Optimization Model Research Articles

Decision support for allocating farmed fish to customer orders using a bi-objective optimization model

Aquaculture is an important industry in certain coastal areas. Focusing on farming of salmon and trout, an operational planning problem arises with the goal of allocating supply of fish to demand expressed through customer orders. This paper provides a conceptual model of such a planning problem, defines a corresponding bi-objective mathematical programming model. The problem is novel with respect to the structure of the transportation of fish, and the rules for satisfying customer orders with respect to fish size, quality, certification, and health status. Computational experiments are conducted to gain further insights into the use of the provided model to provide support for planners involved in the operational decision making. Results indicate that the bi-objective optimization model can be useful in situations where supply is insufficient to cover all the demand within a given planning horizon.

3D Poissonian image deblurring via patch-based tensor logarithmic Schatten-p minimization

In medical and biological image processing, multi-dimensional images are often corrupted by blur and Poisson noise. In this paper, we first propose a new tensor logarithmic Schatten-p (t-log-Sp ) low-rank measure and a tensor iteratively reweighted Schatten-p minimization algorithm for minimizing such measure. Furthermore, we adopt this low-rank measure to regularize the non-local tensors formed by similar 3D image patches and develop a patch-based non-local low-rank model. The data fidelity term of the model characterizes the Poisson noise distribution and blur operator. The optimization model is further solved by an alternating minimization technique combined with variable splitting. Experimental results tested on 3D fluorescence microscope images show that the proposed patch-based tensor logarithmic Schatten-p minimization method outperforms state-of-the-art methods in terms of image evaluation metrics and visual quality.

An LSTM-based prediction model for gradient-descending optimization in virtual learning environments

A virtual learning environment (VLE) is an online learning platform that allows many students, even millions, to study according to their interests without being limited by space and time. Online learning environments have many benefits, but they also have some drawbacks, such as high dropout rates, low engagement, and students' self-regulated behavior. Evaluating and analyzing the students' data generated from online learning platforms can help instructors to understand and monitor students learning progress. In this study, we suggest a predictive model for assessing student success in online learning. We investigate the effect of hyperparameters on the prediction of student learning outcomes in VLEs by the long short-term memory (LSTM) model. A hyperparameter is a parameter that has an impact on prediction results. Two optimization algorithms, adaptive moment estimation (Adam) and Nesterov-accelerated adaptive moment estimation (Nadam), were used to modify the LSTM model's hyperparameters. Based on the findings of research done on the optimization of the LSTM model using the Adam and Nadam algorithm. The average accuracy of the LSTM model using Nadam optimization is 89%, with a maximum accuracy of 93%. The LSTM model with Nadam optimisation performs better than the model with Adam optimisation when predicting students in online learning.

Solving the waste bin location problem with uncertain waste generation rate: A bi-objective robust optimization approach.

An efficient municipal solid waste (MSW) system is critical to modern cities in order to enhance sustainability and liveability of urban life. With this aim, the planning phase of the MSW system should be carefully addressed by decision makers. However, planning success is dependent on many sources of uncertainty that can affect key parameters of the system, for example, the waste generation rate in an urban area. With this in mind, this article contributes with a robust optimization model to design the network of collection points (i.e. location and storage capacity), which are the first points of contact with the MSW system. A central feature of the model is a bi-objective function that aims at simultaneously minimizing the network costs of collection points and the required collection frequency to gather the accumulated waste (as a proxy of the collection cost). The value of the model is demonstrated by comparing its solutions with those obtained from its deterministic counterpart over a set of realistic instances considering different scenarios defined by different waste generation rates. The results show that the robust model finds competitive solutions in almost all cases investigated. An additional benefit of the model is that it allows the user to explore trade-offs between the two objectives.

