Integer Nonlinear Programming Problem Research Articles

Collaborative Computation Offloading and Resource Management in Space–Air–Ground Integrated Networking: A Deep Reinforcement Learning Approach

With the increasing dissemination of the Internet of Things and 5G, mobile edge computing has become a novel scheme to assist terminal devices in executing computation tasks. To elevate the coverage and computation capability of edge computing, a collaborative computation offloading and resource management architecture was proposed in space–air–ground integrated networking (SAGIN). In this manuscript, we established a novel model considering the computation offloading cost constraints of the communication, computing and cache model in the SAGIN. To be specific, the joint optimization problem of collaborative computation offloading and resource management was modeled as a mixed integer nonlinear programming problem. To address this issue, this paper proposed a computation offloading and resource allocation strategy based on deep reinforcement learning (DRL). Differing from traditional methods, DRL does not need a well-established formulation or previous information, and it is capable of revising the strategy adaptively according to the environment. The simulation results demonstrate the proposed approach can achieve the optimal reward values in the case of different terminal device numbers. Furthermore, this manuscript provided the analysis with variant parameters of the proposed approach.

Bidirectional Service Function Chain Embedding for Interactive Applications in Mobile Edge networks

Bidirectional service function chain (BSFC) consists of multiple virtual network functions (VNFs). Through VNF deployment and link mapping, BSFCs can be embedded into resource-constrained mobile edge networks to provide low-latency network function services to users participating in interactive applications such as multi-player online games. Data from these users are routed through BSFCs to the edge node where the application is located for interaction and then returned to the users through the BSFCs, thus enabling synchronization among multiple users. However, the edge nodes or links have limited computing or bandwidth resources to serve only a fraction of users simultaneously. Therefore, the embedding decisions among different users can affect each other. In this paper, we propose a novel BSFC embedding strategy for interactive applications with the goal of minimizing computing and bandwidth resources while satisfying users' latency requirements. We first model the BSFC embedding problem as an integer nonlinear programming problem. Then, by closely examining the complexity of the problem, we propose a distributed algorithm based on game theory. We theoretically analyze the properties of the proposed algorithm and show that it can obtain a solution with a worst-case performance bound. Finally, extensive experiments show that the proposed algorithm outperforms several existing algorithms.

LEO satellites selection-based computation offloading algorithm in aircraft-satellite multi-access edge computing networks

The emergence of sixth-generation (6G) mobile networks and non-terrestrial networks (NTNs) has led to increased interest in low Earth orbit (LEO) satellite-based communication networks for their potential to provide global coverage and ubiquitous connectivity. In this paper, we investigate the LEO satellites selection-based computation offloading problem in the aircraft-satellite multi-access edge computing (ASMEC) network, where LEO satellites and edge computing processors are integrated to provide ubiquitous and low-latency communication and computation services for aircraft during flights. In contrast to most existing works, which directly assume a fixed number of satellites or orbits in satellite-based MEC networks, we investigate the problem of how many satellites and which satellites to select in the ASMEC network. Our objective is to minimize the average total time delay of tasks during aircraft-satellite computation offloading. To achieve this, we formulate a nonlinear integer programming (NLIP) problem and propose the LEO satellites selection-based computation offloading (LSSBCO) algorithm to solve it, which includes the shortest aircraft-satellite distance based access satellite selection (ASS-SD) algorithm and the nearest k(t) neighboring satellites selection (NSS-k(t)) algorithm. We evaluate the performance of the LSSBCO algorithm in terms of the average total time delay, the maximum throughput, the average aircraft-satellite distance, the average connection duration, and the number of satellite handovers. Numerical results show that the proposed algorithm outperforms the benchmark algorithms with a lower average total time delay.

An online integrated satellite–terrestrial IoT task offloading and service deployment strategy

As a core component of 6G networking, low earth orbit (LEO) satellite networks are considered a promising solution for providing network services in remote areas and have received considerable attention in recent years. Meanwhile, with the rapid development of IoT terminals and applications, an increasing emphasis has been placed on task offloading for real-time tasks. However, most existing works on task offloading for integrated satellite–terrestrial IoT (IST-IoT) applications are based on the assumption that the global task and network information is known, an assumption that is obviously not met in online real-time task offloading. In addition, current studies rarely consider the tradeoff among the task offloading volume, satellite endurance and wholesale cost of terrestrial resources, which are precisely the holistic issues that satellite network operators must confront. To address such issues, this study considers task offloading, service deployment and resource allocation in highly dynamic online task offloading scenarios with the goal of maximizing the average task offloading volume. Moreover, virtual queues are constructed in this study to account for the impacts of long-term satellite endurance and terrestrial network resource costs on task offloading. We first decouple the original problem to obtain a single-time-slot optimization problem within the Lyapunov optimization framework, and we then propose a 2-stage optimization approach based on deep reinforcement learning (DRL) to solve the complex single-time-slot mixed integer nonlinear programming (MINLP) problem. Simulation experiments demonstrate that our proposed algorithm can yield near-optimal solutions that show superior performance compared to existing results.

