatic increase in the need to rehabilitate our existing
pavements and the issue of building sustainable road infrastructure in India. With these emergency of the mentioned needs and this
are today’s burning issue and has become the purpose of the study.
In the present study, the samples of existing bituminous layer materials were collected from NH-48(Devahalli to Hassan) site.The
mixtures were designed by Marshall Method as per Asphalt institute (MS-II) at 20% and 30% Reclaimed Asphalt Pavement (RAP).
RAP material was blended with virgin aggregate such that all specimens tested for the, Dense Bituminous Macadam-II (DBM-II)
gradation as per Ministry of Roads, Transport, and Highways (MoRT&H) and cost analysis were carried out to know the economics.
Laboratory results and analysis showed the use of recycled materials showed significant variability in Marshall Stability, and the
variability increased with the increase in RAP content. The saving can be realized from utilization of recycled materials as per the
methodology, the reduction in the total cost is 19%, 30%, comparing with the virgin mixes.
Keywords: Reclaimed Asphalt Pavement, Marshall Stability, MS-II, Dense Bituminous Macadam-II
Laboratory investigation of expansive soil stabilized with natural inorganic ...eSAT Journals
Abstract
Soil stabilization has proven to be one of the oldest techniques to improve the soil properties. Literature review conducted revealed
that uses of natural inorganic stabilizers are found to be one of the best options for soil stabilization. In this regard an attempt has
been made to evaluate the influence of RBI-81 stabilizer on properties of black cotton soil through laboratory investigations. Black
cotton soil with varying percentages of RBI-81 viz., 0, 0.5, 1, 1.5, 2, and 2.5 percent were studied for moisture density relationships
and strength behaviour of soils. Also the effect of curing period was evaluated as literature review clearly emphasized the strength
gain of soils stabilized with RBI-81 over a period of time. The results obtained shows that the unconfined compressive strength of
specimens treated with RBI-81 increased approximately by 250% for a curing period of 28 days as compared to virgin soil. Further
the CBR value improved approximately by 400%. The studies indicated an increasing trend for soil strength behaviour with
increasing percentage of RBI-81 suggesting its potential applications in soil stabilization.
Influence of reinforcement on the behavior of hollow concrete block masonry p...eSAT Journals
Abstract
Reinforced masonry was developed to exploit the strength potential of masonry and to solve its lack of tensile strength. Experimental
and analytical studies have been carried out to investigate the effect of reinforcement on the behavior of hollow concrete block
masonry prisms under compression and to predict ultimate failure compressive strength. In the numerical program, three dimensional
non-linear finite elements (FE) model based on the micro-modeling approach is developed for both unreinforced and reinforced
masonry prisms using ANSYS (14.5). The proposed FE model uses multi-linear stress-strain relationships to model the non-linear
behavior of hollow concrete block, mortar, and grout. Willam-Warnke’s five parameter failure theory has been adopted to model the
failure of masonry materials. The comparison of the numerical and experimental results indicates that the FE models can successfully
capture the highly nonlinear behavior of the physical specimens and accurately predict their strength and failure mechanisms.
Keywords: Structural masonry, Hollow concrete block prism, grout, Compression failure, Finite element method,
Numerical modeling.
Influence of compaction energy on soil stabilized with chemical stabilizereSAT Journals
Abstract
Increase in traffic along with heavier magnitude of wheel loads cause rapid deterioration in pavements. There is a need to improve
density, strength of soil subgrade and other pavement layers. In this study an attempt is made to improve the properties of locally
available loamy soil using twin approaches viz., i) increasing the compaction of soil and ii) treating the soil with chemical stabilizer.
Laboratory studies are carried out on both untreated and treated soil samples compacted by different compaction efforts. Studies
show that increase in compaction effort results in increase in density of soil. However in soil treated with chemical stabilizer, rate of
increase in density is not significant. The soil treated with chemical stabilizer exhibits improvement in both strength and performance
properties.
