Objective Value Research Articles

Adjustable Robust Optimization for Water Distribution System Operation Under Uncertainty

AbstractThe optimal operation of water distribution systems (WDS) is a paramount objective for water utilities due to the substantial energy consumption associated with pumping. A major challenge in optimizing WDS operation is addressing uncertainties such as those related to consumer demands. Real‐time operation under uncertainty necessitates a dynamic approach that can utilize the newly observed information and adjust the operational policy accordingly. This study presents an adjustable robust optimization (ARO) approach to tackle this challenge. Unlike static optimization methods, ARO generates a decision rule policy that is dynamically adjusted as new data becomes available and the operational horizon evolves, thereby ensuring adaptability to changing conditions. Furthermore, the study includes a quantitative analysis of typical demand uncertainty that supports the formulation of the ARO model. The proposed method is evaluated through two case studies and compared with traditional folding horizon approaches. The results indicate that the ARO method is competitive with traditional methods in terms of objective value and surpasses them in terms of robustness. An additional advantage of the method is its offline operation capability which enables it to produce decision rules independent of real‐time programs. This feature facilitates various practical applications such as what‐if analyses, maintenance work planning, and preparation for other special events.

Service Deployment With Priority Queueing for Traffic Processing and Transmission in Network Function Virtualization

Network function virtualization enables service providers to flexibly deploy network services. The existing works mainly focus on function placement and capacity allocation without exploring traffic scheduling for service deployment, by adopting a first-in-first-out policy. It introduces inefficiency considering that different services vary in the delay requirements. This paper proposes a service deployment model with priority queuing for both traffic processing and transmission to minimize the deployment cost with satisfying the service delay constraints. We analyze the problem including proving its NP-hardness and the convexity of a subproblem. Based on the analysis, we develop a reinforcement learning-based approach to address the problem in a decomposition manner with a polynomial-time complexity in each episode. Several specific designs are introduced to fit the learning-based approach to the considered deployment problem with priority queueing. The numerical results show that the introduced approach achieves an objective value comparable to the optimal one obtained by brute force search with a computation time 103 times shorter. Compared to a conventional model with the first-in-first-out policy, the proposed model reduces the deployment cost by adopting a more flexible queueing policy.

Enhancing the performance of radial distribution systems via optimal integration of electric vehicles

<span lang="EN-US">Electric vehicles (EVs) and their associated charging stations (CSs) are a promising avenue for greenhouse gas reduction and energy security. However, improper location and size of the EV charging station (CSs/EVs) negatively affect the power system. It results in some technical challenges such as increased real power-loss, decreased voltage stability and increased voltage deviation. This paper suggests optimum planning of CSs/EVs locations to conserve voltage, improve power-loss and reduce the effect of CSs/</span><span lang="EN-US">EVs in electrical distribution systems. The multi objective genetic algorithm method (MOGA) is utilized to solve the optimization problem and reduce the impact of the random location of CSs/EVs. <span>The simulations are</span> performed on IEEE 33-bus and IEEE 69-bus radial distribution systems (RDS). In addition, the optimal EV allocation is carried out with two fixed levels of loading from 100% to 150% of the candidate EV load. A comparison between the proposed MOGA technique and other optimization techniques is carried out. The results demonstrated the capability of the proposed technique for optimal placement of CSs/EVs in RDS. </span><span lang="EN-US">Moreover, it is providing an objective value to solve a complex multi-objective nonlinear optimization problem to reduce the total power-loss, improve the voltage profile and extend the voltage stability.</span>

Reference value of knee position sense in weight-bearing and non-weight-bearing conditions

