Single-objective Model Research Articles

Modeling and Optimization Algorithm for Rotational Irrigation Group Based on Connectivity Weighted Index

Abstract Manual calculations for rotational irrigation groups are inefficient, and a single objective cannot provide farmers with diverse options. Based on considering both engineering standards and practical needs, this study designs a connectivity index and proposes a new model with the optimization objectives of balanced flow and minimum connectivity. To address infeasible solutions and constraint issues, A hybrid genetic algorithm based on variable neighborhoods is adopted to enhance the search capability of the classical non-dominated sorting genetic algorithm. The effectiveness and universality of the model and algorithm are verified through multiple real-world cases. The research shows that the proposed multi-objective model is more practical than a single-objective model, and farmers can be provided with diverse Pareto solutions by adjusting the weight index ω. The variable neighborhood search algorithm enhances the search capability within the radius threshold, improves population diversity, and analyzes the radius threshold and branch pipe flow parameters to explore factors that affect algorithm performance and indicators.

Reliability design involving optimization with multiple objectives by means of probabilistic multi-objective optimization

Although there have been many achievements on single—objective models, the reliability research involving multi-objective optimization problems has not obtained satisfactory research results. In this paper, the reliability design involving optimization with multiple objectives is developed by means of probabilistic multi-objective optimization (PMOO), which considers the simultaneity of optimization of multiple objectives and treats both beneficial type of utility indexes and unbeneficial type of utility indexes of performance indicators equivalently and conformably. Three cases of reliability design concerning multi—objective optimization, i.e., reliability requirement as the additional constraint condition, reliability assessment as an additional optimized objective, and the mixture of these two cases, are formulated by means of PMOO, respectively. Furthermore, a typical example is given to show the procedure of the approach for reliability assessment involving multiple objectives by means of PMOO, which exhibits the validity of the present approach. The approach is objective without any subjective factors.

An integrated blood supply chain network design during a pandemic

The emergency supply of blood in the wake of pandemic has proved challenging. We develop in this paper a bi-objective blood supply chain (BSC) model that uses two-stage stochastic optimisation to optimise the expected cost of the supply chain and the average blood delivery time when a pandemic occurs. The model considers not only vertically and horizontally integrated mechanisms of the BSC network, but also several specific assumptions about the pandemic, such as the risk of disruption in donor groups, and the restriction of ‘no cross blood donation’. To alleviate blood shortages in the context of a pandemic, we further extended our model, which allows for blood type substitution according to ABO/Rh(d)-compatibility. To efficiently solve the model and generate the Pareto front, we develop a hybrid solution algorithm to solve the proposed model, including the ε-constraint method to transform the bi-objective model into a single-objective model, the subgradient method for finding a lower bound, and two heuristic methods for finding an upper bound. Moreover, we perform extensive numerical studies to assess the performance of the proposed approach. We also discuss the impacts of the key parameters, integration mechanisms, and planning blood type substitution on the BSC. Finally, we also apply the proposed model to a real case study of the BSC in Chongqing, China.

A fuzzy multi-objective model for aggregate production planning considering energy consumption, carbon emission, chemical, solid waste, and wastewater

With a growing focus on environmental conservation, enterprises continuously reevaluate their conventional profit-driven business models. This shift has led to the development of green production planning models, attracting considerable attention in recent years. Previously, energy consumption or carbon emission were the most considered green parameters in the production planning problems. Nevertheless, several other essential green aspects such as reductions in chemical, solid waste, and wastewater are usually neglected. Therefore, this study proposes a multi-objective model for environmentally conscious aggregate production planning, simultaneously considering the above-mentioned green objectives. Additionally, the uncertain parameters of the model, including the green parameters, were modelled through fuzzy programming. Furthermore, this study incorporated a contradicting relationship between energy consumption cost and associated carbon emission, which was previously presented as non-contradicting. This relationship was illustrated by utilizing the time-of-use electricity tariff scheme. To solve the model, the initial step involved the defuzzification of uncertain attributes, followed by the transformation of the multi-objective model into a single-objective model. Finally, the IBM ILOG CPLEX Optimization Studio solver was utilized to solve the model based on the data collected from a precision engineering company. The generated production plan achieved an overall satisfaction level of 71%, which is reasonably acceptable to the decision maker. Moreover, sensitivity analysis has been conducted for the degree of optimism of the objective functions and the feasibility degree of the constraints. A general overview of the results associated with the performed sensitivity analysis indicated that the optimum values of the objective functions deteriorate as the parameters increase, though all remain within an acceptable range. The proposed study will assist decision makers in generating production plans that are both economically and environmentally feasible.