Keywords: compaction, density, subgradestabilization, resilient modulus
Geographical information system (gis) for water resources managementeSAT Journals
Abstract
Water resources projects are inherited with overlapping and at times conflicting objectives. These projects are often of varied sizes
ranging from major projects with command areas of millions of hectares to very small projects implemented at the local level. Thus,
in all these projects there is seldom proper coordination which is essential for ensuring collective sustainability.
Integrated watershed development and management is the accepted answer but in turn requires a comprehensive framework that can
enable planning process involving all the stakeholders at different levels and scales is compulsory. Such a unified hydrological
framework is essential to evaluate the cause and effect of all the proposed actions within the drainage basins.
The present paper describes a hydrological framework developed in the form of a Hydrologic Information System (HIS) which is
intended to meet the specific information needs of the various line departments of a typical State connected with water related aspects.
The HIS consist of a hydrologic information database coupled with tools for collating primary and secondary data and tools for
analyzing and visualizing the data and information. The HIS also incorporates hydrological model base for indirect assessment of
various entities of water balance in space and time. The framework would be maintained and updated to reflect fully the most
accurate ground truth data and the infrastructure requirements for planning and management.
Keywords: Hydrological Information System (HIS); WebGIS; Data Model; Web Mapping Services
Forest type mapping of bidar forest division, karnataka using geoinformatics ...eSAT Journals
Abstract
The study demonstrate the potentiality of satellite remote sensing technique for the generation of baseline information on forest types
including tree plantation details in Bidar forest division, Karnataka covering an area of 5814.60Sq.Kms. The Total Area of Bidar
forest division is 5814Sq.Kms analysis of the satellite data in the study area reveals that about 84% of the total area is Covered by
crop land, 1.778% of the area is covered by dry deciduous forest, 1.38 % of mixed plantation, which is very threatening to the
environmental stability of the forest, future plantation site has been mapped. With the use of latest Geo-informatics technology proper
and exact condition of the trees can be observed and necessary precautions can be taken for future plantation works in an appropriate
manner
Keywords:-RS, GIS, GPS, Forest Type, Tree Plantation
Factors influencing compressive strength of geopolymer concreteeSAT Journals
Abstract
To study effects of several factors on the properties of fly ash based geopolymer concrete on the compressive strength and also the
cost comparison with the normal concrete. The test variables were molarities of sodium hydroxide(NaOH) 8M,14M and 16M, ratio of
NaOH to sodium silicate (Na2SiO3) 1, 1.5, 2 and 2.5, alkaline liquid to fly ash ratio 0.35 and 0.40 and replacement of water in
Na2SiO3 solution by 10%, 20% and 30% were used in the present study. The test results indicated that the highest compressive
strength 54 MPa was observed for 16M of NaOH, ratio of NaOH to Na2SiO3 2.5 and alkaline liquid to fly ash ratio of 0.35. Lowest
compressive strength of 27 MPa was observed for 8M of NaOH, ratio of NaOH to Na2SiO3 is 1 and alkaline liquid to fly ash ratio of
0.40. Alkaline liquid to fly ash ratio of 0.35, water replacement of 10% and 30% for 8 and 16 molarity of NaOH and has resulted in
compressive strength of 36 MPa and 20 MPa respectively. Superplasticiser dosage of 2 % by weight of fly ash has given higher
strength in all cases.
Keywords: compressive strength, alkaline liquid, fly ash
Experimental investigation on circular hollow steel columns in filled with li...eSAT Journals
Abstract
Composite Circular hollow Steel tubes with and without GFRP infill for three different grades of Light weight concrete are tested for
ultimate load capacity and axial shortening , under Cyclic loading. Steel tubes are compared for different lengths, cross sections and
thickness. Specimens were tested separately after adopting Taguchi’s L9 (Latin Squares) Orthogonal array in order to save the initial
experimental cost on number of specimens and experimental duration. Analysis was carried out using ANN (Artificial Neural
Network) technique with the assistance of Mini Tab- a statistical soft tool. Comparison for predicted, experimental & ANN output is
obtained from linear regression plots. From this research study, it can be concluded that *Cross sectional area of steel tube has most
significant effect on ultimate load carrying capacity, *as length of steel tube increased- load carrying capacity decreased & *ANN
modeling predicted acceptable results. Thus ANN tool can be utilized for predicting ultimate load carrying capacity for composite
columns.
