Department of Mathematics

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Subject: search.filters.subject.Multi-objective optimization

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    A comparative study of ε-constraint, lp-metric, and weighted sum multi-objective optimization methods in a circular economy
    (Elsevier, 2024) Kulshrestha, Rakhee; Sangwan, Kuldip Singh
    Approximately 74.7 Mt (Million Metric Tonnes) of e-waste is expected to be produced in 2030, and laptop e-waste is one of the major constituents of this. The goal of this paper is to develop and optimize a mixed-integer linear programming (MILP) mathematical model for a laptop manufacturer in India, based on a framework that integrates secondary reuse concept associated with traditional circular economy waste avoidance strategies. The multi-objective solution techniques of ε-constraint, LP-metric, and weighted sum methods are used to optimize the circular economy model. The proposed model aids as a policy tool to decide the optimum number of inspection/collection centers, sales/distribution centers, disassembly centers, refurbishing centers, recycling centers, and their optimum locations and allocations. This study results suggest that reuse, secondary customer centers, refurbishing, and recycling of the laptops is not only economically beneficial to the organization but also environment friendly and helps to create more jobs in the rural economy.
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    Modelling and simultaneous optimization of environmental, economic, and technological factors in machining
    (Springer, 2023-10) Sangwan, Kuldip Singh; Kulshrestha, Rakhee
    In the current era, manufacturing industries are facing multifaceted challenges related to increasing environmental awareness, decreasing economic gains, and technology obsolesce. These challenges become more apparent during the machining of difficult-to-machine materials due to high tool wear rates, high cutting forces, undesirable surface quality, high tool replacement costs, and a stagnating productivity. The developed approach aims at improving environmental, economic, and technological factors by optimizing four performance characteristics–energy demand, surface roughness, tool wear, and material removal rate during the milling of H13 tool steel by using an integrated artificial neural network and genetic algorithm. The proposed methodology provides Pareto solutions for minimum energy demand, surface roughness, & tool wear, and maximum material removal rate. The novelty of this work lies in generating Pareto fronts for analyzing conflicting responses, and determining preferred solutions without sacrificing environmental, technological, and economic considerations, simultaneously. The present work will be significant to practitioners in adopting better management strategies and simultaneously dealing with these challenges. The potential of the research lies in directly integrating the proposed optimization module with the machine tool system to serve as an online tool for machine tool process optimization.
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    Multi-objective optimization of advanced sleep mode for energy saving in cognitive radio network
    (Elsevier, 2025-09) Kulshrestha, Rakhee
    The Advanced Sleep Modes (ASM) concept corresponds to entering the Base Station (BS) progressively deeper and less energy-intensive states to reduce energy consumption. Introducing the ASM can mitigate energy wastage during low-traffic periods in the Cognitive Radio Network (CRN). In this study, we propose a strategy for integrating ASM within the CRN architecture to effectively handle primary and secondary traffic across varying ASM sleep states. Additionally, we study the general scenario of CRN with heterogeneous secondary users, imperfect sensing, and unreliable BS due to the arrival of negative packets (virus attack). By modeling the entire system as a three-dimensional discrete-time Markov chain, we conduct the transient analysis of the proposed model. Through numerical demonstrations involving reliability and queueing analyses, we substantiate the validity of the proposed model and examine the impact of reliability on its performance. Then, we showcased the effectiveness of the ASM strategy by comparing it with the Sleep Mode (SM) strategy in terms of the waiting time and blocking probability of the secondary user and the degree of energy savings. Also, simulation experiments are conducted to corroborate the accuracy and validity of the numerical results. Finally, we formulate the Cost Benefit Function (CBF), which depends on both the successful transmission and waiting time of secondary packets. Subsequently, we obtain the Pareto optimal solution for CBF and the degree of energy saving using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) techniques for multi-objective optimization.