Optimizing sustainable development in arid river basins: A multi-objective approach to balancing water, energy, economy, carbon and ecology nexus

The ongoing water crisis poses significant threats to the socioeconomic sustainability and ecological security of arid and semi-arid river basins. Achieving Sustainable Development Goals (SDGs) within a complex socio-ecological nexus requires effective and balanced resource management. However, due to the intricate interactions between human societies and environmental systems, the tradeoffs and synergies of different SDGs remain unclear, posing a substantial challenge for collaborative management of natural resources. Here we introduce a gray fractional multi-objective optimization (GFMOP) model to balance multi-dimensional SDGs through a novel water–energy–economy–carbon–ecology nexus perspective. The model was applied to a typical arid river basin in Northwest China, where thirty-two scenarios were explored, considering factors such as shared socioeconomic pathways, carbon removal rates, water conveyance efficiencies, and ecological requirements. The results reveal a strong tradeoff between marginal benefit and carbon emission intensity, indicating that improving the economic efficiency of water use can simultaneously reduce emissions and protect the environment. Given the immense power generation potential, wind power development should be prioritized in the future, with its share in the energy structure projected to increase to 23.3% by 2060. Furthermore, promoting carbon capture technologies and expanding grassland coverage are recommended to achieve regional carbon neutrality, contributing 39.5% and 49.1% to carbon absorption during 2021–2060, respectively. Compared with traditional single-objective models, GFMOP demonstrates a superiority in uncovering interrelationships among multiple SDGs and identifying compromised alternatives within the compound socio-ecological nexus. The model also provides detailed strategies for resource allocation and pollutant control, offering valuable guidance to policymakers and stakeholders in pursuing sustainable and harmonious watershed management.

An uncertain bi-objective mean-entropy model for portfolio selection with realistic factors

In the imprecise investment environment, there are many indeterminate factors impacting security returns. This paper introduces a portfolio optimization problem where cross-entropy is utilized to control portfolio risk within the framework of uncertainty theory and presents an uncertain bi-objective mean-entropy portfolio selection model. To be more realistic, some realistic factors such as minimum transaction lots, dividend factors and tax factors are also considered. By introducing a risk preference coefficient, the bi-objective model is converted into a single-objective model and some equivalents are discussed. Additionally, a hybrid intelligent algorithm integrating a genetic algorithm with uncertain estimation is designed to solve the proposed model. Finally, a case study is executed to confirm the practicability of the model and the performance of the algorithm, and an empirical analysis based on the proposed model and the uncertain mean–variance model is developed to illustrate the advantage of the uncertain mean-entropy model in practical investment.

Optimization of Multibeam Survey Measurement Based on Greedy Algorithm

The effectiveness of multibeam bathymetric technology is widely recognized in marine depth measurements, especially in areas with complex and variable seafloor topography. This study aims to design a multibeam bathymetric survey plan for a specific maritime region, with the objectives of minimizing the total survey line length, ensuring comprehensive coverage of the target area, controlling the overlap between adjacent survey lines, and fully considering variations in seafloor topography. An optimization model was developed to determine the optimal route for comprehensive seafloor depth measurements within the specified maritime area.The model initially considers the influence of seafloor slope, establishing a single optimization objective model with the goal of minimizing the total survey line length. The decision variables primarily include the spacing between adjacent survey lines. The objective function of the model aims to reduce the number of survey lines, thereby achieving the minimization of the total survey line length. Constraints of the model encompass limitations on coverage range, calculations of coverage width, and relationships between survey lines. The model is solved using a greedy algorithm-based optimization approach, iteratively updating the positions of survey lines while determining the spacing based on the relationship between depth and coverage width. Ultimately, a layout of survey lines with the shortest total length, totaling 64 nautical miles with a configuration of 32 survey lines, is obtained for the assumed maritime area. Multibeam bathymetric technology holds broad prospects in the field of marine measurements, particularly in areas characterized by complex and variable seafloor topography. This study, by designing a multibeam bathymetric survey plan for a specific maritime region, not only contributes to improving measurement efficiency and accuracy but also reduces measurement costs and resource consumption. The outcomes of this research have significant practical implications for marine resource development, seafloor engineering construction, environmental protection, providing professionals in related fields with an effective measurement method and optimization strategy.