Multi-market P2P trading of cooling–heating-power-hydrogen integrated energy systems: An equilibrium-heuristic online prediction optimization approach

In this paper, an equilibrium-heuristic online prediction optimization approach is proposed for multi-market peer-to-peer (P2P) electricity–hydrogen trading of integrated energy systems (IESs) with uncertainties. First, the IES, consisting of a hydrogen energy storage subsystem and a combined cooling, heating, and power subsystem, is constructed in the distribution network to improve energy utilization and market efficiency. Then, a bi-level optimization model for IESs, participating in the P2P electricity–hydrogen energy trading, the real-time electricity, and the ancillary service markets, is proposed, in which the top-level model can be formulated as a P2P electricity–hydrogen trading pricing model through the social welfare maximization problem, and the lower-level model is used to maximize the IES operating profit. To effectively solve the bi-level model, the game equilibrium-based ADMM distributed algorithm is used to obtain the P2P trading volume and prices of the top-level model, and a new hybrid heuristic algorithm, called hybrid sand cat swarm optimization and improved honey badger algorithm (SCIHB), is proposed to solve the lower level model. SCIHB utilizes a hybrid mechanism and an adaptive learning rate parameter to balance local exploitation and global exploration. Furthermore, a new online learning probabilistic prediction method based on the hidden Markov model and wavelet transform is introduced to describe the uncertainties of wind power, electricity prices, and frequency regulation prices. Finally, case studies are conducted on an IEEE 33-bus test system, and the numerical results verify the effectiveness of the proposed P2P trading model and solution approach.

Optimal hybrid layout of point and open‐path gas detectors in process facilities of natural gas stations

AbstractBecause open‐path gas detectors offer superior technical performance, leakage monitoring systems tend to use a hybrid layout of point and open‐path gas detectors. However, most research on the optimized layout of leakage monitoring has focused only on point gas detectors. In this paper, an optimization model for a hybrid layout of point and open‐path gas detectors was proposed considering the cost–benefit ratio and detection time. As the measured value of an open‐path gas detector is an integral concentration, a monitor line in the simulation was calculated via the approximate rectangle method. The results showed that the use of a multiobjective gas detector layout considering the cost–benefit ratio and an improved non‐dominated sorting genetic algorithm (NSGA‐II) could optimize the layout of hybrid detectors. The hybrid layout was analyzed in a case study of process facilities at a natural gas station. As the number of detectors increased (safety investment), the proportion of open‐path gas detectors increased, improving both leakage monitoring performance and the cost–benefit ratio. Additionally, the layout of the point gas detectors was analyzed. A comparison of objective function values for detection time showed the superiority of the hybrid layout in our research.

Balancing the cardinality of clusters with a distance constraint: a fast algorithm

AbstractLogistics companies partition the customers they serve into delivery zones as a tactical decision and manage the customers assigned to each zone as a cluster for the purpose of routing, workload allocation, etc. Frequently, this partition is made in accordance with customers’ geographical location, which can result in very unbalanced clusters in terms of the number of customers they include. In addition, in the day-to-day operations, not necessarily all customers need to be served every day so, even if the clusters originally created are balanced, daily needs may lead to unbalanced clusters. Given an a priori assignment of customers to clusters, improving the balance between clusters in advance of workload management is therefore a key issue. This paper addresses the problem of balancing clusters, when there is a distance constraint that prevents reassigning customers to clusters far away from their original pre-assignment. This problem is formulated as a lexicographic biobjective optimization model. The highest priority objective function minimizes the variance of the number of customers in the clusters. The second ranked objective function minimizes the total distance resulting from all reassignments. A fast and effective heuristic algorithm is developed, based on exploring customer reassignments, either by comparing clusters two by two or by extending the search to allow for sequential customer swaps among clusters. Both the quality of the solution and the computational time required encourage the use of this algorithm by logistics companies to balance clusters in real scenarios.