Keywords: Light weight concrete, GFRP, Artificial Neural Network, Linear Regression, Back propagation, orthogonal
Array, Latin Squares
Experimental behavior of circular hsscfrc filled steel tubular columns under ...eSAT Journals
Abstract
This paper presents an outlook on experimental behavior and a comparison with predicted formula on the behaviour of circular
concentrically loaded self-consolidating fibre reinforced concrete filled steel tube columns (HSSCFRC). Forty-five specimens were
tested. The main parameters varied in the tests are: (1) percentage of fiber (2) tube diameter or width to wall thickness ratio (D/t
from 15 to 25) (3) L/d ratio from 2.97 to 7.04 the results from these predictions were compared with the experimental data. The
experimental results) were also validated in this study.
Keywords: Self-compacting concrete; Concrete-filled steel tube; axial load behavior; Ultimate capacity.
Evaluation of punching shear in flat slabseSAT Journals
Abstract
Flat-slab construction has been widely used in construction today because of many advantages that it offers. The basic philosophy in
the design of flat slab is to consider only gravity forces; this method ignores the effect of punching shear due to unbalanced moments
at the slab column junction which is critical. An attempt has been made to generate generalized design sheets which accounts both
punching shear due to gravity loads and unbalanced moments for cases (a) interior column; (b) edge column (bending perpendicular
to shorter edge); (c) edge column (bending parallel to shorter edge); (d) corner column. These design sheets are prepared as per
codal provisions of IS 456-2000. These design sheets will be helpful in calculating the shear reinforcement to be provided at the
critical section which is ignored in many design offices. Apart from its usefulness in evaluating punching shear and the necessary
shear reinforcement, the design sheets developed will enable the designer to fix the depth of flat slab during the initial phase of the
design.
Keywords: Flat slabs, punching shear, unbalanced moment.
Evaluation of performance of intake tower dam for recent earthquake in indiaeSAT Journals
Abstract
Intake towers are typically tall, hollow, reinforced concrete structures and form entrance to reservoir outlet works. A parametric
study on dynamic behavior of circular cylindrical towers can be carried out to study the effect of depth of submergence, wall thickness
and slenderness ratio, and also effect on tower considering dynamic analysis for time history function of different soil condition and
by Goyal and Chopra accounting interaction effects of added hydrodynamic mass of surrounding and inside water in intake tower of
dam
Key words: Hydrodynamic mass, Depth of submergence, Reservoir, Time history analysis,
Evaluation of operational efficiency of urban road network using travel time ...eSAT Journals
Abstract
Efficiency of the road network system is analyzed by travel time reliability measures. The study overlooks on an important measure of
travel time reliability and prioritizing Tiruchirappalli road network. Traffic volume and travel time were collected using license plate
matching method. Travel time measures were estimated from average travel time and 95th travel time. Effect of non-motorized vehicle
on efficiency of road system was evaluated. Relation between buffer time index and traffic volume was created. Travel time model has
been developed and travel time measure was validated. Then service quality of road sections in network were graded based on
travel time reliability measures.
Keywords: Buffer Time Index (BTI); Average Travel Time (ATT); Travel Time Reliability (TTR); Buffer Time (BT).
Estimation of surface runoff in nallur amanikere watershed using scs cn methodeSAT Journals
Abstract
The development of watershed aims at productive utilization of all the available natural resources in the entire area extending from
ridge line to stream outlet. The per capita availability of land for cultivation has been decreasing over the years. Therefore, water and
the related land resources must be developed, utilized and managed in an integrated and comprehensive manner. Remote sensing and
GIS techniques are being increasingly used for planning, management and development of natural resources. The study area, Nallur
Amanikere watershed geographically lies between 110 38’ and 110 52’ N latitude and 760 30’ and 760 50’ E longitude with an area of
415.68 Sq. km. The thematic layers such as land use/land cover and soil maps were derived from remotely sensed data and overlayed
through ArcGIS software to assign the curve number on polygon wise. The daily rainfall data of six rain gauge stations in and around
the watershed (2001-2011) was used to estimate the daily runoff from the watershed using Soil Conservation Service - Curve Number
(SCS-CN) method. The runoff estimated from the SCS-CN model was then used to know the variation of runoff potential with different
land use/land cover and with different soil conditions.
