Greedy Solution Research Articles

Information-theoretic sensor placement for large sewer networks

Utility operators face a challenging task in managing wastewater networks to proactively enhance network monitoring. To address this issue, this paper develops a framework for optimized placing of sensors in sewer networks with the aim of maximizing the information obtained about the state of the network. To that end, mutual information is proposed as a measure of the evidence acquired about the state of the network by the placed sensors. The problem formulation leverages a stochastic description of the network states to analytically characterize the mutual information in the system and pose the sensor placement problem. To circumvent the combinatorial problem that arises in the placement configurations, we propose a new algorithm coined the one-step modified greedy algorithm, which employs the greedy heuristic for all possible initial sensor placements. This algorithm enables further exploration of solutions outside the initial greedy solution within a computationally tractable time. The algorithm is applied to two real sewer networks, the first is a sewer network in the South of England with 479 nodes and 567 links, and the second is the sewer network in Bellinge, a village in Denmark that contains 1020 nodes and 1015 links. Sensor placements from the modified greedy algorithm are validated by comparing their performance in estimating unmonitored locations against other heuristic placements using linear and neural network models. Results show the one-step modified greedy placements outperform others in most cases and tend to cluster sensors for efficiently monitoring parts of the network. The proposed framework and modified greedy algorithm provide wastewater utility operators with a sensor placement method that enables them to design the data acquisition and monitoring infrastructure for large networks.

An interchange property for the rooted phylogenetic subnet diversity on phylogenetic networks

Faith’s Phylogenetic Diversity (PD) on rooted phylogenetic trees satisfies the so-called strong exchange property that guarantees that, for every two sets of leaves of different cardinalities, a leaf can always be moved from the larger set to the smaller set in such a way that the sum of the PD values does not decrease. This strong exchange property entails a simple polynomial-time greedy solution to the PD optimization problem on rooted phylogenetic trees. In this paper we obtain an exchange property for the rooted Phylogenetic Subnet Diversity (rPSD) on rooted phylogenetic networks, which involves a more complicated exchange of leaves. We derive from it a polynomial-time greedy solution to the rPSD optimization problem on rooted semibinary level-2 phylogenetic networks.

Pluto: Sample Selection for Robust Anomaly Detection on Polluted Log Data

Log anomaly detection, critical in identifying system failures and preempting security breaches, finds irregular patterns within large volumes of log data. Modern log anomaly detectors rely on training deep learning models on clean anomaly-free log data. However, such clean log data requires expensive and tedious human labeling. In this paper, we thus propose a robust log anomaly detection framework, PlutoNOSPACE, that automatically selects a clean representative sample subset of the polluted log sequence data to train a Transformer-based anomaly detection model. Pluto features three innovations. First, due to localized concentrations of anomalies inherent in the embedding space of log data, Pluto partitions the sequence embedding space generated by the model into regions that then allow it to identify and discard regions that are highly polluted by our pollution level estimation scheme, based on our pollution quantification via Gaussian mixture modeling. Second, for the remaining more slightly polluted regions, we select samples that maximally purify the eigenvector spectrum, which can be transformed into the NP-hard facility location problem; allowing us to leverage its greedy solution with a (1-(1/e)) approximation guarantee in optimality. Third, by iteratively alternating between the above subset selection, a model re-training on the latest subset, and a subset filtering using dynamic training artifacts generated by the latest model, the data selected is progressively refined. The final sample set is used to retrain the final anomaly detection model. Our experiments on four real-world log benchmark datasets demonstrate that by retaining 77.7% (BGL) to 96.6% (ThunderBird) of the normal sequences while effectively removing 90.3% (BGL) to 100.0% (ThunderBird, HDFS) of the anomalies, Pluto provides a significant absolute F-1 improvement up to 68.86% (2.16% → 71.02%) compared to the state-of-the-art sample selection methods. The implementation of this work is available at https://github.com/LeiMa0324/Pluto-SIGMOD25.

Improved Sparse Mean Reverting Portfolio Selection Using Simulated Annealing and Extreme Learning Machine

We study the problem of selecting a sparse, mean reverting portfolio from a universe of assets using simulated annealing (SA). Assuming that assets follow a first order vector autoregressive process (VAR(1)), we make a number of improvements in existing methods. First, we extend the underlying asset dynamics to include a time-independent additive term, thereby enriching the model’s applicability. Second, we introduce Extreme Learning Machine (ELM) to decide whether to apply SA or settle for the much faster greedy solution. Finally, we improve the SA method by better calibration of the initial temperature and by determining the exact value of the weights within a selected dimension using the Rayleigh quotient. On real data, these changes result in more than 90% improvement in run time on average and 4.78% improvement in optimized mean reversion in our simulations. We also test the trading performance of our method on both simulated and real data and managed to achieve positive mean trading results in both cases.

