arXiv subjects

Mithun Goutham

Publications and source records attributed to Mithun Goutham.

8 recordsLinked to original sources

arXiv2026

A Convex Hull Cheapest Insertion Heuristic for the Non-Euclidean TSP

Autonomous robots frequently encounter routing problems that involve non-Euclidean cost considerations due to obstacles, traffic, or a cost function that is not simply the straight-line distance between locations to be visited. Often, the resulting Non-Euclidean Traveling Salesperson Problem (NETSP) must be solved onboard with limited computational resources, posing a significant challenge due to its NP-hard combinatorial nature. To address this, the Adapted Convex Hull Cheapest Insertion (ACHCI) algorithm is proposed. ACHCI is a lightweight heuristic designed for resource-constrained onboard tour computation, with small form factor robots as its target application. ACHCI combines a multidimensional scaling approach with a convex hull initialized tour construction procedure to generalize the well-known Euclidean CHCI heuristic to non-Euclidean problems. Computational experiments on diverse modified TSPLIB scenarios demonstrate that ACHCI outperforms other lightweight heuristics like Nearest Neighbor and Nearest Insertion in 88\% and 99\% of the cases, as well as population-based metaheuristics such as Genetic Algorithms and Ant Colony Optimization in 87\% and 95\% of test cases respectively. The adoption of ACHCI for resource-limited onboard routing is expected to enhance the operational efficiency of autonomous agents by reducing travel distance, energy consumption, charging-related downtime, task completion duration and operating costs.

cs.AI↗

arXiv2026

Epsilon-Neighborhood Decision-Boundary Governed Estimation (EDGE) of 2D Black Box Classifier Functions

Accurately estimating decision boundaries in black box systems is critical when ensuring safety, quality, and feasibility in real-world applications. However, existing methods iteratively refine boundary estimates by sampling in regions of uncertainty, without providing guarantees on the closeness to the decision boundary and also result in unnecessary exploration that is especially disadvantageous when evaluations are costly. This paper presents $\varepsilon$-Neighborhood Decision-Boundary Governed Estimation (EDGE), a sample efficient and function-agnostic algorithm that leverages the intermediate value theorem to estimate the location of the decision boundary of a black box binary classifier within a user-specified $\varepsilon$-neighborhood. To demonstrate applicability, a case study is presented of an electric grid stability problem with uncertain renewable power injection. Evaluations are conducted on three test functions, where it is seen that the EDGE algorithm demonstrates superior sample efficiency and better boundary approximation than adaptive sampling techniques and grid-based searches.

cs.CG↗

arXiv2024

Resilient Fleet Management for Energy-Aware Intra-Factory Logistics

This paper presents a novel fleet management strategy for battery-powered robot fleets tasked with intra-factory logistics in an autonomous manufacturing facility. In this environment, repetitive material handling operations are subject to real-world uncertainties such as blocked passages, and equipment or robot malfunctions. In such cases, centralized approaches enhance resilience by immediately adjusting the task allocation between the robots. To overcome the computational expense, a two-step methodology is proposed where the nominal problem is solved a priori using a Monte Carlo Tree Search algorithm for task allocation, resulting in a nominal search tree. When a disruption occurs, the nominal search tree is rapidly updated a posteriori with costs to the new problem while simultaneously generating feasible solutions. Computational experiments prove the real-time capability of the proposed algorithm for various scenarios and compare it with the case where the search tree is not used and the decentralized approach that does not attempt task reassignment.

cs.RO↗

arXiv2024

Novel Tour Construction Heuristic for Pick-Up and Delivery Routing Problems

In logistic applications that require the pickup and delivery of items, route optimization problems can be modeled as precedence constrained traveling salesperson problems. The combinatorial nature of this problem restricts the application of exact algorithms to small instances, and heuristics are largely preferred for tractability. However, due to precedence constraints that restrict the order in which locations can be visited, heuristics outside of the nearest neighbor algorithm have been neglected in literature. While the convex hull cheapest insertion heuristic is known to produce good solutions in the absence of precedence constraints, i.e., when locations can be visited in any order, it has not been adapted for pick-up and delivery considerations. This paper presents an adapted convex hull cheapest insertion heuristic that accounts for precedence constraints and compares its solutions with the nearest neighbor heuristic using the TSPLIB benchmark data set. The proposed algorithm is particularly suited to cases where pickups are located in the periphery and deliveries are centrally located, outperforming the Nearest Neighbor algorithm in every examined instance.