Keywords: Watershed, Nallur watershed, Surface runoff, Rainfall-Runoff, SCS-CN, Remote Sensing, GIS.
Estimation of morphometric parameters and runoff using rs & gis techniqueseSAT Journals
Abstract
Land and water are the two vital natural resources, the optimal management of these resources with minimum adverse environmental
impact are essential not only for sustainable development but also for human survival. Satellite remote sensing with geographic
information system has a pragmatic approach to map and generate spatial input layers of predicting response behavior and yield of
watershed. Hence, in the present study an attempt has been made to understand the hydrological process of the catchment at the
watershed level by drawing the inferences from moprhometric analysis and runoff. The study area chosen for the present study is
Yagachi catchment situated in Chickamaglur and Hassan district lies geographically at a longitude 75⁰52’08.77”E and
13⁰10’50.77”N latitude. It covers an area of 559.493 Sq.km. Morphometric analysis is carried out to estimate morphometric
parameters at Micro-watershed to understand the hydrological response of the catchment at the Micro-watershed level. Daily runoff
is estimated using USDA SCS curve number model for a period of 10 years from 2001 to 2010. The rainfall runoff relationship of the
study shows there is a positive correlation.
Keywords: morphometric analysis, runoff, remote sensing and GIS, SCS - method
-
Effect of variation of plastic hinge length on the results of non linear anal...eSAT Journals
Abstract The nonlinear Static procedure also well known as pushover analysis is method where in monotonically increasing loads are applied to the structure till the structure is unable to resist any further load. It is a popular tool for seismic performance evaluation of existing and new structures. In literature lot of research has been carried out on conventional pushover analysis and after knowing deficiency efforts have been made to improve it. But actual test results to verify the analytically obtained pushover results are rarely available. It has been found that some amount of variation is always expected to exist in seismic demand prediction of pushover analysis. Initial study is carried out by considering user defined hinge properties and default hinge length. Attempt is being made to assess the variation of pushover analysis results by considering user defined hinge properties and various hinge length formulations available in literature and results compared with experimentally obtained results based on test carried out on a G+2 storied RCC framed structure. For the present study two geometric models viz bare frame and rigid frame model is considered and it is found that the results of pushover analysis are very sensitive to geometric model and hinge length adopted. Keywords: Pushover analysis, Base shear, Displacement, hinge length, moment curvature analysis
Effect of use of recycled materials on indirect tensile strength of asphalt c...eSAT Journals
Abstract
Depletion of natural resources and aggregate quarries for the road construction is a serious problem to procure materials. Hence
recycling or reuse of material is beneficial. On emphasizing development in sustainable construction in the present era, recycling of
asphalt pavements is one of the effective and proven rehabilitation processes. For the laboratory investigations reclaimed asphalt
pavement (RAP) from NH-4 and crumb rubber modified binder (CRMB-55) was used. Foundry waste was used as a replacement to
conventional filler. Laboratory tests were conducted on asphalt concrete mixes with 30, 40, 50, and 60 percent replacement with RAP.
These test results were compared with conventional mixes and asphalt concrete mixes with complete binder extracted RAP
aggregates. Mix design was carried out by Marshall Method. The Marshall Tests indicated highest stability values for asphalt
concrete (AC) mixes with 60% RAP. The optimum binder content (OBC) decreased with increased in RAP in AC mixes. The Indirect
Tensile Strength (ITS) for AC mixes with RAP also was found to be higher when compared to conventional AC mixes at 300C.
Keywords: Reclaimed asphalt pavement, Foundry waste, Recycling, Marshall Stability, Indirect tensile strength.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
We have compiled the most important slides from each speaker's presentation. This year’s compilation, available for free, captures the key insights and contributions shared during the DfMAy 2024 conference.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Water billing management system project report.pdfKamal Acharya
Our project entitled “Water Billing Management System” aims is to generate Water bill with all the charges and penalty. Manual system that is employed is extremely laborious and quite inadequate. It only makes the process more difficult and hard.