BackgroundOur study aimed to identify age-related changes in knee proprioception to provide reference values for weight-bearing (WB) and non-weight-bearing (NWB) conditions and to identify factors (age, WB condition, dominance, and sex) that can affect knee proprioception.MethodsA total of 84 healthy adult men and women were recruited. Active knee joint position sense (JPS) was measured using a digital inclinometer for knee proprioception. The participants performed the required movements actively, with verbal feedback from the examiner, slowly moving to the target angles (30° and 50°) and maintaining them for 5 s before returning to the starting position. Afterward, without assistance from the examiner, the participants actively moved back to the same angle, and the examiner confirmed the angles. This procedure was repeated twice for each target angle, and the average values were used as the data. The participants were barefoot, wearing shorts, and closed their eyes while the measurements were obtained. The measurements were first obtained on the dominant side under the NWB conditions. When a change in posture was needed during the measurement, the participants sat in a resting position for 2 min.ResultsExcept for age, all other factors (WB condition, dominance, sex) were not statistically significant. Age showed a significant difference in knee JPS, except for the non-dominant side at 30° and the dominant side at 50° in the NWB condition.ConclusionThis study indicates that the WB condition, dominant side, and sex need not be considered when measuring and assessing knee JPS. Age shows a negative correlation with knee joint position sense, and the reference values presented in this study can be used as objective target values during the rehabilitation process.

Long-term effects of maxillary skeletal expander treatment on functional breathing.

: To investigate the long-term effects of maxillary skeletal expander (MSE) treatment on functional breathing. measures of breathing, the peak nasal inspiratory flow (PNIF), and peak oral inspiratory flow (POIF), and subjective measures of breathing, the visual analog scale (VAS) and nasal obstruction symptom evaluation (NOSE) survey, were used to investigate the long-term effects of MSE in functional breathing. Seventeen patients, mean age 19.4 ± 3.9 years treated at the UCLA Orthodontics Clinic were assessed on their functional breathing at 3 timepoints: pre-expansion (T0), post-expansion (T1), and post-orthodontic treatment (T2). : Immediately after expansion (T1), all the objective functional breathing values were significantly increased in comparison to T0 (P < 0.05). The VAS total, VAS right and VAS left were significantly lower at T1 in comparison to T0 (P < 0.05). At 26.8 ± 3.9 months after MSE expansion (T2), PNIF total, PNIF right, PNIF left, and POIF were significantly higher when compared to T0 (P < 0.05). Also, VAS total, VAS right and VAS left were significantly lower at T2 when compared to T0 (P < 0.05). Additionally, there was a positive correlation between PNIF and the magnitude of expansion at anterior nasal spine and zygomaticomaxillary point (ZMA). There was a positive correlation between total VAS and the magnitude of expansion at the ZMA. There were no significant changes for the NOSE subjective breathing measurement at all time comparisons. : Overall, MSE treatment produces an increased objective and subjective airway improvement that continues to remain stable in the long-term post expansion.

Trade-off between optimal design and operation in district cooling networks

Especially in densely populated areas, district cooling represents an opportunity to reduce energy consumption and emissions. Nevertheless, this technology is characterised by large capital costs which impede its diffusion. As a consequence, optimization tools can significantly help to unleash their potential. In this paper, a methodology is proposed to combinedly optimize the design and operation of a district cooling system based on a Mixed Integer Quadratic Programming. The model is compared to the design only optimization, based on a properly tailored heuristic approach. The models, when applied to a case study characterized by seasonal demand, provide similar solutions, which differ by 0.5 % in terms of objective value for a standard scenario. The simultaneous design and operation optimization does not provide sensible savings with respect to optimizing solely the design. A sensitivity analysis is performed to prove the robustness of the results. The results showed that the simultaneous operation and design optimization would be limited to 1 % of total costs in the case of seasonal cooling demand. On the other hand, if the cooling demand persists throughout the year, as in tropical climates, the combined optimization provides significant benefits, since these savings reach 4.7 % of total costs.

Multiproduct Dynamic Pricing with Limited Inventories Under a Cascade Click Model

Problem definition: Designing effective operational strategies requires a good understanding of customer behavior. The classic economic theory of customer choice has long been the paradigm in the operations literature. However, the rise of online marketplaces such as e-commerce has triggered considerable efforts in academia and industry to develop alternative models that not only provide a good approximation of customer behavior but also are easily scalable for large-scale implementations. In this paper, we consider a multiproduct dynamic pricing problem with limited inventories under the so-called cascade click model, which is one of the most popular click models used in practice and has been intensively studied in the computer science literature. Methodology/results: We present some fundamental results. First, we derive a sufficiently general characterization of the optimal pricing policy and show that it has a different structure than the optimal policy under the standard pricing model. Second, we show that the optimal expected total revenue under the cascade click model can be upper bounded by the objective value of an approximate deterministic pricing problem. Third, we show that two policies that are known to have strong performance guarantees in the standard revenue management setting can be properly adapted (in a nontrivial way) to the setting with cascade click model while retaining their strong performance. Finally, we also briefly discuss the joint ranking and pricing problem and provide an iterative heuristic to calculate an approximate ranking. Managerial implications: Taking into account customers’ click-and-search behavior leads to different structures of the optimal pricing policy, and some common insights under the standard pricing models may no longer hold. Moreover, our simulation studies show that pricing under a (misspecified) classic choice model that is oblivious to customers click-and-search behavior can severely impact profitability. Supplemental Material: The online appendix is available at https://doi.org/10.1287/msom.2021.0504 .

