Objective Function Research Articles

An adversarial diverse deep ensemble approach for surrogate‐based traffic signal optimization

AbstractSurrogate‐based traffic signal optimization (TSO) is a computationally efficient alternative to simulation‐based TSO. By replacing the simulation‐based objective function, a surrogate model can quickly identify solutions by searching for extreme points on its response surface. As a popular surrogate model, the ensemble of multiple diverse deep learning models can approximate complicated systems with a strong generalizability. However, existing ensemble methods barely focus on strengthening the prediction of extreme points, which we found can be realized by further diversifying base learners in the ensemble. The study proposes an adversarial diverse ensemble (ADE) method for online TSO with limited computational resources, comprising two stages: In the offline stage, base extractors are diversified with unlabeled data by a designed adversarial diversity training algorithm; in the online stage, base predictors are trained in parallel with limited labeled data, and the ensemble then serves as the surrogate model to search for solutions iteratively for TSO. First, it is demonstrated that the prediction accuracy on extreme points, and associated solution quality, can be constantly improved with base learners’ diversity enhanced by ADE. Case studies of TSO conducted on a four‐intersection arterial further demonstrate the superior solution quality and computational efficiency of the ADE surrogate model in a wide range of traffic scenarios. Moreover, a large‐scale online TSO experiment under dynamic traffic demand proves ADE's effectiveness in practical applications.

Multi-Objetive Dispatching in Multi-Area Power Systems Using the Fuzzy Satisficing Method

The traditional mathematical models for solving the economic dispatch problem at the generation level primarily focus on minimizing overall operational costs while ensuring demand is met across various periods. However, contemporary power systems integrate a diverse mix of generators from both conventional and renewable energy sources, contributing to economically efficient energy production and playing a pivotal role in reducing greenhouse gas emissions. As the complexity of power systems increases, the scope of economic dispatch must expand to address demand across multiple regions, incorporating a range of objective functions that optimize energy resource utilization, reduce costs, and achieve superior economic and technical outcomes. This paper, therefore, proposes an advanced optimization model designed to determine the hourly power output of various generation units distributed across multiple areas within the power system. The model satisfies the dual objective functions and adheres to stringent technical constraints, effectively framing the problem as a nonlinear programming challenge. Furthermore, an in-depth analysis of the resulting and exchanged energy quantities demonstrates that the model guarantees the hourly demand. Significantly, the system’s efficiency can be further enhanced by increasing the capacity of the interconnection links between areas, thereby generating additional savings that can be reinvested into expanding the links’ capacity. Moreover, the multi-objective model excels not only in meeting the proposed objective functions but also in optimizing energy exchange across the system. This optimization is applicable to various types of energy, including thermal and renewable sources, even those characterized by uncertainty in their primary resources. The model’s ability to effectively manage such uncertainties underscores its robustness, instilling confidence in its applicability and reliability across diverse energy scenarios. This adaptability makes the model a significant contribution to the field, offering a sophisticated tool for optimizing multi-area power systems in a way that balances economic, technical, and environmental considerations.

Exit pupil uniformity improvement of holographic waveguide displays based on a genetic algorithm

Waveguide displays based on a volume holographic grating (VHG) have the benefit of expanding the exit pupil. Exit pupil size and exit pupil uniformity are two important indicators of waveguide displays. Most current optimizations for exit pupil uniformity are based on the central viewing angle. However, this does not ensure satisfied exit pupil uniformity for other viewing angles. In this paper, a method based on a genetic algorithm to optimize the exit pupil uniformity under the whole horizontal field of view (HFOV) is proposed. First, the ray-tracing-based mathematical model to analyze the uniformity of the whole HFOV at all wavelengths is established. Based on the mathematical model, the objective function can be defined, which can optimize the refractive index modulation distribution on several regions of the out-coupling VHG. The simulation results show that for a holographic waveguide display with the exit pupil size of 16mm×12mm, the average exit pupil uniformity can reach 86.87% at a diagonal field of view (DFOV) of 30°, a 9.16% improvement over the previous method. The genetic-algorithm-based method proposed in the paper can effectively improve the exit pupil uniformity.