Portfolio optimization with mental accounts under uncertain random environment and butterfly optimization algorithm with adaptive strategies

In complex security markets, uncertainty and randomness may coexist. The investors hold different risk attitudes toward different investment objectives in reality. In order to reflect this phenomenon, this paper applies mental accounts to portfolio optimization in an uncertain random environment. Firstly, considering the influence of transaction costs and diversification degree, this paper establishes an uncertain random mean-absolute semi-deviation-entropy bi-objective optimization model. Then the bi-objective model is converted to two single-objective models through three steps. Secondly, the equivalent forms of the models are deduced when the return rates of random risky securities are assumed to be normal random variables and the return rates of uncertain risky securities are assumed to be linear and zigzag uncertain variables. Furthermore, we propose an improved butterfly optimization algorithm (IBOA) to solve the two single-objective models. Finally, numerical simulations are presented to analyze the practicability and effectiveness of the models with different mental accounts and the IBOA algorithm. The results indicate that the IBOA algorithm is effective and putting money into more mental accounts may gain higher returns.

Joint finance-based scheduling in construction: Internal interest rate approach

Joint finance-based scheduling in construction: Internal interest rate approach

Joint determination of nurse and patient bed positions in an inpatient unit considering equity in visibility

Layout design is considered a crucial aspect of healthcare architecture and its goal is to allow easy access to essential hospital services and effective patient care. Literature suggests that modifying or redesigning the inpatient unit layout is one of the ways to maximize patient visibility in an inpatient layout. However, prior work has been descriptive in nature and limited in their ability to derive optimal layouts. To fill this gap, we propose a non-linear optimization model that optimizes both equity and effectiveness in visibility by jointly determining the optimal location of two nurses and patient bed positions in multiple rooms. The bi-objective model is then converted into a single objective model utilizing the ε-constrained method, with equity in the objective function and effectiveness as a constraint. Patient visibility is estimated using a ray-casting algorithm that also considers nurses’ line of sight, door positions, and obstruction levels. A progressive refinement algorithm embedded in the Particle Swarm Optimization framework is proposed to efficiently solve this model. Our results suggest that optimizing bed position in conjunction with nurse position can enhance equity by over 45.2% compared to just optimizing the nurse position. Similarly, angular layouts are superior to linear layout by up to 53% in patient equity. We also notice that increasing spatial distance between nurses in angular layouts can further increase equity. Our approach provides valuable insights and can serve as a benchmark tool for hospitals looking to improve the design of their inpatient units that promote patient safety and high-quality care.

Minimizing the environmental impacts of waste valorization systems using multi-criteria life cycle optimization

Unsustainable waste management practices impose severe environmental hazards, health risks, and financial burdens. Waste valorization systems have emerged to mitigate the negative impacts of landfilling while recovering finite materials and renewable energy. This study aims to develop a life cycle assessment (LCA)-based multi-criteria framework using linear programming to optimize municipal waste allocation to multiple valorization facilities. The developed optimization model minimizes the life cycle impacts of integrated waste management on several life cycle impact categories. A multi-criteria decision-making analysis is implemented to account for the relative importance of the examined environmental categories, and a sensitivity analysis is conducted to study the effect of varying the importance weights. The variation between different LCA methods, IMPACT, CML, and ReCiPe, is also investigated. The proposed framework is applied to Egypt based on local conditions and strategic priorities. The LCA findings reveal that processing recyclables in material recovery facilities enhances the environmental performance in all impact categories except ozone layer depletion. To achieve minimum environmental effects on the assessed impact categories, single objective models suggest the diversion of recyclables to material recovery facilities and non-recyclables to gasifiers. The Pareto front of IMPACT involves anaerobic digesters and incinerators, CML comprises composting facilities, and ReCiPe includes incinerators. Overall, this study provides a lifecycle-based decision-making guide for the planning and optimization of sustainable waste management systems, and highlights the potential variations in the outcomes of different LCA methods adopted.