Conventional or organic cattle farming? Trade-offs between crop yield, livestock capacity, organic premiums, and government payments

CONTEXTAn important question for farmers is whether to run their farm conventionally or organically. This choice can significantly affect the farm's financial performance and its impact on the environment. OBJECTIVEThe primary objective of this study is to compare the profitability of conventional and organic cattle systems and investigate how it is associated with individual farm characteristics, like forage production capacity, forage quality, milk quota, animal housing capacity, and their relative presences. METHODWe employ a whole farm optimization model, customized for Norwegian cattle farming. The primary goal of this model is to maximize the gross margin by optimizing decisions related to land usage and animal inventory while adhering to a set of constraints. We systematically solve more than 200,000 model instances, with varying farm characteristics. RESULTS AND CONCLUSIONSThe results can be distilled to the following key points: If forage of good quality is readily available, but the livestock operation cannot be expanded due to animal housing and milk quota restrictions, organic may outcompete conventional farming. Otherwise, gross margin is maximized with conventional farming. These findings emphasize the crucial role of forage production capacity and quality in relation to available milk quota and infrastructure when considering the transition from conventional to organic farming. Extensive sensitivity analyses affirm the robustness of these conclusions. Regional regulatory factors, such as government farm payments, also play a significant role, and influence the optimal farming approach. Additionally, we show that increases in organic price premiums can markedly impact the competitiveness of organic farming, even in a system where government payments make out a significant part of the farm revenue. SIGNIFICANCEThe model can support farmers to make informed decisions about converting to organic or conventional farming. It can also be used by policymakers to determine the level of support required to make it worthwhile for different types of farms to convert. We also show that existing government payment schemes give rise to regional differences in the incentives for organic farming in Norway. To ensure equal incentives for organic farming across the country, the organic payments would have to be regionally adjusted, in line with the other already regionally dependent government payments. This insight may be of significant interest to policymakers and other stakeholders.

Constraint‐aware optimization model for plane truss structures via single‐agent gradient descent

AbstractThis study introduces the constraint‐aware optimization model (CAOM), a novel optimization framework designed to optimize the size, shape, and topology of plane truss structures simultaneously. Unlike traditional optimization models, which rely on gradient descent and frequently struggle with managing various constraints due to their dependence on a single optimization agent, CAOM effectively addresses this challenge. It does so by incorporating a variety of assistant modules along with the Adam optimizer, a variant of the gradient descent method. Uniquely, CAOM employs the leaky rectified linear unit (ReLU) activation function beyond its conventional use in neural networks, applying it as a mechanism to integrate constraints and losses seamlessly. The model's effectiveness was validated through two numerical examples and a practical application, demonstrating that CAOM can reduce structural weight by up to 84% compared to unoptimized designs while fully adhering to structural, dimensional, and moveable constraints. Furthermore, the study found that while shape optimization plays a key role for stiffness‐governed structures, size optimization is crucial for strength‐governed structures. Optimizing size, shape, and topology together consistently leads to the most weight‐efficient designs. This emphasizes the significance of a holistic approach in the optimization processes.

A physical simulation-machine learning model for optimal process schemes in laser-based directed energy deposition process

The major challenge faced is the definition of optimal process variables for rich quality of fabricated parts in laser-based directed energy deposition (DED-LB) processes. However, predicting the optimal process scheme using machine learning models is still challenging owing to the need for a large amount of training experimental data with high costs in DED-LB. In view of this, a physical simulation (PS)-machine learning (ML) model using a relatively small accurate data set of 31 simulation data for optimal process schemes is proposed in DED-LB process in this study. Firstly, a powder-scale high precision phenomenon model incorporating the mass transfer, phase transformations and heat transfer and using Lagrangian particle model to add mass is developed to depict the DED-LB process. Then, a Gaussian process regression (GPR) agent model is established to rapidly and accurately predict the geometry and dilution rate of deposition tracks under different manufacturing parameters based on the high precision simulation results. Finally, a PS-ML model for process parameter optimization is developed using the particle swarm algorithm (PSO), and the optimized parameters are experimentally validated. The results show that the developed powder-scale model and GPR model results are consistent with the Inconel 718 alloy experimental results. The proposed PS-ML model can increase the accuracy of the ML models even with a small simulation data set. None of PS-ML model optimization results has a relative error of more than 3% to the experimental results, and the dilution rate is reduced by up to 61.66% compared to the experimental design parameters without optimization. The proposed physical simulation-machine learning model in this study enables inexpensive and accurate optimization of DED-LB process parameters.

