Browsing by Author "Pankaj"

Now showing 1 - 16 of 16

A genetic method using hybrid crossover for solving travelling salesman problem
(Blue Eyes Intelligence Engineering and Sciences Publication, 2019) Anubhav Kumar Prasad; Dharm Raj Singh; Pankaj
This paper proposes a Genetic approach using Hybrid Crossover for Solving the Travelling Salesman Problem. Proposed hybrid method generates an initial population using Nearest Neighbor (NN) approach which is modified using “Sub-Path Mutation” (SPM) process. Modified population undergoes Distance Preserving Crossover (DPX) [2] and 2-opt Optimal mutation (2-opt) [1] to check for possible refinement. SPM searches position for the minimum distant city within a given path. This work is motivated by the algorithm developed by [3] who performed DPX and 2-opt mutation on the initial population generated using NN. For performance comparison, standard TSPLIB data is taken. The proposed hybrid method performances better in terms of % best error. It performs better than methods reported in [3-11]. © BEIESP.
A Study of KVP Approach on Some Transportation Models
(Institute of Electrical and Electronics Engineers Inc., 2018) Anubhav K. Prasad; Pankaj
In this paper Vogel's Approximation Method and Least Cost Method for Transportation Problem were investigated to obtain the solution at a faster rate using Key-Value Pair approach. Computation experiments were carried out to investigate the effectiveness of Key-Value pair over 1900 problem instances for Vogel's Approximation Method and Least Cost Method each. It was seen that Key-Value pair greatly enhanced the rate of solving for both methods over traditional coding approach. Time comparison is shown for square balanced transportation problems. © 2018 IEEE.
E-convex functions and nonsmooth mathematical programs
(International Publications, 2021) Bhuwan Chandra Joshi; Rakesh Mohan; Pankaj
In this paper, we derive sufficient optimality condition for a nonsmooth mathematical program with equilibrium constraints using E-convex functions. We formulate the Wolfe and Mond-Weir type duality models and establish weak and strong duality theorems to relate the mathematical program with equilibrium constraints and the dual models in the framework of convexificators. © 2021, International Publications. All rights reserved.
Future Prospects of Biodegradable Polymers with Potential Application in Food Industry
(Springer Nature, 2022) Tejaswini Patil; Abhishek Dutt Tripathi; Dinesh Chandra Rai; Aparna Agarwal; Veena Paul; Kamlesh Kumar Maurya; Pankaj
Enormous plastic production and its consumption and accumulation are a global concern. Although the solution to this issue is “reuse, recycle, and reduce plastic, " it is not quite enough, and therefore biodegradable packaging material is gaining acceptability in the agriculture and food industry for packaging purposes. This chapter summarizes recent approaches and innovations in the field of biodegradable polymers and future prospects. Here, biodegradable polymers and natural polymers with their properties, their applicability, and their degradation are discussed. Also, improvements in properties of natural polymers by using technologies have been discussed. Biodegradable polymers reduce the burden of greenhouse gases on Earth. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022.
GENERALIZED INVEXITY and MATHEMATICAL PROGRAMS
(Faculty of Organizational Sciences, Belgrade, 2021) Bhuwan Chandra Joshi; Rakesh Mohan; Pankaj
In this paper, using generalized convexity assumptions, we show that M-stationary condition is sufficient for global or local optimality under some mathematical programming problem with equilibrium constraints(MPEC). Further, we formulate and study Wolfe type and Mond-Weir type dual models for the MPEC, and we establish weak and strong duality theorems. © 2021 Faculty of Organizational Sciences, Belgrade. All rights reserved.
Higher order duality in multiobjective fractional programming problem with generalized convexity
(Faculty of Organizational Sciences, Belgrade, 2017) Pankaj; Bhuwan Chandra Joshi
We have introduced higher order generalized hybrid B-b p θ p r-invex function. Then, we have estabilished higher order weak, strong and strict converse duality theorems for a multiobjective fractional programming problem with support function in the numerator of the objective function involving higher order generalized hybrid B-b,p θ p r-invex functions. Our results extend and unify several results from the literature.
Introduction: Scope and Importance of Biodegradable Polymers
(Springer Nature, 2022) Veena Paul; Abhishek Dutt Tripathi; Kamlesh Kumar Maurya; Pankaj; Dinesh; Dinesh Chandra Rai
In today’s world, the interest in biodegradable polymers has grown significantly. The demand for these polymers has skyrocketed, making them broadly utilized polymers with a range of several applications. Plant, animal, and microbially derived biopolymers have piqued the interest of researchers. Because of their inherent properties like biodegradability, biocompatibility, inexhaustibility, and economic availability, the need for biodegradable polymers has been enhanced. Recent trends in the food packaging industry have shown the employment of biodegradable polymers with improved characteristics. This chapter emphasizes biodegradable polymers’ development, classification, application, challenges, and market opportunities. The application of these polymers in active and intelligent packaging are summarized. This chapter also highlights the application of biodegradable polymers as an assuring green technique for assuring the quality and safety of food. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2022.
