Department of Computer Science and Information Systems
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Item The single depot multiple set orienteering problem(Scitepress, 2023) Mishra, AbhishekIn this article, we present the single Depot multiple Set Orienteering Problem (sDmSOP), a new variant of the classical Set Orienteering Problem (SOP). A significant feature of sDmSOP is the presence of many travelers who set off from the same depot and return there at the end of their journey. The objective of the problem is to maximize the profit while remaining within the budget; hence the challenge at hand involves searching multiple paths among the mutually clustered sets for travelers. A set’s profit can be collected with a single node visit only. Supply-chain management, the bus delivery problem, etc., are just a few examples where the sDmSOP has proven useful. By simulating the instances of the Generalized Traveling Salesman Problem (GTSP) using GAMS 37.1.0, we determine the optimal profit for GTSP instances for some small and medium instances which follow the triangular and symmetric properties. We find that the use of multiple travelers is beneficial for both service provid ers and customers, as it allows service providers to offer their services to customers at a lower cost because the service provider gets a significant amount of profit using multiple travelersItem A compact formulation for the mdmsop: theoretical and computational time analysis(Springer, 2023-11) Mishra, AbhishekThe multi-Depot multiple Set Orienteering Problem (mDmSOP) is one of the recently proposed variants of the Set Orienteering Problem (SOP), which has applicability in different real-life applications such as delivering products and mobile crowd-sensing. The objective of the problem is to collect maximum profit from clusters within a given budget. In this paper, we propose an improved integer linear programming (ILP) formulation of the mDmSOP and conduct a time analysis of the results. We solved it using GAMS 39.2.0 and found that we can reduce a large number of constraints while changing sub-tour elimination constraints only. In the case of small instances, the improved mathematical formulation gives better results in all of the test cases for small instances up to 76 vertices except one instance of 16eil76 when , and it gives better results in 93.33% of cases for small instances and 88.23% of cases while simulating on mid-size instances up to 198 nodes when .Item The multi-depot multiple set orienteering problem: an integer linear programming formulation(Scitepress, 2024) Mishra, AbhishekIn this article, we introduce a novel variant of the single Depot multiple Set Orienteering Problem (sDmSOP), which we refer to as the multi-Depot multiple Set Orienteering Problem (mDmSOP). We suggest the integer linear program (ILP) of the mDmSOP also, and analyze the impact of the Sub-tour Elimination Constraints (SECs) based on the Miller–Tucker–Zemlin (MTZ) and the Gavish-Graves (GG) model on it. The mDmSOP is most frequently encountered in distribution logistics. In mDmSOP, a fleet of travelers is utilized to serve a set of customers from a number of depots, with each traveler associated with a specific depot. The challenge is to choose the routes for each traveler to maximize the profit within a specific budget, while the profit can be earned from a set of customers only once by visiting exactly one customer. We show the simulation results conducted on the General Algebraic Modeling System (GAMS) 39.0.2, which is used to model and analyze linear, non-linear, mixed-integer, and other complex optimization problems. The Generalized Traveling Salesman Problem (GTSP) instances of up to 200 vertices are taken as the input data set for the simulations. The results show that the MTZ-based formulation takes less time than the GG-based formulation to converge to the optimal solution for the mDmSOP.Item Variable neighborhood search for the multi-depot multiple set orienteering problem(2024) Mishra, AbhishekThis paper introduces a variant of the Set Orienteering Problem (SOP), the multi-Depot multiple Set Orienteering Problem (mDmSOP). It generalizes the SOP by grouping nodes into mutually exclusive sets (clusters) with associated profits. Profit can be earned if any node within the set is visited. Multiple travelers, denoted by t (>1), are employed, with each traveler linked to a specific depot. The primary objective of the problem is to maximize profit collection from the sets within a predefined budget. A novel formulation is introduced for the mDmSOP. The paper utilizes the Variable Neighborhood Search (VNS) meta-heuristic to solve the mDmSOP on small, medium, and large instances from the Generalized Traveling Salesman Problem (GTSP) benchmark. The results demonstrate the VNS's superiority in robustness and solution quality, as it requires less computational time than solving the mathematical formulation with GAMS 37.1.0 and CPLEX. Additionally, increasing the number of travelers leads to significant improvements in profits.Item New techniques for constructing rare-case hard functions(2025-02) Mishra, AbhishekWe say that a function is rare-case hard against a given class of algorithms (the adversary) if all algorithms in the class can compute the function only on an o(1)-fraction of instances of size n for large enough n. Starting from any NP-complete language, for each α>0, we construct a function that cannot be computed correctly even on a 1/nα-fraction of instances for polynomial-sized circuit families if NP ⊄ P/POLY and by polynomial-time algorithms if NP ⊄ BPP - functions that are rare-case hard against polynomial-sized circuits and polynomial-time randomized algorithms. The constructed function is a number-theoretic polynomial evaluated over specific finite fields. For NP-complete languages that admit parsimonious reductions from all of NP (for example, SAT), the constructed functions are hard to compute even on a 1/nα-fraction of instances by polynomial-time randomized algorithms and polynomial-sized circuit families simply if P# ⊄ BPP and P# ⊄ P/POLY, respectively. We