Evaluating the Impact of the Level of Robustness in Operating Room Scheduling Problems

Managing uncertainty in surgery times presents a critical challenge in operating room (OR) scheduling, as it can have a significant impact on patient care and hospital efficiency. Objectives: By incorporating robustness into the decision-making process, we can provide a more reliable and adaptive solution compared to traditional deterministic approaches. Materials and methods: In this paper, we consider a cardinality-constrained robust optimization model for OR scheduling, addressing uncertain surgery durations. By accounting for patient waiting times, urgency levels and delay penalties in the objective function, our model aims to optimise patient-centred outcomes while ensuring operational resilience. However, to achieve an appropriate balance between resilience and robustness cost, the robustness level must be carefully tuned. In this paper, we conduct a comprehensive analysis of the model’s performance, assessing its sensitivity to robustness levels and its ability to handle different uncertainty scenarios. Results: Our results show significant improvements in patient outcomes, including reduced waiting times, fewer missed surgeries and improved prioritisation of urgent cases. Key contributions of this research include an evaluation of the representativeness and performance of the patient-centred objective function, a comprehensive analysis of the impact of robustness parameters on OR scheduling performance, and insights into the impact of different robustness levels. Conclusions: This research offers healthcare providers a pathway to increase operational efficiency, improve patient satisfaction, and mitigate the negative effects of uncertainty in OR scheduling.

A meta-heuristic extension of the Lagrangian heuristic framework

Lagrangian heuristics for discrete optimization work by modifying Lagrangian relaxed solutions into feasible solutions to an original problem. They are designed to identify feasible, and hopefully also near-optimal, solutions and have proven to be highly successful in many applications. Based on a primal-dual global optimality condition for non-convex optimization problems, we develop a meta-heuristic extension of the Lagrangian heuristic framework. The optimality condition characterizes (near-)optimal solutions in terms of near-optimality and near-complementarity measures for Lagrangian relaxed solutions. The meta-heuristic extension amounts to constructing a weighted combination of these measures, thus creating a parametric auxiliary objective function, which is a close relative to a Lagrangian function, and embedding a Lagrangian heuristic in a search procedure in the space of the weight parameters. We illustrate and make a first assessment of this meta-heuristic extension by applying it to the generalized assignment and set covering problems. Our computational experience show that the meta-heuristic extension of a standard Lagrangian heuristic can significantly improve upon solution quality.

Robust Optimization Models for Planning Drone Swarm Missions

This article presents methods of planning unmanned aerial vehicle (UAV) missions in which individual platforms work together during the reconnaissance of objects located within a terrain. The planning problem concerns determining the flight routes of a swarm, where each UAV has the ability to recognize an object using a specific type of sensor. The experiments described in this article were carried out for drone formation; one drone works as a swarm information hub and exchanges information with the ground control station (GCS). Numerical models for mission planning are presented, which take into account the important constraints, simplifying the description of the mission without too much risk of losing the platforms. Several types of objective functions were used to optimize swarm flight paths. The mission models are presented in the form of mixed integer linear programming problems (MILPs). The experiments were carried out on a terrain model built on the basis of graph and network theory. The method of building a network on which the route plan of a drone swarm is determined is precisely presented. Particular attention was paid to the description of ways to minimize the size of the network on which the swarm mission is planned. The presented methods for building a terrain model allow for solving the optimization problem using integer programming tasks.

Segmenting hotspots from medical thermal images using Density-based modified FC-Pc FS with spatial information

ABSTRACT Thermal cameras complemented with robust and automated computational intelligence-aided diagnostic systems can be deployed at public gathering points and on smartphones to raise alarms about thriving diseases of their body due to inflammation in a timely manner, thereby strengthening human health systems. In this work, we have proposed two robust Density-based modified Picture Fuzzy Clustering methods with spatial information to segment hotspots from human’s abnormal thermal images. We formulated and solved the objective function by combining P c FS-based clustering method with modified Renyi’s Entropy. We demonstrated the robustness of our methods, DSIFC-Pc FS and DSIMFC-Pc FS, on three publicly available datasets and an artificially created noisy dataset of thermal images. We have obtained a ZC score of 0.933, 0.947 and 0.933 for DB-DMR-IR, DB-FOOT-IR and DB-THY-IR datasets, respectively. Also, our method converged to an optimal partition matrix in minimum iterations. The experimental performance shows that the proposed approaches, DSIFC- P c FS and DSIMFC- P c FS, outperformed other ten related approaches in segmenting the medical thermal images with and without noise, indicating their robustness and efficacy, in terms of various unsupervised evaluation metrics. Also, we statistically analysed their performance in contrast to other methods using the Friedman Test, which advocate their superiority.