Energy-based availability warranty policy with considering preventive maintenance and learning-forgetting effect

Ensuring reliable operation and maximum the output is crucial for energy production systems. Traditional time-based availability (TBA) warranty policies often overlook some factors, such as energy loss and the experience gained during the maintenance activities. In this paper, an innovative warranty policy which focuses on the energy-based availability (EBA) is proposed, where imperfect preventive maintenance (IPM) and minimal repair (MR) are taken into account, and hybrid hazard rate model is adopted to describe the effect of preventive maintenance. In addition, the learning-forgetting effect during the maintenance is considered. On this basis, six types of single-objective and multi-objective models are established, and they are solved by genetic algorithm (GA) and non-dominated sorting genetic algorithm-II (NSGA-II), respectively. To illustrate the effectiveness of the proposed warranty policy, a numerical case of wind turbine gearbox is conducted. The results show that the proposed EBA warranty policy can gain around 0.29% energy more than TBA policy. Compared to single-objective models, multi-objective models can provide more selectable maintenance options. Additionally, sensitivity analysis indicates that by considering the learning-forgetting effect, the gearbox can achieve higher EBA and lower warranty cost.

Designing a two-dimensional maintenance policy for products sold under a two-dimensional warranty by considering both warranty servicing cost and lost opportunity

ABSTRACT Based on the manufacturer-consumer context, a two-dimensional preventive maintenance policy is developed for sold products under a two-dimensional warranty by pursuing two objectives: (1) minimization of the imposed warranty servicing cost on the manufacturer and (2) minimization of lost opportunity cost resulting from the product downtime. In addition, in order to adapt the model to real applications, we depart from the literature by taking into consideration the continuous nature of the usage rate variable. To illustrate the advantages of the model, three types of couple-based comparative models are made. Type I consists of two models with a one-dimensional preventive maintenance policy, while type II includes a model with no maintenance activity. Finally, type III involves two single-objective models. The results obtained from the comparison of the suggested model with the type I and II models confirm the significant effect of employing a two-dimensional preventive maintenance policy in improving both manufacturers’ and customers’ satisfaction. In addition, comparisons of the suggested bi-objective model with three types of models indicate the importance of taking into account both the warranty servicing cost and loss opportunity.

An effective strategy for unit commitment of microgrid power systems integrated with renewable energy sources including effects of battery degradation and uncertainties.

The large use of renewable sources and plug-in electric vehicles (PEVs) would play a critical part in achieving a low-carbon energy source and reducing greenhouse gas emissions, which are the primary cause of global warming. On the other hand, predicting the instability and intermittent nature of wind and solar power output poses significant challenges. To reduce the unpredictable and random nature of renewable microgrids (MGs) and additional unreliable energy sources, a battery energy storage system (BESS) is connected to an MG system. The uncoordinated charging of PEVs offers further hurdles to the unit commitment (UC) required in contemporary MG management. The UC problem is an exceptionally difficult optimization problem due to the mixed-integer structure, large scale, and nonlinearity. It is further complicated by the multiple uncertainties associated with renewable sources, PEV charging and discharging, and electricity market pricing, in addition to the BESS degradation factor. Therefore, in this study, a new variant of mixed-integer particle swarm optimizer is introduced as a reliable optimization framework to handle the UC problem. This study considerssix various case studies of UC problems, including uncertainties and battery degradation to validate the reliability and robustness of the proposed algorithm. Out of which, two case studies defined as a multiobjective problem, and it has been transformed into a single-objective model using different weight factors. The simulation findings demonstrate that the proposed approach and improved methodology for the UC problem are effectivethan itspeers. Based on the average results, the economic consequences of numerous scenarios are thoroughly examined and contrasted, and some significant conclusions are presented.