Exact and heuristic approaches for the ship-to-shore problem

After a natural disaster such as a hurricane or flooding, the navy can help by bringing supplies, clearing roads, and evacuating victims. If destinations cannot be reached over land, resources can be transported using smaller ships and helicopters, called connectors. To start aid on land as soon as possible this must be done efficiently. In the ship-to-shore problem, trips with their accompanying resources are determined while minimising the makespan. Limited (un)loading capacities, heterogeneous connector characteristics and constraints posed by priority of the resources and grouping of the resources (resource sets) all require that the connector trips are carefully coordinated. Despite the criticality of this coordination, existing literature does not consider resource sets and has only developed heuristics. We provide a formulation that incorporates resource sets and develop (i) an exact branch-and-price algorithm and (ii) a tailored greedy heuristic that can provide upper bounds. We find that 84% of our 98 practical instances terminate within an hour in on average 80 s. Our greedy heuristic can find optimal solutions in two-thirds of these instances, mostly for instances that are very constrained in terms of the delivery order of resources. When improvements are found by the branch-and-price algorithm, the average gap with the makespan of the greedy solution is 40% and, in most cases, these improvements are obtained within three minutes. For the 20 artificial instances, the greedy heuristic has consistent performance on the different types of instances. For these artificial instances improvements of on average 35% are found in reasonable time.

Joint Deployment of Sensors and Chargers in Wireless Rechargeable Sensor Networks

As a promising technology to achieve the permanent operation of battery-powered wireless sensor devices, wireless rechargeable sensor networks (WRSNs) by radio-frequency radiation have attracted considerable attention in recent years. Determining how to save the deployment cost of WRSNs has been a hot topic. Previous scholars have mainly studied the cost of deploying chargers, thus ignoring the impact of sensor deployment on the network. Therefore, we consider the new problem of joint deployment of sensors and chargers on a two-dimensional plane, i.e., deploying the minimum number of sensors and chargers used to monitor points of interest (PoIs). Considering the interaction of deployed sensors and chargers, we divide the problem into two stages, P1 and P2. P1 addresses the sensor deployment, while P2 addresses the deployment of chargers. Both P1 and P2 have proved to be NP-hard. Meanwhile, we notice that the aggregation effect of sensors can effectively reduce the number of chargers deployed; therefore, we propose a greedy heuristic approximate solution for deploying sensors by using the aggregation effect (GHDSAE). Then, a greedy heuristic (GH) solution and a particle swarm optimization (PSO) solution are proposed for P2. The time complexity of these solutions is analyzed. Finally, extensive simulation results show that the PSO solution can always reduce the number of chargers deployed based on the GHDSAE solution sensor deployment approach. Therefore, it is more cost-effective to jointly deploy sensors and chargers by using the GHDSAE solution and the PSO solution.

Large-W limit of the knapsack problem.

We formulate the knapsack problem (KP) as a statistical physics system and compute the corresponding partition function as an integral in the complex plane. The introduced formalism allows us to derive three statistical-physics-based algorithms for the KP: one based on the recursive definition of the exact partition function, another based on the large weight limit of that partition function, and a final one based on the zero-temperature limit of the second. Comparing the performances of the algorithms, we find that they do not consistently outperform (in terms of runtime and accuracy) dynamic programming, annealing, or standard greedy algorithms. However, the exact partition function is shown to reproduce the dynamic programming solution to the KP, and the zero-temperature algorithm is shown to produce a greedy solution. Therefore, although dynamic programming and greedy solutions to the KP are conceptually distinct, a statistical physics formalism introduced reveals that the large weight-constraint limit of the former leads to the latter. We conclude by discussing how to extend this formalism in order to obtain more accurate versions of the introduced algorithms and other similar combinatorial optimization problems.