Analysis of optimization models under different approaches to deal with uncertainty regarding pre-disaster planning in food bank supply chains

Purpose: Pre-positioning is a crucial choice in pre-disaster humanitarian logistics planning that consists of deciding in advance how much aid and where should it be located to enable effective and prompt operations in the case of an emergency. To support managers making such decisions, we propose four mathematical formulations that, considering the uncertainty on the demand to satisfy, seek to optimize aid prepositioning (before the event) and further distribution (after the event) in order to minimize unmet demand (MUD). The purpose of this paper is to evaluate and compare the performance of these formulations on a real case to discuss when and why should each approach be applied.Design/methodology/approach: The two first formulations adopt the cardinality-constrained (CC) approach to handle uncertainty. These formulations differ in their objective functions, the first formulation’s objective seeks to MUD, whilst the second incorporates equity in the way that demand is satisfied. The two remaining formulations are scenario-based (SB) and as in the previous two formulations, seek to MUD with and without equity considerations, respectively.Findings: Applying our formulations to a case study, we compare the differences between the solutions produced by the proposed formulations and the solutions that would have been produced without uncertainty (perfect information) to have a better understanding of their performance and their behavior. A discussion of the strengths and weaknesses of each model is provided to help managers choose the model that best suits their needs.Originality/value: The formulations are applied to a case study where a food bank is faced with the arrival of a hurricane in Mexico. As far as our knowledge, it is the first work in literature to deal with humanitarian logistics under a cardinality-constrained approach.

Weather shocks affect trade policy: Evidence from preferential trade agreements

AbstractWe show that weather shocks affect government trade policy decisions. We exploit variation in rainfall during the growing season within and across countries to show that weather shocks impact agricultural output and trade. Using information on tariff cuts by commodity from preferential trade agreements signed between 1995 and 2014, we then show that weather shocks that happen during the negotiation period correlate strongly with the size of tariff cuts. When weather shocks increase (decrease) a country's capacity to produce a given crop, its government negotiates a smaller (larger) tariff cut. These results are consistent with a political economy trade model with sector‐specific inputs in which the government places more weight on producers relative to consumers in its objective function. They also reveal that governments update their beliefs about domestic agricultural production capacity in response to weather shocks.

Data-driven approximations of topological insulator systems

A data-driven approach to calculating tight-binding models for discrete coupled-mode systems is presented. In particular, spectral and topological data are used to build an appropriate discrete model that accurately replicates these properties. This work is motivated by topological insulator systems that are often described by tight-binding models. The problem is formulated as the minimization of an appropriate residual (objective) function. Given bulk spectral data and a topological index (e.g., winding number), an appropriate discrete model is obtained to arbitrary precision. A nonlinear least squares method is used to determine the coefficients. The effectiveness of the scheme is highlighted against a Schrödinger equation with a periodic potential that can be described by the Su–Schrieffer–Heeger model.

Optimization of Load-transfer Functions for a Large-diameter Pile in Multi-layered Geological Conditions via a Stochastic Search Algorithm

The paper presents the combination of the load transfer method (computational model) and the genetic algorithm (optimization model) for the automated inverse analysis of instrumented pile load tests. The output of this process are the input parameters governing the shape of the load-transfer functions and thus the prediction accuracy when the load-transfer method is used as a design tool for deep foundations. The optimization problem is converted into an unconstrained task by applying the static penalty approach. Two types of measurements are considered in a newly proposed objective function: the load-displacement curve monitored in a pile head and the axial force profiles along a pile derived from strain gauges. Firstly, the local sensitivity analysis via the Design of Experiments is carried out to identify the parameters of the genetic algorithm which significantly influences the rate of convergence during the optimization process. Subsequently, a fully automated inverse analysis of the loading test of the large-diameter bored pile in multilayered geological conditions is presented. The simultaneous combination of two instrumentation sources leads to a stable unique solution with a sufficient match between the prediction and measurements despite a larger number of unknown – optimized variables.