An integrated water resources management model considering carbon source and sink under uncertainty: A case study of agricultural water-dominated basin

The global drive for carbon neutrality promotion through integrated water resource management (IWRM) in the face of burgeoning water demand is of great importance. This study developed an interval fuzzy-credibility chance-constrained multi-objective programming (IFCMP) model for water resources-carbon system (WCS) planning, which not only accounts for multiple uncertainties within system parameters, such as interval, fuzzy, and stochastic, but also effectively balances the conflicting objectives of water scarcity, benefits, emissions, and carbon sinks. The IFCMP-WCS model was applied to an agricultural water-dominated zone in the Tarim River Basin, China. Multiple water-allocation scenarios were examined, encompassing five prefecture-level cities, five departments, and three planning years. The results indicated that: (1) the water deficit was increasing over time, limited by water supply capacity, reaching 0–3.49 × 109 m3 in 2035; (2) as water allocation rises, system benefits and pollutant emissions increase, with the agricultural sector contributing the most economic benefits and pollutant emission; (3) the Tarim River Basin is an important carbon sink area, with the net carbon sink increasing from 8781.7–10,771.1 × 103 to 8851.1–10,937.9 × 103 tonnes during the planning horizon; (4) compared to single-objective models, the IFCMP-WCS model can offer more applicable water resource management options. These findings provide useful information for decision-making regarding IWRM and enhancing the net carbon sink in the Tarim River Basin.

Resilience-economy-environment equilibrium based configuration interaction approach towards distributed energy system in energy intensive industry parks

Because unexpected, high-impact, extreme events and disasters can seriously threaten power system safety and resilience, there has been an increased research focus on power system resilience. This study proposes a bi-level multi-objective model for industrial park distributed energy configuration optimization to deal with extreme events, which considers the interactions between the authority and the industrial park in a leader–follower decision process and seeks to trade-off between economic cost, environmental protection, and power system resilience. An interactive algorithm is designed and the ɛ-constraint method is used to convert the model into a bi-level single objective model to solve the proposed complex model. A case example from an industrial park in Wuxi, Jiangsu Province, China, is given to demonstrate the practicality and efficiency of the proposed optimization method. The joint analysis of the power supply and financial losses found that a distributed energy system with an optimal resilience configuration could guarantee 95.85% of demand for three consecutive hours after an extreme event, maintain more than 50% of demand at any time, and reduce power outage financial losses at any time to a minimum of 0.232 million CNY. Based on the analyses and discussion, this model was proven to provide a reasonable and practical strategy for a resilience-economy-environment trade-off in industrial park distributed energy systems.

A bi-objective optimization approach for carbon capture and storage supply chain network combining with pricing policies: Economic and social aspects

Carbon capture and storage (CCS) technology and pricing policies are two mitigation strategies that attempt to tackle the carbon emission problem. Nonetheless, the uncertainty of public reaction to CCS infrastructure installation has been noted as a significant issue that may lead to either cancelations, delays, or influence the deployment cost of CCS infrastructure. Although these strategies are solutions to reduce carbon emissions, the entire supply chain itself needs to align with sustainability policy. While some previous studies have addressed mitigation strategies or the combination of social objective and CCS technology, the impact of social objectives on reservoir openness has not been explored. This article contributes to the literature by illustrating the effect of social objectives on reservoir openness and the total cost of the CCS supply chain. Through the development of a two-stage mixed-integer linear programming model, we optimize the supply chain network design. In the first stage, a single-objective model minimizes capture, transportation, and sequestration costs along with CO2 emission costs to the atmosphere, considering various carbon tax prices. In the second stage, a bi-objective model maximizes social acceptance towards CO2 injection wells (reservoirs) to analyze the impact of cultural dimensions. Our findings reveal that maximizing the social objective leads to increased costs compared to the economic optimum, and it significantly influences the openness of reservoirs based on cultural dimensions. Furthermore, we demonstrate that an increase in the CO2 tax enhances the amount of captured carbon and the complexity of the pipeline network in the supply chain. This insight has implications for governments and decision-makers who can encourage industries to adopt CCS technology by setting appropriate carbon tax prices. To validate the model, we apply it to a case study in the European Union cement industry, one of the major carbon emitters among all industries. Our results not only confirm the model's effectiveness but also show its potential for practical application. Overall, our study presents a comprehensive framework for designing a two-stage sustainable supply chain network for CCS technology that optimizes economic and social objectives while considering CO2 pricing.