Optimization model of monthly continuous bidding transaction in electricity market considering risk hedging

In order to further alleviate the problems of large assessment deviations, low efficiency of trading organisation and difficulties in system optimisation in medium- and long-term market trading, the article proposes an optimisation model for continuous intra-month bidding trading in the electricity market that takes into account risk hedging. Firstly, the current situation of market players’ participation in medium and long-term trading is analysed; secondly, the impact of contract trading on reducing operational risks is analysed based on the application of hedging theory in the primary and secondary markets; finally, the continuous bidding trading mechanism is designed and its optimisation effect is verified. The proposed model helps to improve the efficiency of contract trading in the secondary market, maintain the stability of market players’ returns and accelerate the formation of a unified, open, competitive and well-governed electricity market system.

Towards carbon neutrality: Transition pathways for the Chinese ethylene industry

Ethylene is one of the most important products in the emissions-intensive petrochemical industry. Decarbonizing the ethylene industry is thus important for achieving global carbon neutrality. This study is the first to explore future long-term zero-emissions production pathways for the ethylene industry in China, the world's biggest ethylene producer. An optimization model was built in the context of China's carbon neutrality target of 2060. Four scenarios were developed where the policy ambitions for climate mitigation and for plastic management including waste were varied. Based on this, authors assessed the cumulative total emissions, technology options, future geographical location of ethylene production, and policy challenges associated with each scenario. This is also the first time that scope 3 emissions from waste incineration are included, motivated by the short lifetime of most ethylene products. Results show the cumulative CO2 emissions for the scenarios differ considerably, ranging from 4.3 to 7.8 Gt, even if carbon neutrality by 2060 is achieved in all scenarios. The results suggest that ambitious plastic focused policies can result in lower costs and less cumulative emissions compared to ambitious climate focused policies. The results demonstrate the importance of adopting CCS for waste incineration. This reduces cumulative CO2 emissions by up to 2 Gt. However, reduced overall demand and increased recycling rates should be priority options due to CCS challenges. Results suggest Chinese ethylene industry should adopt a mixed portfolio of production technologies, where the share of emission-intensive coal-based methanol-to-olefins is limited. These findings on decarbonization pathways can contribute to achieving the Paris agreement.

Optimal predictive selective maintenance for fleets of mission-oriented systems

ABSTRACT In many settings, fleets of assets must perform series of missions with in-between finite breaks. For such fleets, a widely used maintenance strategy is the fleet selective maintenance (FSM). Under resource constraints, the FSM problem selects an optimal subset of feasible maintenance actions to be performed on a subset of components to minimise the maintenance cost while ensuring high system reliability during the upcoming mission. The majority of extant FSMP models are focussed on traditional physics-based reliability models. With recent advances in Machine Learning (ML) and Deep Learning (DL) algorithms, data-driven methods have shown accuracy in predicting remaining useful life (RUL). This paper proposes a predictive FSM strategy for fleets of complex and large multicomponent systems. It relies on a concurrent ML/DL and optimisation approach where a clustering algorithm is used to determine the health states of components and a probabilistic RUL prognostics model is used for component reliability assessment. An optimisation model is developed to solve the predictive FSM problem to ensure high reliability of all systems within the fleet. An efficient two-phase solution approach is developed to solve this complex optimisation problem. Numerical experiments show the validity of the approach and highlight the improved maintenance plans achieved.