Time scale analysis of enzymatic reduction of uric acid in a microfluidic biomedical device

Time Scale Analysis (TSA) is an investigative tool used in engineering design to identify locations in processes that should be a focus of Process Intensification (PI). Furthermore, TSA points to process variables and parameters that could be used to advance and measure PI improvement. However, TSA cannot suggest any specific design solution to intensify process performance. Instead, design engineers should use their fundamental knowledge and creative intelligence to specify detailed design transformations. TSA will then provide a specific quantitative measure of the improvement. TSA implementation improves an explicitly defined process performance, thus helping achieve process intensification goals. TSA is based on first principles, and it utilizes Characteristic Times (CT) such as diffusion, mean residence, and reaction times to improve an existing process. In this study, we specifically consider microfluidic biomedical devices. To illustrate the genesis of CT and TSA, we start by developing a mathematical model of an enzymatic degradation process in a biomedical device called iCore based on mass, momentum, and kinetic equations. After introducing user-defined scaling parameters, we extract CTs pertinent to the enzymatic degradation of uric acid in this microfluidic biomedical device. Diffusion coefficients, microchannel architectural characteristics, enzyme loading, hydrogel thickness, and characteristic parameters of enzyme kinetics are the parameters and process variables incorporated in this analysis. Finally, we compared the extracted CTs with a COMSOL Multiphysics parametric study to demonstrate how time scale analysis as a design tool and adjusting design parameters, such as diffusion coefficient, hydrogel layer thickness, substrate concentration, and enzyme concentration, can enhance the enzymatic reaction process without a need for complex computational modeling. It is crucial to recognize that pertinent CTs can be determined by understanding the type and nature of the observed process, previous experience, published data, and other foundational engineering design work. There is no need for mathematical modeling and numerical simulations to identify and acknowledge the CTs relevant and essential to the observed process; in this work, we only illustrate the principal origin of CTs via a detailed mathematical model of the process, as previously reported by Jovanovic et al. Therefore, in a routine application of TSA, it is important to remember that mathematical modeling and detailed numerical simulations are not necessary. This is a very comforting fact when TSA is deployed as a tool in higher-level process design functions. The investigations on how best to apply TSA in these higher level design functions such as Process Intensification, scale-up/numbering-up, change of device architecture, change of operating conditions, change of process feed characteristics, change of material physical and chemical properties, parametric optimization of the system for various objective functions, and techno-economic analysis, are yet to be studied and reported.

Compressed sensing with smooth L0 constraints for moving force identification from bridge response measurements

Abstract Compressed sensing (CS), as an emerging information sampling technique, has been successfully applied in the field of moving force identification (MFI). However, existing MFI compressed sensing models often fail to obtain the optimal sparse solutions and frequently underestimate the amplitude of local impact forces. To effectively address this issue, a new compressed sensing method is proposed for MFI based on smooth L0 norm constraints and bridge response measurements. Firstly, a smooth function is used to approximate the L0 norm, establishing a noise CS reconstruction model for MFI. The introduction of the smoothing function can locally convexify the original MFI problem and enhance the smoothness and differentiability of the objective function, making the optimization problem easier to solve. Subsequently, the Polak-Ribiere-Polyak (PRP) formula is adopted to point the descent direction of the new objective function, and the sparse solution is iteratively advanced through the conjugate gradient algorithm. Finally, the applicability and feasibility of the proposed method is confirmed by numerical simulations and vehicle-bridge interaction tests, respectively. The results show that the proposed method can accurately identify moving forces from limited measurements of bridge responses. Compared with existing methods, it can provide more precise sparse solutions with higher robustness to measurement noises, and address the issue of underestimating on the amplitude of local impact forces, which is expected to enhance the performance and in-situ applicability of MFI.

Fast heuristics for the time‐constrained immobile server problem

AbstractWe propose easy‐to‐implement heuristics for time‐constrained applications of a problem referred to in the literature as the facility location problem with immobile servers, stochastic demand, and congestion, the service system design problem, or the immobile server problem (ISP). The problem is typically posed as one of allocating capacity to a set of M/M/1 queues to which customers with stochastic demand are assigned with the objective of minimizing a cost function composed of a fixed capacity‐acquisition cost, a variable customer‐assignment cost, and an expected‐waiting‐time cost. The expected‐waiting‐time cost results in a nonlinear term in the objective function of the standard binary programming formulation of the problem. Thus, the solution approaches proposed in the literature are either sophisticated linearization or relaxation schemes, or metaheuristics. In this study, we demonstrate that an ensemble of straightforward, greedy heuristics can rapidly find high‐quality solutions. In addition to filling a gap in the literature on ISP heuristics, new stopping criteria for an existing cutting plane algorithm are proposed and tested, and a new mixed‐integer linear model requiring no iterating algorithm is developed. In many cases, our heuristic approach finds solutions of the same or better quality than those found by exact methods implemented with expensive, state‐of‐the‐art mathematical programming software, in particular a commercial nonlinear mixed‐integer linear programming solver, given a five‐minute time limit.