Multi-objective optimisation for energy saving and high efficiency production oriented multidirectional turning based on improved fireworks algorithm considering energy, efficiency and quality

To promote energy saving, high efficiency and quality production in mechanical manufacturing industry, a large number of studies have been conducted on parameters optimisation, especially for turning. However, most of the approaches have focused on single objective model and unidirectional turning (UDT). This paper presents a multi-objective parameter optimisation method for energy consumption, cutting time and surface roughness using new process of forward-and-reverse multidirectional turning (MDT). Firstly, the composition characteristics of cutting parameters for energy consumption, cutting time and surface roughness of MDT are analyzed to establish the corresponding models through nonlinear regression fitting, respectively. Then taking the minimum energy consumption, cutting time and surface roughness as the optimisation objectives, the improved fireworks algorithm can generate nearly 100 groups of optimal solutions. The most suitable processing parameters solution needs to be selected according to different machining requirements. In application scenarios, most relative errors of the models are within 10%. Comparing the machining performance of MDT and UDT under the same cutting parameters, the processing efficiency is increased by 25.97% and energy consumption is reduced by 12.38%, using the MDT. This study provides a multi-objective optimisation approach and models for MDT to reduce energy consumption, improve production efficiency and quality.

Designing an efficient humanitarian supply chain network during an emergency: A scenario-based multi-objective model

Efficient humanitarian supply chain (HSC) management plays an underlying role in saving lives, reducing human torment, and contributing to sustainable development during a disaster. Accordingly, the issue of locating and allocating relief facilities in the first hours after the occurrence of a disaster has a great impact on providing timely service. This study addresses a sustainable location-allocation-inventory problem (LAIP) to design an efficient HSC through concurrently optimizing four objectives of fairness, timeliness, economic productivity, and social justice. To do so, a novel scenario-based multi-objective mixed-integer linear programming (MILP) model is developed to formulate the problem under uncertainty. According to this model, the process of taking care of injured people is carried out in three stages of decision-making. Maximum facilities for sending relief supplies are used to supply the demand at each stage. In addition, the three factors of supply, demand, and communication routes between the centers and the affected areas are defined as fuzzy random parameters. Since the proposed model contains multiple objectives, goal programming (GP) is applied to provide a single-objective model. The validation of the developed methodology is made with the help of an illustrative example in the literature, and the results are obtained and evaluated using sensitivity analysis of the objective functions’ weights. As one of the main findings, sending the maximum available supplies in MDCs to the affected areas in three stages using surplus vehicles is the best solution to cover the shortage of products. Finally, it is revealed that the proposed methodology can be utilized by managers to tackle the complexity of the problem during natural disasters.

A multi-objective closed-loop supply chain under uncertainty: An efficient Lagrangian relaxation reformulation using a neighborhood-based algorithm

Population growth and unprecedented industrialization have contributed to a significant surge in global waste generation, underscoring the need for efficient waste management practices such as recycling, disassembling, restoration, and disposal. Closed-loop supply chain (CLSC) networks offer a solution for effective waste management by enabling the recycling, reassembly, and reuse of waste products. However, designing an optimal CLSC network presents challenges due to uncertainties associated with various parameters, including customer demand, sustainable development goals, and the complexity of network design optimization. This paper addresses these challenges by proposing a comprehensive CLSC network that optimizes environmental, economic, and social footprints through a multi-objective optimization approach. To account for parameter uncertainties, we employ scenario generation using a scenario-based stochastic programming procedure. To solve the proposed model, we transform the multi-objective formulation into a single-objective model using a weighted sum method considering a set of problem-specific heuristics. Furthermore, we leverage Lagrangian relaxation theory to formulate various problem reformulations, aimed at attaining an optimal lower bound for the CLSC problem. We complement this with a neighborhood-based algorithm that helps identify a feasible upper bound. By utilizing a sub-gradient framework, we iteratively reoptimize both the selected reformulation and the neighborhood-based algorithm, culminating in the achievement of an optimal solution. To exemplify the practical applicability of our research, we present a case study focusing on the light engineering industry in Bangladesh. Through rigorous analyses, we showcase that our proposed algorithm can deliver an optimal solution with an optimality gap of 0.06. By offering insights into the successful implementation of our CLSC network in a real-world context, we aim to provide valuable guidance for practitioners seeking to establish efficient and sustainable waste management systems.