The aim of our project is to develop a system that is meant to partially computerize the work performed in the Water Board like generating monthly Water bill, record of consuming unit of water, store record of the customer and previous unpaid record.
We used HTML/PHP as front end and MYSQL as back end for developing our project. HTML is primarily a visual design environment. We can create a android application by designing the form and that make up the user interface. Adding android application code to the form and the objects such as buttons and text boxes on them and adding any required support code in additional modular.
MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software. It is a stable ,reliable and the powerful solution with the advanced features and advantages which are as follows: Data Security.MySQL is free open source database that facilitates the effective management of the databases by connecting them to the software.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressionsVictor Morales
K8sGPT is a tool that analyzes and diagnoses Kubernetes clusters. This presentation was used to share the requirements and dependencies to deploy K8sGPT in a local environment.
KuberTENes Birthday Bash Guadalajara - K8sGPT first impressions
Method of solving multi objective optimization problem in the presence of uncertainty
1. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Issue: 01 | Jan-2014, Available @ http://www.ijret.org 496
METHOD OF SOLVING MULTI-OBJECTIVE OPTIMIZATION
PROBLEM IN THE PRESENCE OF UNCERTAINTY
Mingliqulov Zafar
Centre for development of software and hardware - software systems at the Tashkent University of Information
Technologies, Uzbekistan
Abstract
Multi-objective formulations are realistic models for many complex engineering optimization problems. In many real-life problems
considered objectives conflict with each other and optimization of one target solutions can lead to unacceptable results for other
purposes. A reasonable solution of the multi-objective problem is to study the set of solutions, each of which satisfies the objectives at
an acceptable level with no dominance of any of the solutions. The article provides a brief overview of multi-objective optimization
methods (by Pareto criteria) and their improvement.
Keywords: A fuzzy set, forecasting, risk, weakly formalized process for Pareto multi-objective optimization.
---------------------------------------------------------------------***---------------------------------------------------------------------
1. INTRODUCTION
The goal of this work is to present an overview of the methods
of multi-criteria optimization on Pareto criteria and its
improvement. In most cases objectives of the multi-objective
problem conflict with each other, thereby preventing
simultaneous optimization of each objective. Many, if not all,
real engineering problems actually have more than one
objective, that is, minimize costs, maximize productivity,
increase reliability, etc. They are challenging, but real
problems.
There are two approaches to the multi-criteria optimization.
One of them is the convolution of the individual objective
functions into a single component or to impose on all criteria
except one the set of restrictions. In the first case the
determination of the total objective function is possible with
the help of the theory of utility, the weighted sum, etc., but the
problem lies in the proper choice of weights or utility
functions that characterize the preferences of the customer.
This optimization method doesn’t provide a set, but a unique
solution, which can be examined to identify possible trade-
offs.
The second approach is to define a set of Pareto optimal
solutions, or a representative subset. Pareto solution is the set
of non-dominant to each other solutions. When moving from
one Pareto solutions to another, there are always some loss in
one solution, and certain improvements in others. Pareto-
optimal set of solutions are often preferred by single results
because they are more practical when considering the trade-
offs in the real life problems. The set of Pareto solutions may
be any size, but typically the size increases with increasing
number of purposes.
Note that the Pareto principle is not universal and applies only
if a number of axioms are met. And even if these axioms are
met, the construction of the Pareto set can cause significant
difficulties [1, 7-8].
2. STATEMENT OF THE PROBLEM OF MULTI-
OBJECTIVE OPTIMIZATION
In the formulation of multi-objective optimization problem
mandatory condition to meet all individual criteria and
constraints is introduced as a requirement for the optimality of
solutions, namely all of the functions belonging to the set of
optimal solutions must be different from zero in the optimum
point, the optimum criteria must be satisfied to the extent
possible. The increase in the value of the generalized criterion
should not happen while improving the value of some
indicators of quality at the expense of the deterioration of
others. In the terminology of decision theory, the latter
requirement is equivalent to the condition of belonging to a
Pareto optimum [1].