NOMA Assisted Two-Tier VR Content Transmission: A Tile-Based Approach for QoE Optimization

Virtual reality (VR) provides users with an immersive and interactive experience through head-mounted devices, which has attracted increasing attention in recent years. Specifically, tile-based VR content transmission provides a promising approach to alleviate the conflict between limited bandwidth and high-performance requirements (e.g., high-resolution and low-delay). However, the tiling pattern affects the encoding efficiency and visual distortion of the VR content. Accounting for this issue, in this paper, a quality of experience (QoE)-aware cost minimization problem is investigated for a tile-based VR content transmission scenario. In particular, an edge server (ES) co-located at a cellular base station (BS) separates its generated VR content into several tiles according to the tiling pattern selection, and a weighted-to-spherically-uniform quality model is used to evaluate the effect of different tiling patterns on QoE. Moreover, to improve the transmission performance between the edge server and VR users (VRUs), unmanned aerial vehicles (UAVs) are leveraged as relay points to provide line of sight channels. Then, we formulate an optimization problem to minimize the sum of weighted total energy consumption and VR content distortion (i.e., QoE-aware cost) by jointly optimizing the tiling pattern selections, the VRUs-UAV grouping, partial computing decisions, and resource allocation. The formulated problem is a mixed integer non-linear programming problem, which is challenging to solve. To address this difficulty, we equivalently decompose the formulated problem into three subproblems and propose corresponding algorithms to solve them, respectively. Numerical results demonstrate that our proposed solution can effectively reduce the QoE-aware cost for VR content transmission in comparison with other baseline algorithms.

Network-level pavement maintenance and rehabilitation planning considering uncertainties using chance-constrained programming

ABSTRACT In practice, given limited funds, to consider multiple strategic goals/objectives that different stakeholders concern, pavement network-level maintenance and rehabilitation (M&R) planning becomes a multi-objective optimisation (MOO) based project selection and budget allocation problem. In an attempt to solve this problem, most agencies established MOO models under the deterministic situation without appropriate consideration of uncertainties. However, ignoring performance uncertainties often leads to unreasonable decisions. To provide more convincing and reliable pavement M&R decisions, this paper proposes a Chance-Constrained Programming (CCP) based MOO method to incorporate performance uncertainties in network-level single period pavement M&R planning. First, a general deterministic MOO model with budget and network performance constraints is established. Then, three commonly-used statistical forms of network-level performance measures are introduced. To incorporate uncertainties, the probability distribution of each form of performance measure is derived. Based on the CCP method, the MOO model is transformed to an equivalent deterministic formulation as a mixed non-linear integer programming (MNLIP) problem. To demonstrate the proposed method, a case study using real data is conducted. The results show that the proposed method can effectively help decision-makers to appropriately incorporate performance uncertainties in conducting network-level pavement M&R planning.

A Multi-Agent RL Algorithm for Dynamic Task Offloading in D2D-MEC Network with Energy Harvesting.

Delay-sensitive task offloading in a device-to-device assisted mobile edge computing (D2D-MEC) system with energy harvesting devices is a critical challenge due to the dynamic load level at edge nodes and the variability in harvested energy. In this paper, we propose a joint dynamic task offloading and CPU frequency control scheme for delay-sensitive tasks in a D2D-MEC system, taking into account the intricacies of multi-slot tasks, characterized by diverse processing speeds and data transmission rates. Our methodology involves meticulous modeling of task arrival and service processes using queuing systems, coupled with the strategic utilization of D2D communication to alleviate edge server load and prevent network congestion effectively. Central to our solution is the formulation of average task delay optimization as a challenging nonlinear integer programming problem, requiring intelligent decision making regarding task offloading for each generated task at active mobile devices and CPU frequency adjustments at discrete time slots. To navigate the intricate landscape of the extensive discrete action space, we design an efficient multi-agent DRL learning algorithm named MAOC, which is based on MAPPO, to minimize the average task delay by dynamically determining task-offloading decisions and CPU frequencies. MAOC operates within a centralized training with decentralized execution (CTDE) framework, empowering individual mobile devices to make decisions autonomously based on their unique system states. Experimental results demonstrate its swift convergence and operational efficiency, and it outperforms other baseline algorithms.