Sparse-Coding Variational Autoencoders.

The sparse coding model posits that the visual system has evolved to efficiently code natural stimuli using a sparse set of features from an overcomplete dictionary. The original sparse coding model suffered from two key limitations, however: (1) computing the neural response to an image patch required minimizing a nonlinear objective function via recurrent dynamics and (2) fitting relied on approximate inference methods that ignored uncertainty. Although subsequent work has developed several methods to overcome these obstacles, we propose a novel solution inspired by the variational autoencoder (VAE) framework. We introduce the sparse coding variational autoencoder (SVAE), which augments the sparse coding model with a probabilistic recognition model parameterized by a deep neural network. This recognition model provides a neurally plausible feedforward implementation for the mapping from image patches to neural activities and enables a principled method for fitting the sparse coding model to data via maximization of the evidence lower bound (ELBO). The SVAE differs from standard VAEs in three key respects: the latent representation is overcomplete (there are more latent dimensions than image pixels), the prior is sparse or heavy-tailed instead of gaussian, and the decoder network is a linear projection instead of a deep network. We fit the SVAE to natural image data under different assumed prior distributions and show that it obtains higher test performance than previous fitting methods. Finally, we examine the response properties of the recognition network and show that it captures important nonlinear properties of neurons in the early visual pathway.

Optimising seismic imaging design parameters via bilevel learning

Abstract Full waveform inversion (FWI) is a standard algorithm in seismic imaging. It solves the inverse problem of computing a model of the physical properties of the earth’s subsurface by minimising the misfit between actual measurements of scattered seismic waves and numerical predictions of these, with the latter obtained by solving the (forward) wave equation. The implementation of FWI requires the a priori choice of a number of ‘design parameters’, such as the positions of sensors for the actual measurements and one (or more) regularisation weights. In this paper we describe a novel algorithm for determining these design parameters automatically from a set of training images, using a (supervised) bilevel learning approach. In our algorithm, the upper level objective function measures the quality of the reconstructions of the training images, where the reconstructions are obtained by solving the lower level optimisation problem—in this case FWI. Our algorithm employs (variants of) the BFGS quasi-Newton method to perform the optimisation at each level, and thus requires the repeated solution of the forward problem—here taken to be the Helmholtz equation. This paper focuses on the implementation of the algorithm. The novel contributions are: (i) an adjoint-state method for the efficient computation of the upper-level gradient; (ii) a complexity analysis for the bilevel algorithm, which counts the number of Helmholtz solves needed and shows this number is independent of the number of design parameters optimised; (iii) an effective preconditioning strategy for iteratively solving the linear systems required at each step of the bilevel algorithm; (iv) a smoothed extraction process for point values of the discretised wavefield, necessary for ensuring a smooth upper level objective function. The algorithm also uses an extension to the bilevel setting of classical frequency-continuation strategies, helping avoid convergence to spurious stationary points. The advantage of our algorithm is demonstrated on a problem derived from the standard Marmousi test problem.

Applying portfolio theory to benefit endangered amphibians in coastal wetlands threatened by climate change, high uncertainty, and significant investment risk

The challenge of selecting strategies to adapt to climate change is complicated by the presence of irreducible uncertainties regarding future conditions. Decisions regarding long-term investments in conservation actions contain significant risk of failure due to these inherent uncertainties. To address this challenge, decision makers need an arsenal of sophisticated but practical tools to help guide spatial conservation strategies. Theory asserts that managing risks can be achieved by diversifying an investment portfolio to include assets – such as stocks and bonds – that respond inversely to one another under a given set of conditions. We demonstrate an approach for formalizing the diversification of conservation assets (land parcels) and actions (restoration, species reintroductions) by using correlation structure to quantify the degree of risk for any proposed management investment. We illustrate a framework for identifying future habitat refugia by integrating species distribution modeling, scenarios of climate change and sea level rise, and impacts to critical habitat. Using the plains coqui (Eleutherodactylus juanariveroi), an endangered amphibian known from only three small wetland populations on Puerto Rico’s coastal plains, we evaluate the distribution of potential refugia under two model parameterizations and four future sea-level rise scenarios. We then apply portfolio theory using two distinct objective functions and eight budget levels to inform investment strategies for mitigating risk and increasing species persistence probability. Models project scenario-specific declines in coastal freshwater wetlands from 2% to nearly 30% and concurrent expansions of transitional marsh and estuarine open water. Conditional on the scenario, island-wide species distribution is predicted to contract by 25% to 90%. Optimal portfolios under the first objective function – benefit maximization – emphasizes translocating frogs to existing protected areas rather than investing in the protection of new habitat. Alternatively, optimal strategies using the second objective function – a risk-benefit tradeoff framework – include significant investment to protect parcels for the purpose of reintroduction or establishing new populations. These findings suggest that leveraging existing protected areas for species persistence, while less costly, may contain excessive risk and could result in diminished conservation benefits. Although our modeling includes numerous assumptions and simplifications, we believe this framework provides useful inference for exploring resource dynamics and developing robust adaptation strategies using an approach that is generalizable to other conservation problems which are spatial or portfolio in nature and subject to unresolvable uncertainty.