The problem of multi-criteria optimization has the following
form:
,
min,,...,, 21
Xx
xfxfxfxf T
q
(1)
Where
2. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Issue: 01 | Jan-2014, Available @ http://www.ijret.org 497
.,1,
,0,|
,,...,2,1
,
1
1
n
j
ijij
n
n
j
jkjk
mibxa
xbAxRxX
qQk
xcxf
The problem of multi-objective optimization with fuzzy goal
involves finding such х that satisfy the following constraints
[2-4]:
,,,...,2,1,~ Xxqkgxf kk
(2)
Where kg~
- fuzzy set,
.,0
,,1
,,1
kkk
kkkk
k
kk
kk
kk
tgxf
tgxfg
t
gxf
gxf
xf
(3)
The solving the Fuzzy problem (2) can be reduced to the
solving the following unfuzzy problem:
.
,
max,
Xx
xfkk
(4)
3. FINDING THE PARETO OPTIMAL
SOLUTIONS
The solution Xx 0
is called Pareto optimal solution if
0
xfyf kkkk
for all y, and 0
xfyf SSSS
for at
least one.
The solution Xx 0
is called optimal solution on the Pareto
type criteria if there is no Xy better than
0
x on the Pareto
type criteria.
We introduce the concept the improvability of solution Xy
on the Pareto type criteria in fuzzy environment: we call
solution Xy improvable if there is the solution Xx 0
,
which is better than у on the Pareto type criteria.
The solution Xx 0
is improvable in finding multi-objective
fuzzy solutions xfxfxfxf p,...,, 21
if and only if there is a
vector
Q
R , for which the following inequalities are met:
S
SS
k
kk cxfcxf 00
,
For all Qk ,...,1 and at least one QS ,...,1 , where
k
k
cc
,
k
kkk
y
yfc minmax
.
Let required inequalities are satisfied, then according to the
definition of
k
c Xy , for which the inequality
kkk yfc
, and therefore
yfcxfyfc SS
S
SSkk
k
0
,
, yfcxf kk
k
SS 0
are
met for all Qk ,...,1 or at least one QS ,...,1 , exists. These
inequalities show that the solution Xx 0
is improvable.
Let solution Xx 0
is improvable and let Xy is the solution,
which is better than the solution
0
x on Pareto criteria. We
assume that yfyf kkSSk
for all Qk ,...,1 , where
.: 0
xfyfS SSSS
Then
.][min][max yfyfyf SSkkk
y
kkk
k
Considering
cyf kkk
k
][min
for all form Q
R , we get
][max0
kkk
k
kkkkkk yfyfxf
cyf kkk
y
][min
For all Qk ,...,1 and
cyfxf SSSSSS 0
for at least one QS ,...,1 . Thus
the validity of these inequalities is proved.
Solution Xx 0
is improvable in situation of making
multipurpose decisions if and only if there exists a vector γ
from the set
,minmax:R{ Q
k
y
kk
y
yfyfГ
kQk ,,...,1,
such that inequalities
S
SS
k
kk cxfcxf 00
,
are met. The validity of these
inequalities follows from the following considerations
,
minmax0
cyfyfyfxf kkk
k
kkkkkk
for
every Qk ,...,1, , cyfxf SSSSSS 0
.
It follows that if the evaluation functionals
Q
kkk yf 1
are
obtained after the application of the natural normalization,
then the domain Г has following form:
kQkГ k ;,...,1,,1;RQ
.
3. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Issue: 01 | Jan-2014, Available @ http://www.ijret.org 498
Thus, the solution to the problem about improvability, Pareto
optimality of multi-purpose solution Xx 0
on Pareto
criterion is reduced to the existence (absence) of a vector
for which the inequalities S
SS
k
kk cxfcxf 00
are
met.
Thus the following inequalities should be met (be
incompatible) for the solution Xy to be improvable
(optimal on Pareto):
.,...,1,
minmaxmax Qkzfyf k
z
kk
The validity of these inequalities follows from the following
considerations:
,minmaxaxminmax
minmax0
zfmzf
zfzfyfxf
zz
kkk
z
kkkkkk
zfyfxf SS
z
SSSSSS minminmax0
for all kQk ,,...,1,
or at least one QS ,...,1
.