Robust optimal power flow considering uncertainty in wind power probability distribution

This paper proposes an optimal power flow model that takes into account the uncertainty in the probability distribution of wind power. The model can schedule controllable generators under any possible distribution of wind power to ensure the safe and economic operation of the system. Firstly, considering the incompleteness of historical wind power data, the paper models the uncertainty of wind power using second-order moments of probability distribution and their fluctuation intervals. Subsequently, a robust optimal power flow model based on probability distribution model and joint chance constraints is established. The Lagrangian duality theorem is then employed to eliminate random variables from the optimization model, transforming the uncertainty model into a deterministic linear matrix inequality problem. Finally, a convex optimization algorithm is used to solve the deterministic problem, and the results are compared with traditional chance-constrained optimal power flow model. The feasibility and effectiveness of the proposed method are validated through case study simulations.

A risk-averse distributionally robust optimisation approach for drone-supported relief facility location problem

Drone-supported last-mile humanitarian logistics applications play a crucial role in the rapid and efficient delivery of essential relief items, such as medicine, blood, and vaccines, during disaster and emergency situations. This paper explores a novel drone-supported relief facility location problem (DSRFLP) aimed at establishing an effective drone-supported last-mile humanitarian logistics system. The problem involves making joint decisions for both pre-disaster and post-disaster phases while considering the characteristics of drone-based delivery operations and uncertain demands. In the pre-disaster phase, we make the decisions regarding the locations of drone-supported relief facilities, inventory prepositioning of relief items, assignment of drones to the opened facilities, and allocation of drones to disaster demand sites. In the post-disaster phase, we make decisions related to delivery quantities. To tackle the challenge of incomplete demand distribution information in chaotic disaster environments, we establish a distributionally robust optimisation (DRO) model to handle the uncertainty of demands. This model adopts worst-case mean Conditional Value-at-Risk as the risk measurement, reflecting the risk-averse attitude of humanitarian organisers. In this paper, three ambiguity sets (box, ellipsoidal, and polyhedral) are considered to describe the ambiguity distributions of demands. To overcome the computational challenge, we reformulate the DRO model under three ambiguity sets into two mixed-integer linear programming models and one second-order cone programming model, which can be efficiently solved by off-the-shelf solvers. Furthermore, we validate our proposed DRO model through a small-scale example and a large-scale case study based on the Lushan earthquake in China. The computational outcomes underscore the superior performance of the proposed DRO model to mitigate the impact arising from incomplete probability distributions. We propose managerial implications and insights to support the decision-making of humanitarian organisations based on the experimental results. Finally, we propose two extended models to incorporate multiple relief items and equity constraints in priority settings and conduct numerical experiments to adapt to various real-world disaster scenarios.

A multi-stage optimization model for managing epidemic outbreaks and hospital bed planning in Intensive Care Units

Intensive Care Unit (ICU) capacity can be significantly affected by disease outbreaks, epidemics, and pandemics, impeding the operational efficiency of healthcare systems and compromising patient care. This paper presents a multi-stage optimization approach to planning the location and distribution of ICU beds to increase accessibility and reduce mortality caused by a shortage of beds in a geographic region during epidemic events. Using a Brazilian state monthly hospital admissions due to Covid-19 from October 2020 to April 2021, we show the amount and the allocation of extra ICU beds that could reduce mortality, minimize patient travel and transportation, and increase accessibility while considering budget limitations. Our findings show coverage for 21 previously underserved municipalities, providing extra ICU beds for 69 municipalities, ranging from 880 to 1670 beds across seven months. On average, patients are displaced 56% less and access ICUs within 17 ± 2.3 kilometres (CI 95%). The strategy contributes to public health planning and the equitable allocation of hospital resources among the population.