A stochastic moving ball approximation method for smooth convex constrained minimization

AbstractIn this paper, we consider constrained optimization problems with convex objective and smooth convex functional constraints. We propose a new stochastic gradient algorithm, called the Stochastic Moving Ball Approximation (SMBA) method, to solve this class of problems, where at each iteration we first take a (sub)gradient step for the objective function and then perform a projection step onto one ball approximation of a randomly chosen constraint. The computational simplicity of SMBA, which uses first-order information and considers only one constraint at a time, makes it suitable for large-scale problems with many functional constraints. We provide a convergence analysis for the SMBA algorithm using basic assumptions on the problem, that yields new convergence rates in both optimality and feasibility criteria evaluated at some average point. Our convergence proofs are novel since we need to deal properly with infeasible iterates and with quadratic upper approximations of constraints that may yield empty balls. We derive convergence rates of order $${\mathcal {O}} (k^{-1/2})$$ O ( k - 1 / 2 ) when the objective function is convex, and $${\mathcal {O}} (k^{-1})$$ O ( k - 1 ) when the objective function is strongly convex. Preliminary numerical experiments on quadratically constrained quadratic problems demonstrate the viability and performance of our method when compared to some existing state-of-the-art optimization methods and software.

Residual Adversarial Subdomain Adaptation Network Based on Wasserstein Metrics for Intelligent Fault Diagnosis of Bearings

Subdomain adaptation plays a significant role in the field of bearing fault diagnosis. It effectively aligns the pertinent distributions across subdomains and addresses the frequent issue of lacking local category information in domain adaptation. Nonetheless, this approach overlooks the quantitative discrepancies in distribution between samples from the source and target domains, leading to the vanishing gradient issue during the training of models. To tackle this challenge, this paper proposes a bearing fault diagnosis method based on Wasserstein metric residual adversarial subdomain adaptation. The Wasserstein metric is introduced as the optimized objective function of the domain discriminator in RASAN-W. The distribution discrepancy between the source domain and target domain samples is quantitatively measured, achieving the alignment of the relevant subdomain distributions between the source domain and the target domain. Ultimately, extensive experiments conducted on two real-world datasets reveal that the diagnostic accuracy of this method is significantly enhanced when compared to various leading bearing fault diagnosis techniques.

EXPRESS: Distributionally Robust Appointment Scheduling That Can Deal with Independent Service Times

Consider a single server that should serve a given number of customers during a fixed period. The Appointment Scheduling Problem (ASP) determines the schedule of planned appointments that minimizes some cost function that accounts for both the cost of idle times and the cost of waiting. When service time distributions are fully specified, the ASP presents a much investigated computationally challenging stochastic program. When service time distributions are only partially specified, one can apply distributionally robust optimization (DRO) to find the schedule that minimizes costs in worst-case circumstances. We assume that only the mean, mean absolute deviation and range of the service times are known, and develop a DRO method that finds the optimal (minimax) schedule. For independent service times, the minmax problem becomes nonlinear and difficult, if not impossible, to solve exactly. Existing DRO methods for ASP with partial information (such as mean and variance) therefore consider relaxations that allow correlations between service times. Such relaxations have major repercussions, as the worst-case scenario will then be highly correlated. Our method thus deals with independent service times and finds the robust schedule as the solution to a linear program. We identify several new structural features of optimal robust schedules. We also apply the method to model extensions including sequencing and alternative objective functions.