Let yfkk
be the membership function of yfk , which is
defined as (3).
0
x is optimal solution of improvable problem
.0,,,...,1max, *
1
kkkk
Q
k
k XxQkxf
(5)
Then solution Xx 0
is Pareto optimal solution of the problem
(1).
We suppose inverse case. Let Xx 0
be Pareto optimal solution
of (1). Then there exists such solution Xy that 0
xfyf kk
for
all ( Qk ,...,1 ) and 0
xfyf SS
for some .,..,1 QS Since the vector
Qkk ,...,1,
is positive and satisfies the following equations:
Qkxf kkk ,...,1,*0
And
Q
k
Q
k
kkk Qxf
1 1
*0
.
Nevertheless, there is 0
xfyf kk
for all ( Qk ,...,1 ) and
0
xfyf SS
for some .S
This leads to the following inequality:
.
1
*
1
*00
1 1
*0
Q
Sk
k
SSkk
Q
Sk
k
SSkk
Q
k
Q
k
kkk
Qyfyf
QxfxfQxf
This means that the solution (5) Xx 0
is not optimal.
Finding Pareto optimal solution (5) in condition of (3) leads to
solving following problem of linear programming:
.,...,1,0
,,...,1,
max,cR
1
q
1k
k
njx
mqkbxa
x
j
n
j
kjkj
k
We solve this problem using recurrent neural networks.
For calculating the model with recurrent neural networks
moving to the opposite function
q
kk xcR
1k and to write the
value of kc
in the appropriate table with opposite sign is
needed.
When vector is given to the input of the network, the state of
neurons are determined, but then because the outputs of
neurons are the feedbacks, to their inputs again a new vector is
entered and the state changes again. The concept of stability is
connected with recurrent networks [6]. The network is
considered to be stable if, after a finite number of iterations,
the neurons receive state that no further changes. When a
vector is given to the input of stable recurrent networks, the
output signals of neurons are generated, which are then
applied to the inputs again, generating a new state vector
again, but while the network is not set to the final state, with
the increasing number of iterations, the number of changes of
nodes’ states is reduced. Network without feedback is always
stable, since when one vector is given to the input, nodes of
the network change their states only once due to the constancy
of input neurons.
4. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Issue: 01 | Jan-2014, Available @ http://www.ijret.org 499
For solving the problem (1)-(2) recurrent neural network,
which is defined with the following differential equation, is
proposed:
t
cbxa
t
tu
k
n
j
kjkj
k
exp
)(
1
,
Where )exp(1
1
)()),((
u
uftufx kk
. As in the Hopfield network,
it uses neurons matrix with the size of nn , but the neurons
interact not on the principle “with each other”, but by the rows
and columns.
The difference version of this equation has the following form:
t
cbxatuu k
n
j
kjkj
t
k
t
k exp
1
1
(6)
Where t - step by time. Parameters ,,,,t
are selected
experimentally and they significantly impact to the speed of
problem solving and to the quality of solution.
To speed up the solving of equations (6) the principle of
«Winner takes all» is proposed [2-4]:
Matrix
0
kx
of random values ]1,0[0
kx
is generated.
Iteration (6) is continued until following inequality is met:
n
j
kjkj bxa
1
,
Where - the specified accuracy of the constraints
Steps 1 and 2 are repeated.
One of the main properties of artificial neural networks is the
reliability of the neural network models. This property may
allow building fo neural network systems for areas where high
reliability is required.
No less important is the learning property of neural networks.
Because of this property, not only they can recognize patterns
applied to their input, but also adjust their parameters with the
help of the appropriate procedure to carry out correct
recognition as much as possible. Thus, the neural networks
can operate in two modes or phases: a learning mode and the
recognition mode.
The ability of neural networks to generalize is also very
important property. Due to this property not only the network
can show the imaged given during the training, but also build
new ones. This increases the “competence” of systems based
on neural networks.