Workflow migration in uncertain edge computing environments based on interval many-objective evolutionary algorithm

In edge computing (EC), when the edge server (ES) is processing tasks delivered by the mobile devices (MDs), the MDs move outside the coverage of the ES, where task migration is required to ensure service continuity. Most current research on task migration ignores inter-task dependencies and uncertain computing environments, and it focuses mainly on migration scenarios where MDs have a one-to-one or many-to-one relationship with ESs. Aiming at the problem of workflow migration with multi-MDs and multi-ESs in uncertain environments, this paper proposes an interval many-objective optimized workflow migration in uncertain environments (I-MaOWMUE) model that considers transforming uncertainty factors into interval parameters for processing, along with the migration delay, maximum completion time, energy consumption, and load balancing as an objective function, and at the same time, utilize real-time priority scheduling strategies to achieve the fast response of the tasks. Considering the dependency of tasks and the changing characteristics of ES load in a migration environment, this paper designs a migration-based interval many-objective evolutionary algorithm (MI-MaOEA), which adopts an interval confidence strategy to improve algorithm convergence and formulates an objective-value-dominated hierarchical sorting and dual-migration selection strategy based on the migration delay and the success rate of the migration to improve the diversity of the populations. Simulation results show that MI-MaOEA optimizes 27%, 35%, 14%, and 80% in solving the four objective values of I-MaOWMUE, and enables the solution to have faster converse speed and better distribution.

Relaxation approaches for nonlinear sparse optimization problems

In many recent applications, sparse solutions of the optimization problems are favoured over non-sparse solutions with comparable objective values. A standard method to induce the sparsity of the solution is based on the use of the norm in the objective. However, if the underlying optimization problem is nonlinear, the solution of the nonlinear (sparse) -optimization problem is difficult. Therefore, it is often approximated using the convex -norm although this can lead to suboptimal solutions for the sparsity of the solution. In this paper, we follow another direction. We present exact reformulations (with respect to the norm) and their relaxations leading to standard nonlinear but nonconvex programmes. We discuss and relate the relations between the different reformulations with repect to the original problem. We accompany our theoretical results by some numerical tests using randomly generated datasets.

Optimal [formula omitted]-matrix completion with majorization ordered objectives

We propose and examine two inherently symmetric (0,1)-matrix completion problems with majorization ordered objectives, which provides a unique perspective for electric vehicle charging, portfolio optimization, and multi-agent cooperation. Our work elevates the seminal study by Gale and Ryser from feasibility to optimality in partial order programming (POP), referring to optimization with partially ordered objectives. Solving such integer POP (iPOP) problems is challenging because of the integer requirements and the fact that two objective values may not be comparable. Nevertheless, we prove the essential uniqueness of all optimal objective values and identify two particular ones for each iPOP problem. Furthermore, for every optimal objective value of each iPOP problem, we respectively develop a “peak-shaving” and a “valley-filling” algorithm to construct an associated optimal (0,1)-matrix via a series of sorting processes. We show that the resulting algorithms have linear time complexities and numerically verify their efficiency compared to the commonly used order-preserving method for POP.