SMITS: Social and Mobility aware Intelligent Task Scheduling in Vehicular Fog Computing — A Federated DRL Approach

Vehicular fog computing (VFC) has become an enticing research hot spot to provide resources for the Internet of Vehicles (IoV) application requests. Moreover, with the massive expansion of services in vehicular fog networks such as augmented reality, 3-D gaming, and autonomous driving, the allocation of fog computing resources to IoV applications constraining the deadline and energy consumption of the vehicles is becoming challenging. In this paper, we investigate a task scheduling problem in vehicular fog networks to jointly optimize the success rate of vehicular tasks and energy consumption of vehicles by considering the moving paths of the vehicles and the social relationships among the vehicles. In this problem, we model the social relationship among the vehicles based on their communication patterns and social characteristics to improve the success rate of the tasks. We also incorporate the mobility of vehicles using the Markov renewal process (MRP) technique. Initially, we formulate a mixed integer nonlinear programming (MINLP) problem for the proposed problem and further prove it to be an NP-hard problem. To solve the proposed problem, we design a federated deep reinforcement learning (FDRL) mechanism by converting the problem into a Markov decision process (MDP) problem. We compare our proposed algorithm with existing scheduling approaches, and simulation results show that the proposed algorithm performs efficiently for task scheduling problems. The proposed algorithm achieved a substantial improvement of 12% in the maximization of the success rate and 36% in the minimization of the energy consumption compared to the existing algorithms.

Multi-User Computation Offloading and Resource Allocation Algorithm in a Vehicular Edge Network.

In Vehicular Edge Computing Network (VECN) scenarios, the mobility of vehicles causes the uncertainty of channel state information, which makes it difficult to guarantee the Quality of Service (QoS) in the process of computation offloading and the resource allocation of a Vehicular Edge Computing Server (VECS). A multi-user computation offloading and resource allocation optimization model and a computation offloading and resource allocation algorithm based on the Deep Deterministic Policy Gradient (DDPG) are proposed to address this problem. Firstly, the problem is modeled as a Mixed Integer Nonlinear Programming (MINLP) problem according to the optimization objective of minimizing the total system delay. Then, in response to the large state space and the coexistence of discrete and continuous variables in the action space, a reinforcement learning algorithm based on DDPG is proposed. Finally, the proposed method is used to solve the problem and compared with the other three benchmark schemes. Compared with the baseline algorithms, the proposed scheme can effectively select the task offloading mode and reasonably allocate VECS computing resources, ensure the QoS of task execution, and have a certain stability and scalability. Simulation results show that the total completion time of the proposed scheme can be reduced by 24-29% compared with the existing state-of-the-art techniques.

Decision-Making for Land Conservation: A Derivative-Free Optimization Framework with Nonlinear Inputs

Protected areas (PAs) are designated spaces where human activities are restricted to preserve critical habitats. Decision-makers are challenged with balancing a trade-off of financial feasibility with ecological benefit when establishing PAs. Given the long-term ramifications of these decisions and the constantly shifting environment, it is crucial that PAs are carefully selected with long-term viability in mind. Using AI tools like simulation and optimization is common for designating PAs, but current decision models are primarily linear. In this paper, we propose a derivative-free optimization framework paired with a nonlinear component, population viability analysis (PVA). Formulated as a mixed integer nonlinear programming (MINLP) problem, our model allows for linear and nonlinear inputs. Connectivity, competition, crowding, and other similar concerns are handled by the PVA software, rather than expressed as constraints of the optimization model. In addition, we present numerical results that serve as a proof of concept, showing our models yield PAs with similar expected risk to that of preserving every parcel in a habitat, but at a significantly lower cost. The overall goal is to promote interdisciplinary work by providing a new mathematical programming tool for conservationists that allows for nonlinear inputs and can be paired with existing ecological software. The code and data are available at https://github.com/cassiebuhler/conservation-dfo.