Content Promotion for Online Content Platforms with the Diffusion Effect

Problem definition: Content promotion policies are crucial for online content platforms to improve content consumption and user engagement. However, traditional promotion policies generally neglect the diffusion effect within a crowd of users. In this paper, we study the candidate generation and promotion optimization (CGPO) problem for an online content platform, emphasizing the incorporation of the diffusion effect. Methodology/results: We propose a diffusion model that incorporates platform promotion decisions to characterize the adoption process of online content. Based on this diffusion model, we formulate the CGPO problem as a mixed-integer program with nonconvex and nonlinear constraints, which is proved to be NP-hard. Additionally, we investigate methods for estimating the diffusion model parameters using available online platform data and introduce novel double ordinary least squares (D-OLS) estimators. We prove the submodularity of the objective function for the CGPO problem, which enables us to find an efficient [Formula: see text]-approximation greedy solution. Furthermore, we demonstrate that the D-OLS estimators are consistent and have smaller asymptotic variances than traditional ordinary least squares estimators. By utilizing real data from a large-scale video-sharing platform, we show that our diffusion model effectively characterizes the adoption process of online content. Compared with the policy implemented on the platform, our proposed promotion policy increases total adoptions by 49.90%. Managerial implications: Our research highlights the essential role of diffusion in online content and provides actionable insights for online content platforms to optimize their content promotion policies by leveraging our diffusion model. Funding: R. Zhang is grateful for the financial support from the Hong Kong Research Grants Council General Research Fund [Grants 14502722 and 14504123] and the National Natural Science Foundation of China [Grant 72293560/72293565]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2022.0172 .

Modeling and evaluating the travel behaviour in multimodal networks: A path-based unified equilibrium model and a tailored greedy solution algorithm

The modeling and efficient solution of the combined mode split and traffic assignment (CMSTA) problem serve as a powerful tool for capturing complex travel behavior in multimodal transportation networks under different planning scenarios and incentive programs. In this paper, we propose a path-based unified equilibrium condition that combines the cross-nested logit (CNL)-based mode split and the user equilibrium (UE)-based traffic assignment to address the CMSTA problem on a multimodal transportation network. The equilibrium condition is further formulated as a novel path-based variational inequality (VI) model. A general path-based algorithm framework that integrates a tailored greedy algorithm and a novel modified intelligent acceleration strategy (MIAS) is then developed for solving the proposed CMSTA model. Numerical examples demonstrate the effectiveness and efficiency of the proposed model and algorithm in both small-size and large-scale networks. The proposed model and algorithm can help to provide some policy implications for multimodal transportation planning and management. The lessons learned from our analysis results include (1) the removal of some existing key park-and-ride (P&R) interchanges that carry more flows from the multimodal network can result in a significant increase in total travel costs, but the removal of others may instead reduce total travel costs; (2) increasing the number of P&R interchanges in a multimodal network may degrade the performance of the network, even though it may encourage the use of green travel modes.

Bi-Objective Incentive Mechanism for Mobile Crowdsensing With Budget/Cost Constraint

In recent years, mobile crowdsensing (MCS) has been widely adopted as an efficient method for large-scale data collection. In MCS systems, insufficient participation and unstable data quality have become two crucial issues that prevent crowdsensing from further development. Thus designing a valid incentive mechanism is essentially significant. Most of the existing works on incentive mechanism design focus on single-objective optimization with various constraints. However, in the real-world crowdsensing, it is common that several objectives to be optimized exist. Furthermore, constraints on budget or cost are often seen in MCS systems as the feasibility of implementing incentive mechanism is indispensable. This paper studies a bi-objective optimization scenario of MCS to simultaneously optimize total value function and coverage function with budget/cost constraint through a set of problem transformations. Then a budget- or cost-feasible bi-objective incentive mechanism is further proposed to solve the aforementioned bi-objective optimization problem through the combination of binary search and greedy heuristic solution under budget or cost constraint, respectively. Through both rigorous theoretical analysis and extensive simulations, the obtained results demonstrate that the mechanisms achieve computation efficiency, individual rationality, truthfulness, and budget or cost feasibility, while one mechanism obtains an approximation.