also show that if the Randomized Exponential Time Hypothesis (RETH) is true, none of these constructed functions can be computed even on a 1/nα-fraction of instances in subexponential time. These functions are very hard, almost always. While one may not be able to efficiently compute the values of these constructed functions themselves, in polynomial time, one can verify that the evaluation of a function, s=f(x), is correct simply by asking a prover to compute f(y) on targeted queries. We have extended our work to give an alternative proof of a variant of Lipton's theorem (Lipton, 1989). We also compare our techniques for constructing rare-case hard functions with two other existing methods in the literature (Sudan et al., 2001; Feige and Lund, 1996).Item Hardness amplification via group theory(2024-11) Mishra, AbhishekWe employ techniques from group theory to show that, in many cases, counting problems on graphs are almost as hard to solve in a small number of instances as they are in all instances. Specifically, we show the following results. 1. Goldreich (2020) asks if, for every constant δ<1/2, there is an O~(n2)-time randomized reduction from computing the number of k-cliques modulo 2 with a success probability of greater than 2/3 to computing the number of k-cliques modulo 2 with an error probability of at most δ. In this work, we show that for almost all choices of the δ2(n2) corrupt answers within the average-case solver, we have a reduction taking O~(n2)-time and tolerating an error probability of δ in the average-case solver for any constant δ<1/2. By "almost all", we mean that if we choose, with equal probability, any subset S⊂{0,1}(n2) with |S|=δ2(n2), then with a probability of 1−2−Ω(n2), we can use an average-case solver corrupt on S to obtain a probabilistic algorithm. 2. Inspired by the work of Goldreich and Rothblum in FOCS 2018 to take the weighted versions of the graph counting problems, we prove that if the RETH is true, then for a prime p=Θ(2n), the problem of counting the number of unique Hamiltonian cycles modulo p on n-vertex directed multigraphs and the problem of counting the number of unique half-cliques modulo p on n-vertex undirected multigraphs, both require exponential time to compute correctly on even a 1/2n/logn-fraction of instances. Meanwhile, simply printing 0 on all inputs is correct on at least a Ω(1/2n)-fraction of instances.Item Exploring the performance of genetic algorithm and variable neighborhood search for solving the single depot multiple set orienteering problem: a comparative study(2024-11) Mishra, AbhishekThis article discusses the single Depot multiple Set Orienteering Problem (sDmSOP), a recently suggested generalization of the Set Orienteering Problem (SOP). This problem aims to discover a path for each traveler over a subset of vertices, where each vertex is associated with only one cluster, and the total profit made from the clusters visited is maximized while still fitting within the available budget constraints. The profit can be collected only by visiting at least one cluster vertex. According to the SOP, each vertex cluster must have at least one of its visits counted towards the profit for that cluster. Like to the SOP, the sDmSOP restricts the number of clusters visited based on the budget for tour expenses. To address this problem, we employ the Genetic Algorithm (GA) and Variable Neighborhood Search (VNS) meta-heuristic. The optimal solution for small-sized problems is also suggested by solving the Integer Linear Programming (ILP) formulation using the General Algebraic Modeling System (GAMS) 37.1.0 with CPLEX for the sDmSOP. Promising computational results are presented that demonstrate the practicability of the proposed GA, VNS meta-heuristic, and ILP formulation by demonstrating substantial improvements to the solutions generated by VNS than GA while simultaneously needing much less time to compute than CPLEXItem A Simulated Annealing based Energy Efficient Task Scheduling Algorithm for Multi-core Processors(IJCCI, 2021) Mishra, AbhishekIn this paper we propose a Simulated Annealing (SA) based energy-efficient task scheduling algorithm for multi-core processors, the Simulated Annealing Energy Efficient Task Scheduling Algorithm (SAEETSA), and compare it with another algorithm, the Energy Efficient Task Scheduling Algorithm (EETSA). Our results show that for dual-core processors the SAEETSA algorithm is taking up to 16.78% less energy as compared to the EETSA algorithm, and for tri-core processors, the SAEETSA algorithm is taking up to 26.97% less energy as compared to the EETSA algorithm. 1 IItem The Orienteering Problem: A Review of Variants and Solution Approaches(WMSCI, 2022) Mishra, AbhishekOrienteering Problem (OP) fetched great attention in recent years because apart from the NP-hard routing problems, it is applicable in various applications like mobile crowd-sensing, manufacturing, etc. OP intends to maximize the overall price collected from the places covered in the itinerary within a timebound. In this paper, the latest improvements in NP-hard routing problems are discussed. Some variations of the traveling salesman problem (TSP), OP, and their recent solutions based on nature-inspired algorithms are explored. Finally, we present the future scope of the OP and its variants.Item Performance Evaluation of Simulated Annealing-Based Task Scheduling Algorithms(Springer, 2020-09) Mishra, AbhishekThe performance of simulated annealing (SA)-based task scheduling algorithms is evaluated. First, various parameters of SA are varied, and it is seen how it affects the schedule length (SL). The parameters that are varied are initial temperature, number of iterations, initial clustering, and cooling schedule. Then, one SA-based task scheduling algorithm is selected and compared with other task scheduling algorithms. The algorithms selected for comparison are cluster pair priority scheduling (CPPS), dominant sequence clustering (DSC), edge zeroing (EZ), and linear clustering (LC). Random task graphs are used for comparison
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