Agile earth observation satellite constellations scheduling for large area target imaging using heuristic search

Demand for imaging of large area targets by space-based assets such as constellations of Earth Observation Satellites (EOS) is on the rise for different applications. The area targets coverage cannot be achieved by a single satellite in a single observation opportunity, as the region for imaging spreads wider than the coverage swaths of imaging sensors. Hence, the imaging satellites are scheduled in a cooperative way to achieve maximum coverage of the area in a given planning time horizon. The scheduling algorithms also aim to maximize or minimize some specific objectives of interest while simultaneously complying with all resource constraints for an efficient use of precious space resources. As the current generation satellites are highly agile, there are many ways of choosing an imaging location in the target area for each single observation opportunity of a satellite. Even though the possible imaging region in continuous space is discretized into a finite number of strips for each observation, the huge combinatorial search space formed with all satellites’ imaging opportunities makes the problem intractable. Thus, the area target imaging scheduling is a complex combinatorial NP-hard optimization problem. Many exact and heuristic methods were evolved to provide a solution to this scheduling problem. Even though the exact methods solve the problem to optimality, they are limited to smaller problem instances because of the high computational complexities involved in those methods. More focus is seen in the literature on heuristic approaches as they guarantee scheduling performance with feasible solutions within an acceptable computational complexity. This paper presents our efficient heuristic approach proposed for the scheduling problem for imaging a large area target using a constellation of multiple satellites. Our approach is an extension of a widely used greedy approach in combination with insights from dynamic programming. In this paper, first we addressed the scheduling problem by describing it in detail and formulating it into a non-linear integer programming problem, considering the multi-objectives of achieving maximum coverage and minimum imaging resolution. The solution to the problem comprises two phases, namely the area decomposition phase and the scheduling phase. In the area decomposition phase, the area target is divided into strips dynamically for each observation opportunity of a satellite. Then exact observation period of each strip is computed using a simplified semi-analytical computational method. In the scheduling phase, we applied our heuristic search strategy, namely Forward and Backward Heuristic Search (FBHS) to obtain a near optimal solution within an acceptable computational time. Through the extensive simulations conducted under various scenarios, the effectiveness of the proposed method is verified in comparison with the baseline greedy approach.

Particle Swarm Optimization for Directional Overcurrent Relay Coordination with Distributed Generation

The Directional Overcurrent Relays (DOCRs) Coordination with Distributed Generation (DG) optimization problem is addressed in this study using the optimization method Particle Swarm Optimization (PSO). Changes in fault current, bus voltages, power flow, and reliability may result from DG integration. Thus, it might have an impact on the current protection coordination system. The formulation is built on a Mixed Integer Non-Linear Programming (MINLP) problem to address this DOCR issue. MATLAB was used to validate the technique on the IEEE-14 bus system, and Electrical Test Transient Analyzer Programming (ETAP) version 2021 software was used to model the test system. According to the simulation results, the suggested PSO with DG for Case 2 has reduced power loss by 6.24% and relay operating time by 46.79% when compared to PSO without the presence of DG.

Joint Dataset Reconstruction and Power Control for Distributed Training in D2D Edge Network

The intrinsic nature of non-independent and identically distributed datasets on heterogeneous devices slows down the distributed model training process and reduces the training accuracy. To settle this problem, we propose a dataset reconstruction scheme to transform the data distribution of training device’s dataset into independent and identically distributed dataset via data exchange among trusted devices. For energy efficiency, we further consider power control for the devices. We then formulate an optimization problem, which is a mixed integer non-linear programming problem, to minimize the total energy consumption for each round of distributed training. Due to the NP-hardness and coupling property of the optimization problem, we decompose it into two subproblems for dataset reconstruction and power control, respectively. An approximation algorithm is designed to obtain a near-optimal auxiliary devices set for dataset reconstruction with minimum energy consumption, while meeting the variance constraint of the optimization problem. We prove that approximation algorithm has a worst-case approximation ratio of 1+ln|Ωi(t)|, where |Ωi(t)| is the required data samples for dataset reconstruction of each training device. For power control, we design a dynamic programming algorithm to further reduce the energy consumption. For comparison, we propose three benchmark schemes that adopt either one of the algorithms or neither. We also customize three baseline algorithms based on the state-of-the-arts to compare with our proposed algorithm. Numerical results show that, our proposed algorithm outperforms three benchmarks on the average energy consumption for one round for different cases. When varying the labels that each device owns, our proposed algorithm outperforms the other three baseline algorithms on training accuracy. Besides, when setting a target accuracy, our proposed algorithm always has the lowest energy consumption.