Destruction of n-hexane from the air stream by pulsed discharge plasma: Modelling and key process parameters optimization by CCD-RSM

In this study, a Dielectric-Barrier Discharge (DBD) plasma reactor was used for the degradation of n-hexane from an air stream. a Central Composite Design (CCD) based Response Surface Methodology (RSM), (CCD-RSM) was utilized to explore the effects of experimental parameters including discharge voltage, initial concentration, gas flow rate, relative humidity and their interactions on the reactor performance. The proposed optimization model showed a satisfactory correlation between the predicted and actual results. According to the results, discharge voltage was the most significant parameter affecting the removal efficiency, CO2 selectivity and the level of O3 and NOx formation, whereas energy yield was mainly influenced by gas flow rate and initial concentration. At optimized conditions (discharge voltage of 8.5 kV, inlet concentration of 94.3 ppm, relative humidity of 55 % and gas flow rate of 733.16 ml/min with combined desirability of 0.921), removal efficiency of 92.57 %, CO2 selectivity of 58.87 %, energy efficiency of 0.25 g/kWh, O3 formation of 140.88 mg/m3 and NOx formation of 122.46 ppm were obtained. Water vapour significantly increased the removal efficiency and CO2 selectivity as well as reduced O3 and NOx. The results revealed that the CCD-RSM provided the optimum process parameters for the Non-Thermal Plasma (NTP) system.

Scheduling of Container Transportation Vehicles in Surface Coal Mines Based on the GA–GWO Hybrid Algorithm

The coal loading operation of the coal preparation plant of an open pit coal mine causes chaos in coal mine vehicle scheduling due to the unreasonable arrival times of outgoing and container transportation vehicles. To further reduce the length of time that vehicle transportation equipment waits for each other and to reduce the total cost of container transportation, the optimisation model of container transportation vehicle scheduling in an open pit coal mine is constructed to minimise the minimum sum of the shortest time of container reversal and the lowest cost of container transportation. To accurately measure the total cost of container backward transportation, waiting time and unit waiting time cost parameters are introduced, and the total cost of container transportation is measured using the transportation cost and the waiting time cost transformation method. An improved grey wolf algorithm is proposed to speed up the convergence of the algorithm and improve the quality of the solution. When employing the genetic algorithm (GA) and grey wolf optimisation algorithm (GWO) for optimising the scheduling of container transport vehicles in coal mines, it is noted that while the GA can achieve the global optimum, its convergence speed is relatively slow. Conversely, the GWO converges more quickly, but it tends to be trapped in local optima. To accelerate the convergence speed of the algorithm and improve the solution quality, a hybrid GA−GWO algorithm is proposed, which introduces three genetic operations of selection, crossover, and mutation of GA into the GWO algorithm to prevent the algorithm from falling into the local optimum due to the fall; at the same time, it introduces hunting and attacking operations into the elite retention strategy of GA, which improves the stability of the algorithm’s global convergence. Analysis indicates that, compared to SA, GWO, and GA, the hybrid algorithm enhances optimisation speed by 43.1%, 46.2%, and 43.7%, increases optimisation accuracy by 4.12%, 6.1%, and 3.2%, respectively, and reduces the total container reversal time by 35.46, 22, and 31 h. The total cost of container transportation is reduced by 2437 RMB, 3512 RMB, and 1334 RMB, respectively.

Correction: A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

Correction: A scenario-based robust optimization model for the sustainable distributed permutation flow-shop scheduling problem

An Optimization Strategy for Truncating Ultralong Bus Lines Integrated with Metro Networks

For most ultralong bus lines, low punctuality rates and vehicle bunching are two main challenges. One potential strategy to solve these two problems is to split an ultralong line into two or three shorter lines according to historical passenger flow patterns as well as other presetting objectives and constraints. Thus, in this paper, a multiobjective optimization model is first established in consideration of both passenger flow distribution and coline metro networks. Then, the optimal truncated stop is determined by estimating the model results generated by enumerating each potential bus stop derived from related metro stops. The nondominated sorting genetic algorithm II (NSGA-II) is applied to solve the model efficiently. A case study conducted on a real bus line associated with metro networks in Beijing, China, demonstrates the efficiency of the optimization strategy adoption in terms of operating cost and passenger travel time, even with a slight increase in passenger cost. Besides, the multivehicle type is also referred in the experiments to verify economic efficiency to reduce operational costs.