Ethical Theories in Business Ethics: A Critical Review

Numerous ethical theories have been proposed as a foundation of business ethics, and this often brings about appreciable perplexity. This article seeks to identify specific problems for a sound foundation of this discipline. A first problem is this multiplicity of ethical theories, each with its own metaethics, often accepted without a serious discussion of their philosophical grounds. A second problem is the fragmentation of theories; some centred on duties or obligations, others on consequences, virtues, or moral sentiments. In addition, some theories focus on universal principles, while others take the singularity of each situation as their focal point. A third problem is that not every ethical theory covers the personal, organizational and societal dimensions of business ethics, and this introduces reductionism. These problems cannot be satisfactorily addressed through ‘ethical pluralism’, in which all theories are accepted, without falling into ethical relativism. ‘Ethical pragmatism’, which welcomes any ethical theory only on the basis of their practically, is also questioned. Furthermore, there is the problem of integrating ethics into business theory, which is often extrinsic to the economic function. After analysing these problems, the article concludes by exploring some proposals that might serve to build a sound and complete ethical theory which includes human goods (objective values), principles (or norms) and virtues. The necessity of reconsidering the human action for a closer integration of ethics into business theory is also suggested.

Optimal Radio Propagation Modeling and Parametric Tuning Using Optimization Algorithms

Benchmarking different optimization algorithms is tasky, particularly for network-based cellular communication systems. The design and management process of these systems involves many stochastic variables and complex design parameters that demand an unbiased estimation and analysis. Though several optimization algorithms exist for different parametric modeling and tuning, an in-depth evaluation of their functional performance has not been adequately addressed, especially for cellular communication systems. Firstly, in this paper, nine key numerical and global optimization algorithms, comprising Gauss–Newton (GN), gradient descent (GD), Genetic Algorithm (GA), Levenberg–Marguardt (LM), Quasi-Newton (QN), Trust-Region–Dog-Leg (TR), pattern search (PAS), Simulated Annealing (SA), and particle swam (PS), have been benchmarked against measured data. The experimental data were taken from different radio signal propagation terrains around four eNodeB cells. In order to assist the radio frequency (RF) engineer in selecting the most suitable optimization method for the parametric model tuning, three-fold benchmarking criteria comprising the Accuracy Profile Benchmark (APB), Function Evaluation Benchmark (FEB), and Execution Speed Benchmark (ESB) were employed. The APB and FEB were quantitatively compared against the measured data for fair benchmarking. By leveraging the APB performance criteria, the QN achieved the best results with the preferred values of 98.34, 97.31, 97.44, and 96.65% in locations 1–4. The GD attained the worst performance with the lowest APE values of 98.25, 95.45, 96.10, and 95.70 in the tested locations. In terms of objective function values and their evaluation count, the QN algorithm shows the fewest function counts of 44, 44, 56, and 44, and the lowest objective values of 80.85, 37.77, 54.69, and 41.24, thus attaining the best optimization algorithm results across the study locations. The worst performance was attained by the GD with objective values of 86.45, 39.58, 76.66, and 54.27, respectively. Though the objective values achieved with global optimization methods, PAS, GA, PS, and SA, are relatively small compared to the QN, their function evaluation counts are high. The PAS, GA, PS, and SA recorded 1367, 2550, 3450, and 2818 function evaluation counts, which are relatively high. Overall, the QN algorithm achieves the best optimization, and it can serve as a reference for RF engineers in selecting suitable optimization methods for propagation modeling and parametric tuning.

The Role of Anchoring Effect in the Stock Market Investment Decisions

Price anomalies in the stock market are often difficult to explain using traditional financial theories, and such price anomalies severely affect the specific investment behavior of investors in the stock market and the trend of stock price movements. In order to study the causes of these anomalies and conclude certain countermeasures, this paper combines behavioural economic theories to analyze the causes of stock price movements over a certain period of time in terms of stock price trends caused by psychological deviations of investors in a specific industry. In this paper, this study finds that relevant stock price data by analyzing stock price movements over a certain period of time and integrate them to further understand the impact of investors' psychological biases or heuristics on stock price movements. Finally, this paper provides targeted suggestions for investors and stock market policy makers to address the importance of psychological biases on investment decisions, and suggests investors to consider the influence of different psychological mechanisms in the process of stock investment and make more objective value estimates for stocks. Second, it is recommended that government departments should reduce their intervention in the stock market to reduce the impact of policy changes on the stock market and promote a healthier investment environment for the stock market. In addition, stock market policy makers establish stricter laws for the stock market to regulate the price changes and valuation system of the stock market.