4. COMPUTATIONAL EXPERIMENT
We consider an example taken from [5]. For solving multi-
criteria problem
8
10
5
3
min2)(
min64)(
1
21
2
21
212
211
x
xx
x
xx
xxxz
xxxz
(7)
With the following fuzzy objectives:
9;20 21 gg
And tolerances
2;2 21 tt
We form following membership functions:
rxz
rxz
xzr
xz
2)(0
2)(
2
)(2
)(
1
1
1
11
7)(0
7)(
2
)(7
)(
1
1
2
11
xz
xz
xz
xz
Then model (7) takes the following form:
8
10
5
3
27
2
1
6422
2
1
max
1
21
2
21
21
21
x
xx
x
xx
xx
xx
5. IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
__________________________________________________________________________________________
Volume: 03 Issue: 01 | Jan-2014, Available @ http://www.ijret.org 500
The solution of this model is
,0;5,4, *
2
*
1
*
xxx
Optimal value is 1*
, the values of the objective function
are
.9,18 **
xzxz
We consider the existence of the vector 21,
, which
may improve the solution
*
x .
For this we solve the following problem:
8
10
5
3
922
20264
max
1
21
2
21
221
121
21
x
xx
x
xx
xx
xx
(8)
The solution of the model (8) is
)5;2(, **
2
**
1
**
xxx
Optimal values are:
0;21 21
, the values of the objective function are
;22)( **
1 xz .9)( **
2 xz
Thus there is a vector
,, 21
where the Pareto-optimal
solution is improvable, i.e.
*
1
**
1 xzxz
и
*
2
**
2 xzxz
5. CONCLUSIONS
Thus, the solving the problem of Pareto optimality of the
multi-objective solution
n
Rx 0
on Pareto criteria or its
improvability is reduced to establishing the existence or
absence of a vector that satisfies the inequalities
S
ss
k
kk cxfcxf 00
.
REFERENCES
[1] Nogin V. D. Edgeworth-Pareto principle and the
relative importance of the criteria in the case of fuzzy
preference relations // Journal of Comp. Mathematics
and physics 2003. - Т. 43, № 11. - 1666-1676 p. [in
Russian]
[2] Rotshtein A.P. Fuzzy Multicriteria Analysis of Variants
with the Use of Paired Comparisons // Journal of
Computer and Systems Sciences International, Vol. 40,
No. 3, 2011, pp. 499-503. [in Russian]
[3] Rotshtein A.P. Fuzzy multicriteria choice among
alternatives: Worst-case approach // Journal of
Computer and Systems Sciences International, June
2009, Volume 48, Issue 3, pp 379-383.
[4] Rotshtein A. P., Intelligent Identification Technologies:
Fuzzy Sets, Neural Networks, Genetic Algorithms
(Universum, Vinnitsa, 1999) [in Russian], 320 p.
[5] N.N.Vilyams. Parametric programming in the economy.
Moscow. [in Russian] 1976 y. 96 p.
[6] Yazenin A.V. The problem of vector optimization with
fuzzy information concerning the pair comparisons of
the coefficients of importance of criteria. //
Mathematical methods of optimization and control in
complex systems, Interuniv. Collect, Kalinin 1982, pp.
28-32, [in Russian].
[7] Liu B. Theory and Practice of Uncertain Programming
2nd ed. // Studies in Fuzziness and Soft Computing,
Vol. 239. Springer. 2009, 205 p.
[8] Malyshev V. A., Piyavsky B. S., Piyavsky S. A.
Method of decision making under uncertainty diversity
of accounting methods / / Theory and control systems.
2010. Vol. 1, 46-61 p. [in Russian].
BIOGRAPHIES
He got his BSc and MSc degrees from
"Software engineering for Computer
Systems, networks and complexes"
department, Tashkent University of
Information Technology in 2005 and 2007
respectively. He published several papers on
the topic of Data mining, such as fuzzy sets
theory and neural networks in many international conferences
and journals. Currently, He is working as senior researcher at
Centre for development of software and hardware - software
systems at the Tashkent University of Information
Technologies.