Loop formation in transportation problem: Semi-cycle formation in restricted graph
(Institute of Advanced Scientific Research, Inc., 2018) Anubhav Kumar Prasad; Pankaj
Loop formation in Transportation Problem using Modified Distribution Method can be termed as Semi-Cycle formation in Restricted Graph, from given starting vertex with some vertices participating in it which is different form cycle formation in Hamiltonian Cycle, where each vertex is involved. The participating vertices must be used exactly once except the first and last vertex which is same. The restriction is imposed by allowing only horizontal and vertical connection in the semi-cycle formation. This paper presents the algorithm for such semi-cycle formation for Transportation Problem. © 2018, Institute of Advanced Scientific Research, Inc. All rights reserved.
Mathematical programs involving e-convex functions
(Politechnica University of Bucharest, 2021) Bhuwan Chandra Joshi; Pankaj
In this paper, we have shown that generalized M-stationary condition is sufficient for global optimality under the assumptions of E-convexity and mathematical programming problems with equilibrium constraints. Further, we formulate and study Wolfe type and Mond-Weir type dual models for the MPEC and we establish weak and strong duality theorems relating to the MPEC and the two dual models. © 2021, Politechnica University of Bucharest. All rights reserved.
On nonsmooth mathematical programs with equilibrium constraints using generalized convexity
(Faculty of Organizational Sciences, Belgrade, 2019) Bhuwan Chandra Joshi; Shashi Kant Mishra; Pankaj
In this paper, we derive the sufficient condition for global optimality for a nonsmooth mathematical program with equilibrium constraints involving generalized invexity.We formulate the Wolfe and Mond-Weir type dual models for the problem using convexificators.We establish weak and strong duality theorems to relate the mathematical program with equilibrium constraints and the dual models in the framework of convexificators. © 2019 Faculty of Organizational Sciences, Belgrade. All rights reserved.
Optimality and duality results for fractional programming problems under E-univexity
(Springer, 2024) S.K. Mishra; D. Singh; Pankaj
In this article, we deal with nonconvex fractional programming problems involving E-differentiable functions (FPE). The so-called E-Karush-Kuhn-Tucker sufficient E-optimality conditions are established for nonsmooth optimization problems under E-univexity hypothesis. The established optimality conditions are explained with a numerical example. The so-called vector dual problem in the sense of Schaible (SDE) involves E-differentiable functions for (FPE) is defined under E-univexity hypothesis. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Optimality and duality results for fractional programming problems under E-univexity
(Springer, 2025) Shashi Kant Mishra; Dhruv Singh; Pankaj
In this article, we deal with nonconvex fractional programming problems involving E-differentiable functions (FPE). The so-called E-Karush-Kuhn-Tucker sufficient E-optimality conditions are established for nonsmooth optimization problems under E-univexity hypothesis. The established optimality conditions are explained with a numerical example. The so-called vector dual problem in the sense of Schaible (SDE) involves E-differentiable functions for (FPE) is defined under E-univexity hypothesis. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.
Optimality conditions for multiple objective fractional subset programming with (ρ,σ,θ)-type-I and related non-convex functions
(Springer-Verlag Italia s.r.l., 2012) S.K. Mishra; M. Jaiswal; Pankaj
In this paper, we introduce a class of generalized invex n-set functions, called (ρ,σ,θ)-type-I and related non-convex functions, and then establish a number of parametric and semi-parametric sufficient optimality conditions for the primal problem under the aforesaid assumptions. This work partially extends an earlier work of Mishra et al. (Math. Methods Oper. Res. 67, 493-504, 2008) to a wider class of functions. © 2011 Springer-Verlag.
Optimality conditions for multiple objective fractional subset programming with invex and related non-convex functions
(2010) S.K. Mishra; M. Jaiswal Banaras; Pankaj
In this paper, we introduce a class of generalized invex n-set functions and related nonconvex functions, and then establish a number of parametric and semi-parametric sufficient optimality conditions for the primal problem under the aforesaid assumptions.
Sufficiency and duality for mathematical programming problems with equilibrium constraints, involving generalized convex functions
(International Publications, 2019) Bhuwan Chandra Joshi; Pankaj; Shashi Kant Mishra
In this paper, we show that M-stationary condition is sufficient for global or local optimality under some mathematical programming problem with equilibrium constraints(MPECs) and generalized invexity assumptions. Further, we formulate and study, Wolfe type and Mond-Weir type dual models for the MPEC and we establish weak and strong duality theorems relating to the MPEC and the two dual models under invexity and generalized invexity as-sumptions. © 2019, International Publications. All rights reserved.
Vector Variational Inequalities in Terms of Fréchet Subdifferentials with Genralized Convex Function
(International Publications, 2022) Bhuwan Chandra Joshi; Rakesh Mohan; Pankaj
In this paper,nonsmooth vector optimization problem involving approximate starshaped preinvex functions and strongly locally starshaped invex functions in terms of the Fréchet subdifferentials is considered. Further, we derive optimality conditions for a point to be a local sharp and local weak sharp efficient solution of the vector optimization problem involving approximately starshaped preinvex and strongly locally starshaped invex functions in terms of the Fréchet subdifferentials and superdifferentials. In order to justify the theorems some examples are also given. © 2022, International Publications. All rights reserved.