Equitable Top-k Results for Long Tail Data

For datasets exhibiting long tail phenomenon, we identify a fairness concern in existing top-k algorithms, that return a "fixed" set of k results for a given query. This causes a handful of popular records (products, items, etc) getting overexposed and always be returned to the user query, whereas, there exists a long tail of niche records that may be equally desirable (have similar utility). To alleviate this, we propose θ-Equiv-top-k-MMSP inside existing top-k algorithms - instead of returning a fixed top-k set, it generates all (or many) top-k sets that are equivalent in utility and creates a probability distribution over those sets. The end user will be returned one of these sets during the query time proportional to its associated probability, such that, after many draws from many end users, each record will have as equal exposure as possible (governed by uniform selection probability). θ-Equiv-top-k-MMSP is formalized with two sub-problems. (a) θ-Equiv-top-k-Sets to produce a set S of sets, each set has k records, where the sets are equivalent in utility with the top-k set; (b) MaxMinFair to produce a probability distribution over S, that is, PDF(S), such that the records in S have uniform selection probability. We formally study the hardness of θ-Equiv-top-k-MMSP. We present multiple algorithmic results - (a) An exact solution for θ-Equiv-top-k-Sets, and MaxMinFair. (b) We design highly scalable algorithms that solve θ-Equiv-top-k-Sets through a random walk and is backed by probability theory, as well as a greedy solution designed for MaxMinFair. (c) We finally present an adaptive random walk based algorithm that solves θ-Equiv-top-k-Sets and MaxMinFair at the same time. We empirically study how θ-Equiv-top-k-MMSP can alleviate a equitable exposure concerns that group fairness suffers from. We run extensive experiments using 6 datasets and design intuitive baseline algorithms that corroborate our theoretical analysis.

Performance-Aware Orchestration of P4-Based Heterogeneous Cloud Environments

The recent trend to deploy programmable packet processors in cloud environments enhances the packet processing capability without losing the flexibility to adapt the functions at runtime. In particular, distributed edge clouds can have a heterogeneous programmable processing substrate made up of different classes of devices: CPUs, NPUs, FPGAs, etc. However, managing the allocation of workloads in such a heterogeneous programmable processing substrate, in particular deciding where to instantiate a certain function, is a non-trivial task with many decisive functional and QoS-related factors. In this paper, we propose a mathematical model for optimizing the embedding of Service Function Chains implemented in P4, while considering the functional and QoS requirements associated with embedding requests, and the various types of processing devices that have different properties in terms of processing delay and supported features. To satisfy delay requirements, the problem formulation utilizes performance models to predict the forwarding latency associated with different candidate embedding options. Furthermore, a greedy solution is proposed to solve the problem in an efficient manner. Finally, a detailed numerical evaluation is conducted to evaluate the formulated model when different workload and infrastructure characteristics are varied and to evaluate the effectiveness of the proposed greedy solution.

Greedy+Singleton: An efficient approximation algorithm for k-submodular knapsack maximization

A k-submodular function takes k distinct, non-overlapping subsets of a ground set as input and outputs a value. It is a generalization of the well-known submodular function, which is the case when k=1 and takes a single subset as input. We study the problem of maximizing a non-negative k-submodular function under a knapsack constraint. Greedy+Singleton is an algorithm that chooses the better solution between the fully greedy solution and the best single-element solution, with query complexity and running time of O(n2k). We show that Greedy+Singleton has an approximation ratio of 0.273 for monotone functions, which improves the previous analysis of 0.158 in the literature. Moreover, we give the first analysis of Greedy+Singleton for non-monotone k-submodular functions, and prove an approximation ratio of 0.219.

Multi-Agent Learning-Based Optimal Task Offloading and UAV Trajectory Planning for AGIN-Power IoT

UAV-based air-ground integrated computing networks (AGIN) have gained significant traction in remote areas for the Power Internet of Things (PIoT). This paper considers an AGIN-PIoT, where computing tasks generated by ground PIoT devices are offloaded to aerial UAVs that perform edge computing. Jointly optimizing task offloading and UAV trajectory poses challenges such as many decision variables, information uncertainty, and long-term queue delay constraints. Due to the limited battery capacity of PIoT devices and UAVs, our objective is to minimize system energy consumption under long-term queue delay constraints by jointly optimizing task offloading, trajectory planning, and computing resource assignment. In light of Lyapunov optimization, we decompose the original challenging optimization problem into two sub-problems: (1) task offloading and UAV trajectory planning and (2) aerial edge resource allocation. Accordingly, we develop a multi-agent deep reinforcement learning-based algorithm called AGIN-MADDPG for the former to achieve the maximum accumulative reward and propose a greedy solution for the latter. Extensive experiments and numerical results demonstrate that our approach can avoid the problem of gradient vanishing and outperforms other benchmark methods in terms of power consumption, task backlog, queue delay, and system throughput.