Joint optimization of multi-dimensional resource allocation and task offloading for QoE enhancement in Cloud-Edge-End collaboration

Cloud-Edge-End Collaboration (CEEC) computing architecture inherits many merits from both edge computing and cloud computing and thus is considered as a promising candidate for future network services. In CEEC, user’s QoE is impacted by offload performance which should consider offload strategy, computational resources and network status simultaneously. However, previous offload optimization studies neglect the joint consideration of dependent task offloading, computational resources and channel resources, which may not produce potential performance improvement. In this paper, we investigate the joint optimization of dependent task offloading, computational resource allocation, user transmission power control, and channel resource allocation in the CEEC scenario, with the goal of maximizing user’s QoE. Initially, a new QoE metric is defined to capture the impacts of delay and energy consumption on user’s QoE. Following this definition, we formulate the joint optimization problem as a Mixed Integer Nonlinear Programming (MINLP) problem and introduce a method of multi-agent deep reinforcement learning to solve our MINLP problem with high computation complexity. Extensive experiments are performed, and experimental results show that our proposed scheme outperforms baselines in a series of metrics.

A multi-objective scheduling model in medical tourism centers considering multi-task staff training

In the present era, hospitals are actively encouraging their International Patient Departments (IPD) to provide high-quality medical services at a cost-effective rate for international patients. To accomplish this objective, several crucial factors must be taken into account, including capacity constraints, hospital waiting lists, and the presence of a highly skilled workforce. The waiting time experienced by patients is a significant indicator of the quality of hospital services and is often used by patients to evaluate healthcare professionals, sometimes even surpassing their knowledge and expertise. This becomes particularly critical when dealing with international patients as longer waiting times indirectly lead to additional accommodation costs. One potential solution is to schedule international patients on different days within a specific timeframe to minimize patient flow time. However, this can only be realistically achieved if staff productivity is enhanced through in-service training. These challenges, coupled with the uncertainty surrounding treatment duration, create a complex problem for IPDs. This study proposes an optimization approach for scheduling medical tourists who visit destination medical centers with two primary objectives: 1) reducing patient waiting times and 2) decreasing training costs while enhancing the skill level of the staff serving patients. The proposed model is formulated as a bi-objective nonlinear integer programming problem, which is subsequently transformed into a linear model using theoretical techniques. Given that this problem is NP-hard, two efficient meta-heuristic methods are developed to solve it for real-world scenarios of varying sizes. The findings of this study present a comparative analysis between the outcomes generated by the proposed algorithms and an exact method (CPLEX), showcasing their effectiveness and superiority. Additionally, a sensitivity analysis highlights that despite the costs associated with in-service training, enhancing staff skills can substantially reduce patient waiting times, resulting in significant cost savings for medical services while ensuring the delivery of high-quality care. Moreover, the improved staff skills enable IPD managers to gain valuable insights into the financial well-being of the medical center, including its ability to attract medical tourists.

Secure User Pairing and Power Allocation for Downlink Non-Orthogonal Multiple Access against External Eavesdropping.

We propose a secure user pairing (UP) and power allocation (PA) strategy for a downlink Non-Orthogonal Multiple Access (NOMA) system when there exists an external eavesdropper. The secure transmission of data through the downlink is constructed to optimize both UP and PA. This optimization aims to maximize the achievable sum secrecy rate (ASSR) while adhering to a limit on the rate for each user. However, this poses a challenge as it involves a mixed integer nonlinear programming (MINLP) problem, which cannot be efficiently solved through direct search methods due to its complexity. To handle this gracefully, we first divide the original problem into two smaller issues, i.e., an optimal PA problem for two paired users and an optimal UP problem. Next, we obtain the closed-form optimal solution for PA between two users and UP in a simplified NOMA system involving four users. Finally, the result is extended to a general 2K-user NOMA system. The proposed UP and PA method satisfies the minimum rate constraints with an optimal ASSR as shown theoretically and as validated by numerical simulations. According to the results, the proposed method outperforms random UP and that in a standard OMA system in terms of the ASSR and the average ASSR. It is also interesting to find that increasing the number of user pairs will bring more performance gain in terms of the average ASSR.

Deep Progressive Reinforcement Learning-Based Flexible Resource Scheduling Framework for IRS and UAV-Assisted MEC System.