math.CO↗

arXiv2024

Recomputing Solutions to Perturbed Multi-Commodity Pickup and Delivery Vehicle Routing Problems using Monte Carlo Tree Search

The Multi-Commodity Pickup and Delivery Vehicle Routing Problem aims to optimize the pickup and delivery of multiple unique commodities using a fleet of several agents with limited payload capacities. This paper addresses the challenge of quickly recomputing the solution to this NP-hard problem when there are unexpected perturbations to the nominal task definitions, likely to occur under real-world operating conditions. The proposed method first decomposes the nominal problem by constructing a search tree using Monte Carlo Tree Search for task assignment, and uses a rapid heuristic for routing each agent. When changes to the problem are revealed, the nominal search tree is rapidly updated with new costs under the updated problem parameters, generating solutions quicker and with a reduced optimality gap, as compared to recomputing the solution as an entirely new problem. Computational experiments are conducted by varying the locations of the nominal problem and the payload capacity of an agent to demonstrate the effectiveness of utilizing the nominal search tree to handle perturbations for real-time implementation.

eess.SY↗

arXiv2024

A Convex Hull Cheapest Insertion Heuristic for Precedence Constrained Traveling Salesperson Problems or Sequential Ordering Problems

The convex hull cheapest insertion heuristic is a well-known method that efficiently generates good solutions to the Traveling Salesperson Problem. However, this heuristic has not been adapted to account for precedence constraints that restrict the order in which locations can be visited. Such constraints result in the precedence constrained traveling salesperson problem or the sequential ordering problem, which are commonly encountered in applications where items have to be picked up before they are delivered. In this paper, we present an adapted version of this heuristic that accounts for precedence constraints in the problem definition. This algorithm is compared with the widely used Nearest Neighbor heuristic on the TSPLIB benchmark data with added precedence constraints. It is seen that the proposed algorithm is particularly well suited to cases where delivery nodes are centrally positioned, with pickup nodes located in the periphery, outperforming the Nearest Neighbor algorithm in 97\% of the examined instances.

cs.RO↗

arXiv2023

Development and Evaluation of an Online Home Energy Management Strategy for Load Coordination in Smart Homes with Renewable Energy Sources

In this paper, a real time implementable load coordination strategy is developed for the optimization of electric demands in a smart home. The strategy minimizes the electricity cost to the home owner, while limiting the disruptions associated with the deferring of flexible power loads. A multi-objective nonlinear mixed integer programming is formulated as a sequential model predictive control, which is then solved using genetic algorithm. The load shifting benefits obtained by deploying an advanced coordination strategy are compared against a baseline controller for various home characteristics, such as location, size and equipment. The simulation study shows that the deployment of the smart home energy management strategy achieves approximately 5% reduction in grid cost compared to a baseline strategy. This is achieved by deferring approximately 50\% of the flexible loads, which is possible due to the use of the stationary energy storage.

eess.SY↗

arXiv2022

A Semi Empirical Approach to a Physically Based Aging Model for Home Energy Management Systems

A growing interest in the study of aging related phenomena in lithium-ion batteries is propelled by the increasing utilization of energy storage systems in electric vehicles and in buildings as stationery energy accumulators paired with renewable energy sources. This paper proposes a mixed-degradation model approach that combines the benefits of a semi-empirical approach with that of a physics-based model. This enables easy calibration for different battery chemistries, the ability to extrapolate when necessary, and is computationally efficient enough to be coupled with real-time running control systems. To demonstrate the effectiveness of the proposed approach, the effect of two different control strategies in a smart home energy management system is demonstrated on the aging of a Lithium iron phosphate (LFP) battery.

eess.SY↗