AN ADVANCED FLIGHT SCHEDULING APPLICATION BASED ON DIJKSTRA`S ALGORITHM

Dijkstra`s Algorithm is a popular example of a greedy solution to the problem of determining the shortest path. This algorithm calculates the most direct and shortest journey and is majorly used in routing, rail networks, maps, etc. Its application to both directed and undirected graphs has the same goal, which is to determine the path that travels the least distance from the starting node, also known as the origin node, to any other node along the tracks. In this article, we are going to implement an application of this algorithm, but this time with a minor tweak. a travel agency asks for software that can create flight schedules for their customers, and the agent has the access to a database that lists all of the airports and flights. In this scenario, the agent is able to create flight schedules for their customers. In addition to the flight number, the airport of departure and arrival, and the destination, each trip`s times of departure and arrival are listed. The agent is interested in finding out the earliest possible arrival time at the destination, given both the airport of departure and the time at which the trip will begin. It was observed during implementation that, if the method is correctly applied, the overall cost for building every flight priority queue is O(m). For the airport priority queue, the overall cost using a heap is O((n + m) log n))

A Formal Metareasoning Model of Concurrent Planning and Execution

Agents that plan and act in the real world must deal with the fact that time passes as they are planning. When timing is tight, there may be insufficient time to complete the search for a plan before it is time to act. By commencing execution before search concludes, one gains time to search by making planning and execution concurrent. However, this incurs the risk of making incorrect action choices, especially if actions are irreversible. This tradeoff between opportunity and risk is the problem addressed in this paper. Our main contribution is to formally define this setting as an abstract metareasoning problem. We find that the abstract problem is intractable. However, we identify special cases that are solvable in polynomial time, develop greedy solution algorithms, and, through tests on instances derived from search problems, find several methods that achieve promising practical performance. This work lays the foundation for a principled time-aware executive that concurrently plans and executes.

Multi-agent deep reinforcement learning for user association and resource allocation in integrated terrestrial and non-terrestrial networks

Integrating the terrestrial network with non-terrestrial networks to provide radio access as anticipated in the beyond 5G networks calls for efficient user association and resource allocation strategies. In this work, a weighted sum single objective optimization problem that maximizes the total network data rate while minimizing the mobility-induced handoffs and prioritizing service provisioning of mission-critical users in the integrated terrestrial and non-terrestrial network is formulated. The problem’s complexity is reduced by solving the defined problem in two phases; the user association followed by the resource distribution phase. Several proposed approaches to the user association sub-problem utilize a central node that requires nearly-complete information, which may not be available in real time. On the contrary, this paper proposes a centralized training and distributed execution multi-agent dueling double deep Q network (MA3DQN) solution. Each user collects the channel state and access node loading information in this approach and makes an association decision that considers its quality of service requirements. The algorithm’s performance is validated through comparison with the genetic algorithm (GA), the integer linear programming (ILP), a heuristic approximation-based solution, the greedy approach, and the random user association (RUA) algorithm. Moreover, the paper simulates the multi-agent deep Q network solution as an additional benchmark algorithm. Simulation results reveal that as the number of users in the network increases, the acquired data rate of the MA3DQN is within 0.48% and 0.4% of that achieved by the GA and ILP, respectively, and outperforms all other algorithms. Notably, the proposed MA3DQN algorithm presents the best running time, attaining a gain of 99.9% over the GA algorithm, which performs the poorest among the algorithms characterized by polynomial worst-case time complexity. Besides, the MA3DQN approach maintains a handoff probability of zero, unlike the ILP, the approximation-based, greedy, and RUA solutions.

Trans-population graph-based coverage optimization of allogeneic cellular therapy.