Reinforcement learning for humanitarian relief distribution with trucks and UAVs under travel time uncertainty

Effective humanitarian relief operations are challenging in the aftermath of disasters, as trucks are often faced with considerable travel time uncertainties due to damaged transportation networks. Efficient deployment of Unmanned Aerial Vehicles (UAVs) potentially mitigates this problem, supplementing truck fleets in an impactful manner. To plan last-mile relief distribution in this setting, we introduce a multi-trip, split-delivery vehicle routing problem with trucks and UAVs, soft time windows, and stochastic travel times for last-mile relief distribution, formulated as a stochastic dynamic program. Within a finite time horizon, we aim to maximize a weighted objective function comprising the number of goods delivered, the number of different locations visited, and late arrival penalties. Our study offers insights into dealing with travel time uncertainty in humanitarian logistics by (i) deploying Unmanned Aerial Vehicles (UAVs) as partial substitutes for trucks, (ii) evaluating dynamic solutions generated by two deep reinforcement learning (RL) approaches – specifically value function approximation (VFA) and policy function approximation (PFA) – and (iii) comparing the RL solutions with solutions stemming from mathematical programming and dynamic heuristics. Experiments are performed on both Solomon-based instances and two real-world cases. The real-world cases – the 2015 Nepal earthquake and the 2018 Indonesia tsunami – are based on locally collected field data and real-world UAV specifications, and aim to provide practical insights. The experimental results show that dynamic decision-making improves both performance and robustness of humanitarian operations, achieving reductions in lateness penalties of around 85% compared to static solutions based on expected travel times. Furthermore, the results show that replacing half of the trucks with UAVs improves the weighted objective value by 11% to 56%, benefitting both reliability and location coverage. The results indicate that both the deployment of UAVs and the use of dynamic methods successfully mitigate travel time uncertainties in humanitarian operations.

Complementarity reformulations for the optimal design of distributed energy systems with multiphase optimal power flow

The optimal design of grid-connected distributed energy systems (DES) has been previously investigated, but most studies exclude nonlinear multiphase optimal power flow (MOPF) constraints which capture imbalances in alternating current (AC) distribution networks. Previous DES design studies considering AC power flow assume balanced loads and networks, which is an assumption that does not hold for distribution networks that are often inherently unbalanced. This is the first study to present an optimisation framework for designing grid-connected DES while simultaneously considering multiphase optimal power flow (MOPF) constraints to accurately represent unbalanced low-voltage distribution. This study proposes a new algorithm for obtaining DES designs subject to nonlinear multiphase power flow constraints with regularised complementarity reformulations for operational constraints containing binary variables. DES design models with either MOPF or OPF are tested using an unbalanced distribution network, where rooftop solar, gas boilers, and battery storage are considered as distributed resources. Despite the increased complexity, DES design with MOPF obtains the best solution, with 81% greater solar capacity and 6% lower total annualised cost when compared to DES with OPF. Designs from a commonly-used linear DES design framework based on direct current (DC) approximations produce the highest costs (8% more than initially predicted) when tested with MOPF. The proposed algorithm with complementarity reformulations achieves a 19% improvement in the objective value over a previous two-stage decomposition for DES with OPF, where the entire binary topology in the nonlinear model is fixed. The study therefore enables the acquisition of DES designs that can work symbiotically within unbalanced distribution networks.

Historical information based iterated greedy algorithm for distributed flowshop group scheduling problem with sequence-dependent setup times

Distributed flowshop group scheduling problem (DFGSP) is commonly seen in modern industry. However, research works on DFGSP with total flow time criterion are rarely reported. The DFGSP consists of three coupled sub-problems, i.e., factory assignment for each group, group sequence in each factory, and job sequence within each group. A historical information-based iterated greedy algorithm (HIG) is proposed for solving the DFGSP with the objective of minimizing total flow time. The HIG integrates an iterated greedy algorithm (IG) with a group-based insertion operator, a job-based insertion operator, a domination criterion-based swap operator, and a historical information-based constructive solution method. The domination criterion is an effective inequality, which can deterministically optimize the objective value of a partial sequence even if the scheduling sequence of subsequent jobs is unknown. In the constructive solution method, a set covering model is designed to capture the effective factory allocation patterns for the groups hidden in the historical solutions to speed up the search for the IG. The comprehensive experiments on 810 test instances demonstrate the effectiveness of HIG.