The intelligent reflecting surface (IRS) and unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system is widely used in temporary and emergency scenarios. Our goal is to minimize the energy consumption of the MEC system by jointly optimizing UAV locations, IRS phase shift, task offloading, and resource allocation with a variable number of UAVs. To this end, we propose a flexible resource scheduling (FRES) framework by employing a novel deep progressive reinforcement learning that includes the following innovations. First, a novel multitask agent is presented to deal with the mixed integer nonlinear programming (MINLP) problem. The multitask agent has two output heads designed for different tasks, in which a classified head is employed to make offloading decisions with integer variables while a fitting head is applied to solve resource allocation with continuous variables. Second, a progressive scheduler is introduced to adapt the agent to the varying number of UAVs by progressively adjusting a part of neurons in the agent. This structure can naturally accumulate experiences and be immune to catastrophic forgetting. Finally, a light taboo search (LTS) is introduced to enhance the global search of the FRES. The numerical results demonstrate the superiority of the FRES framework, which can make real-time and optimal resource scheduling even in dynamic MEC systems.

Computing and Communication Cost-Aware Service Migration Enabled by Transfer Reinforcement Learning for Dynamic Vehicular Edge Computing Networks

Due to the high mobility of vehicles, service migration is inevitable in vehicular edge computing (VEC) networks. Frequent service migrations incur prohibitive migration cost including the computing cost (e.g., increased computing delay) and communication cost (e.g., occupied backhaul bandwidth). Yet existing service migration schemes are usually designed without considering the impact of the computing cost. This paper considers the impact of computing and communication cost jointly, and proposes a computing and communication cost-aware service migration scheme for VEC networks (i.e., CA-migration). Taking the service delay as a QoS metric for VEC networks, this paper formulates a migration optimization problem aiming to maximize the services' satisfaction degree of delay (i.e., the probability that the service delay is smaller than the service delay requirement), where both the communication cost and computing cost affect the services' satisfaction degree. Since the optimization problem is a constrained non-linear integer programming problem, it is difficult to solve. Moreover, the VEC networks are highly dynamic. Thus, a fast transfer reinforcement learning (fast-TRL) method combining transfer learning and reinforcement learning is proposed to provide an adaptive service migration scheme in dynamic VEC networks. Simulation results show that compared with existing schemes, the proposed CA-migration scheme can increase the satisfaction degree by up to 30%, and needs 25% less training time to obtain the optimal service migration policy.

Balancing Total Energy Consumption and Mean Makespan in Data Offloading for Space-Air-Ground Integrated Networks

We study the data offloading problem in space-air-ground integrated networks (SAGINs) by jointly optimizing task scheduling and power control to balance the total energy consumption and mean makespan. We consider a mixed integer nonlinear programming problem to minimize a normalized weighted combination of these two conflicting objectives. We first propose an approximation algorithm to find a high-quality solution, which is shown to be at most <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\frac{1}{2}$</tex-math></inline-formula> from the optimum to this problem for given power allocation. We further show that optimal power allocation can be obtained in closed form under the assumption that satellite-ground links have low signal-to-noise ratio (SNR). Thus, the proposed approximation algorithm can be directly utilized to obtain a constant-factor solution to the studied problem in low-SNR scenarios. To extend our solution to more general scenarios, we further propose an efficient hybird algorithm based on a genetic framework. Our simulation results demonstrate the near-optimality and correctness of the proposed algorithms, and they unveil the interplay between total energy consumption and mean makespan in SAGINs as well.

Bi-Objective Job-Shop Scheduling Considering Human Fatigue in Cobotic Order Picking Systems: A Case of an Online Grocer

Increasing online retail has resulted in increased automation in order picking systems, leading to new challenges and opportunities in task scheduling. The job-shop scheduling problem is an optimization problem essential in such systems, but existing JSP literature often overlooks workplace fatigue, which harms employees’ well-being and costs U.S. employers up to €127 billion annually. In this work, we propose fatigue consideration in the job-shop scheduling problem in a cobotic order picking system to mitigate its negative effects. We present a new bi-objective mixed integer nonlinear programming problem formulation that considers worker fatigue and productivity during schedule optimisation. To put the results of simulated optimisation in perspective, we experimentally validate the fatigue model and scheduling results in a real operation. The mathematical model finds solutions that conventional single-objective optimisation cannot, allowing fractional fatigue distribution improvements more than 4x larger than the decrease in productivity they require in 53% of the considered virtual cases. The experiments show that our predictive fatigue model has an average RMSE of 2.20 kcal/min in estimating energy expenditure rates compared to heart rate measurements. It also shows a low correlation, meaning it is unfit for application. On the other hand, fatigue-conscious schedules show no clear benefit regarding measured and perceived fatigue. However, the scheduling model could also use heart rate measurements that do not show these inaccuracies. Our study highlights the need to further develop and validate the mathematical formulation and fatigue model and extend to other human factors and indirect fatigue effects.