Pre-clinical development and in-human trials of 'off-the-shelf' immune effector cell therapy (IECT) are burgeoning. IECT offers many potential advantages over autologous products. The relevant HLA matching criteria vary from product to product and depend on the strategies employed to reduce the risk of GvHD or to improve allo-IEC persistence, as warranted by different clinical indications, disease kinetics, on-target/off-tumor effects, and therapeutic cell type (T cell subtype, NK, etc.). The optimal choice of candidate donors to maximize target patient population coverage and minimize cost and redundant effort in creating off-the-shelf IECT product banks is still an open problem. We propose here a solution to this problem, and test whether it would be more expensive to recruit additional donors or to prevent class I or class II HLA expression through gene editing. We developed an optimal coverage problem, combined with a graph-based algorithm to solve the donor selection problem under different, clinically plausible scenarios (having different HLA matching priorities). We then compared the efficiency of different optimization algorithms - a greedy solution, a linear programming (LP) solution, and integer linear programming (ILP) -- as well as random donor selection (average of 5 random trials) to show that an optimization can be performed at the entire population level. The average additional population coverage per donor decrease with the number of donors, and varies with the scenario. The Greedy, LP and ILP algorithms consistently achieve the optimal coverage with far fewer donors than the random choice. In all cases, the number of randomly-selected donors required to achieve a desired coverage increases with increasing population. However, when optimal donors are selected, the number of donors required may counter-intuitively decrease with increasing population size. When comparing recruiting more donors vs gene editing, the latter was generally more expensive. When choosing donors and patients from different populations, the number of random donors required drastically increases, while the number of optimal donors does not change. Random donors fail to cover populations different from their original populations, while a small number of optimal donors from one population can cover a different population. Graph-based coverage optimization algorithms can flexibly handle various HLA matching criteria and accommodate additional information such as KIR genotype, when such information becomes routinely available. These algorithms offer a more efficient way to develop off-the-shelf IECT product banks compared to random donor selection and offer some possibility of improved transparency and standardization in product design.

Resource Allocation for Multiuser Edge Inference With Batching and Early Exiting

The deployment of inference services at the network edge, called edge inference, offloads computation-intensive inference tasks from mobile devices to edge servers, thereby enhancing the former’s capabilities and battery lives. In a multiuser system, the joint allocation of communication-and-computation (C2) resources (i.e., scheduling and bandwidth allocation) is made challenging by adopting efficient inference techniques, batching and early exiting, and further complicated by the heterogeneity in users’ requirements on accuracy and latency. Batching groups multiple tasks into a single batch for parallel processing to reduce time-consuming memory access and thereby boosts the throughput (i.e., completed task per second). On the other hand, early exiting allows a task to exit from a deep-neural network without traversing the whole network, thereby supporting a tradeoff between accuracy and latency. In this work, we study optimal C2 resource allocation with batching and early exiting, which is an NP-complete integer programming problem. A set of efficient algorithms are designed under the criterion of maximum throughput by tackling the challenge. First, consider the case with batching but without early exiting. The target problem is solved optimally using a proposed best-shelf-packing algorithm that nests a threshold-based scheme, which selects users with the best channels and meeting the computation-time constraints, in a sequential search for the maximum batch size. Next, consider the general case with batching and early exiting. A low-complexity sub-optimal algorithm for C2 resource allocation is developed by modifying the preceding algorithm to exploit early exiting for latency reduction. On the other hand, the optimal approach is developed based on nesting a depth-first tree-search with intelligent online pruning into a sequential search for the maximum batch size. The key idea is to derive pruning criteria based on the simple greedy solution for the target problem without a bandwidth constraint and apply the result to designing an intelligent online pruning scheme. Experimental results demonstrate that both optimal and sub-optimal C2 resource allocation algorithms can leverage integrated batching and early exiting to double the inference throughput compared with conventional schemes.

An optimization model for vehicle routing problem in last-mile delivery

Due to rapid urbanization, timely delivery using vehicle routing is the most pressing issue for E-commerce logistics and distribution. In this study, we articulate multiple vehicle routing problems with a maximum capacity constraint and no time constraint. A brief literature review is conducted to identify the widely used optimization models for perishable goods delivery in the last mile. We have implemented and compared optimization algorithms such as Intra-Route Local Search, Inter-Route Local Search, and Tabu Search that provide a suboptimal solution to the greedy solution of this NP-hard problem. We compared the solution provided by these algorithms with the optimal solution that can be obtained in exponential time using processing time and precision. The results demonstrate that Tabu search outperforms other techniques for larger instance sizes, but for smaller instance sizes, Local search can produce results that are comparable to TABU search in a significantly shorter amount of time. In addition, the impact of instance size on the performance of the aforementioned algorithms is evaluated. The real-life evaluation is done to understand the use cases of this problem for an e-commerce company that will repeatedly face this challenge during warehouse storage management, last-mile delivery planning, and execution. A comprehensive performance comparison of various algorithms is presented to optimize last-mile delivery for future cases in order to reduce the overall carbon footprint and achieve profitability through the use of sustainable modes of distribution.