Ensemble deep learning enabled multi-condition generative design of aerial building machine considering uncertainties

The Aerial Building Machine (ABM) is a complex construction equipment used in high-rise building construction, facing challenges due to environmental uncertainties. This paper introduces a multi-condition generative design framework to improve ABM's visualization, operability, and intelligence. It seamlessly integrates real-time data between geometric and physical models and employs an ensemble deep learning model for objective value prediction, using a snapshot strategy. Combining structural reliability concepts with Latin hypercube sampling-based stochastic optimization, an optimal design scheme is obtained for uncertain loads. An ABM case study in China illustrates the approach's feasibility, showing it meets reliability requirements across different conditions and achieves significant improvements (16.59% under normal conditions and 16.91% under extreme wind conditions). Additionally, ensemble deep learning outperforms existing methods for ABM structural reliability estimation. Identifying optimal designs and evaluation options, this paper contributes a multi-condition optimization approach for enhanced structural reliability and establishes an efficient generative design workflow and system for exploring a vast solution space.

Solving the Inter-Terminal Truck Routing Problem for Delay Minimization Using Simulated Annealing with Normalized Exploration Rate

The growth in containerized shipping has led to the expansion of seaports, resulting in the emergence of multiple terminals. While multi-terminal systems increase port capacity, they also pose significant challenges to container transportation, particularly in inter-terminal movements. Consequently, the transportation delay of containers in inter-terminal operations demands crucial attention, as it can adversely affect the efficiency and service levels of seaports. To minimize the total transportation delays of the inter-terminal truck routing problem (ITTRP), we introduce simulated annealing with normalized acceptance rate (SANE). SANE improves the exploration capability of simulated annealing (SA) by dynamic rescaling of the transportation delay objective to modify the acceptance probability. To validate the quality of solutions provided by SANE, we have developed a mathematical model that provides a set of linear formulations for ITTRP constraints, avoiding the known set-partitioning alternative. Experimental results showed that for small-scale ITTRP instances, SANE achieved a solution close to the optimal. In larger instances with 100–120 orders, SANE found feasible suboptimal solutions within 15–21 seconds, which is unattainable using the exact solver. Further comparison with baselines indicates that SANE provides considerable improvements compared to both SA and Tabu search in terms of the objective value.

On the softplus penalty for large-scale convex optimization

We study a penalty reformulation of constrained convex optimization based on the softplus penalty function. For strongly convex objectives, we develop upper bounds on the objective value gap and the violation of constraints for the solutions to the penalty reformulations by analyzing the solution path of the reformulation with respect to the smoothness parameter. We use these upper bounds to analyze the complexity of applying gradient methods, which are advantageous when the number of constraints is large, to the reformulation.

Estimating the rejection risk of Indonesian shrimp exports from Salmonella spp. contamination using the food safety objective approach

Contamination by non-typhoidal Salmonella spp. in aquacultured shrimp poses a risk for human health. In Indonesia, the presence of the pathogen in shrimp raises a major concern for international trade because shrimp is one of the important exported fishery commodities. The aim of this study was to use food safety objective approach in combination with a quantitative microbiological risk assessment to determine the contamination of Salmonella spp. in raw materials, to estimate the risk of export rejection and to identify the contributing factors of export rejections. The prevalence and concentration of Salmonella spp. in shrimp based on real-time polymerase chain reaction of 7.02% and 0.72–1.46 log CFU/gr (mean: 1.00 ± 0.28 log CFU/g), respectively, were used to develop an exposure model. The exposure model was used to estimate the level of Salmonella spp. in frozen shrimp at the border of an export destination country, which was ca. −6.02 to −2.07 (mean −3.73 ± 0.73) log CFU/g. The value was compared to the food safety objective value determined from the required microbiological criterion of Salmonella spp. of n = 30, c = 0, and m = negative/25 g. As a result, the risk estimate for rejection was 27 rejections per 100,000 exports. The Salmonella spp. contamination level in raw materials and freezing technology were the primary factors contributing to the rejections. Moreover, maintaining the quality control of raw materials purchased or controlled quick freezing may be the mitigation formulae of export rejection of frozen shrimp due to Salmonella spp.