Multi-objective Mathematical Model Research Articles

Self-Adaptive Risk-Based Inspection Planning in Petrochemical industry by evolutionary algorithms

This research proposes a multi-objective mathematical model for Self-Adaptive Risk-Based Inspection Planning (SARBIP). Risk management is essential to organizations to ensure that a proper maintenance strategy is in place. An inspection plan is required to improve the overall safety and achieve optimal configurations for the investment, repair, and maintenance, in order to minimize the total expenses. To this end, a SARBIP model is proposed to obtain optimal solutions. The proposed model serves a dual purpose by reducing both the expenses and risk level. The proposed algorithm, which is used as the model's solution, is validated by being applied to a real case study in the Iranian petrochemical industry. The model is executed through two algorithms, the Non-dominated Sorting Genetic Algorithm II (NSGA-II) and the Multi-Objective Particle Swarm Optimization (MOPSO). The outcomes indicate that MOPSO outperforms other algorithms in large-scale problems.

Designing a Cost-Time-Quality-Efficient Grinding Process Using MODM Methods

In this paper, a multi-objective mathematical model is developed to optimize the grinding parameters Such as grinding time, cost, and related surface quality metrics such as workpiece speed, depth of cut and wheel speed. The mathematical model consists of three conflicting objective functions subject to wheel wear and production rate constraints. Exact methods cannot solve the NLP model in few seconds, therefore using Meta-heuristic algorithms that provide near-optimal solutions is not suitable. Considering this, five multi-objective decision-making (MODM) have been used to solve the multi-objective mathematical model using general algebraic modelling system (GAMS) software to achieve the optimal parameters of the grinding process. The MODM methods provide different effective solutions where the decision-maker (DM) can choose each solution in different situations. Different criteria have been considered to evaluate the performance of the five MODM methods. Also, a technique for order of preference by similarity to ideal solution (TOPSIS) has been used to obtain the priority of each method and determine which MODM method performs better considering all criteria simultaneously. The results indicated that the weighted sum method (WSM) and goal programming method (GP) are the best MODM methods, as both of them provide competitive solutions. In addition, these methods obtained solutions that have minimum grinding time, cost, and surface roughness among other MODM methods.

6σ uncertainty optimisation strategy for USV navigation performance based on reliability analysis

This study presents a Design for Six Sigma (DFSS) optimisation strategy to improve the robustness and reliability of uncertainty parameters, focusing on the problem of navigation performance failure for unmanned surface vehicles (USVs) when uncertainty exists. The three aspects of USV performance are speedability, manoeuvrability, and seakeeping, and its multi-objective mathematical model is accurately constructed through validation. A design of experiment (DOE) technique is conducted to assign the weights using normalised processing. Based on this, a sensitivity analysis is implemented via the optimal Latin hypercube (OLH) method to reveal the correlation relationships between the variables and determine the main factors. A deterministic optimisation design (DOD) is performed using different exploratory optimisation techniques to obtain optimal certainty results. However, the design variables tend to leap across the boundary constraints once they experience a slight interference. Therefore, uncertainty optimisation is conducted to restrict the responses within the constraints. A six sigma (6σ) optimisation based on DFSS is adopted here to improve the reliability of the USV performance parameters. The DFSS results show a high credibility compared to the DOD results, indicating that the proposed 6σ optimisation strategy has a great degree of immunity to uncertainty in actual situations.

Research on Optimal Access Point and Capacity of Multiscenario Wind Turbine Based on Voltage Sag

Aiming at reducing the impact on sensitive loads and the economic losses caused by voltage sags in the distribution network containing wind turbines, a multiobjective mathematical model of the optimal access point and access capacity is established from the three perspectives of the basic costs of wind turbines, the economic losses of voltage sags, and the economic losses of the power grid. A scene generation method based on the similarity of wind curve changes and a scene reduction algorithm based on DPC & k-means are proposed to solve the mathematical problem of wind turbine uncertainty. Based on the analysis of the voltage sag of the distribution network containing wind turbines, the evaluation indicator of the voltage sag depth of the bus and the evaluation indicator of the economic loss of the voltage sag of the sensitive load are proposed. The simulation results of the IEEE 33-bus system show that the reasonable access of wind turbines can help reduce the power loss and voltage sag of the distribution network, thereby ensuring the safe and economical operation of the system.

Coordinated routing system for fire detection by patrolling trucks with drones

Vehicle routing problem with drones (VRPD) is an extension of classical vehicle routing, which involves the usage of trucks and drones. Nowadays, bushfires are taken into account as a major global challenging subject. Indeed, forests are very vulnerable to fires, and the classical patrol systems cannot patrol all areas of the forest and pastures due to the difficult crossing of some routes.The literature survey demonstrated that the mathematical models are an efficient approach for planning forest and rangeland patrols. Drones and trucks are used in cooperation for forest monitoring in this study, with drones acting as an efficient and accurate means of monitoring routes that are impassable to ground vehicles. However, this novel approach deals with several substantial challenges, including limitation in the drone's battery and the routing problem in an integrated truck-drone system based on considering hard-to-reach areas and creating a trade-off between time and cost of the patrol process. These issues make significant differences between the proposed novel approach and the classical vehicle routing problem. Thus, it is essential to develop a comprehensive approach to resolve these crucial issues. The present study develops a multi-objective mathematical programming model as mixed-integer programming for simultaneous patrolling of trucks and drones. The augmented epsilon constraint (AEC) method has been considered to solve the two-objective mathematical programming model. Besides, Benders' decomposition (BD) algorithm has been employed to evaluate the achieved results in large-size problems. The performance of the BD algorithm has been confirmed in this study. The findings indicated that the proposed model efficiently protected the forest via monitoring all areas, including impassable areas where ground patrolling is impossible (e.g., the lack of roads due to dense vegetation). Also, it was proved that this system was a novel, cost-effective patrol, which prevents uncontrollable fires in the shortest possible time.

Multi-objective collaborative agreements amongst shipping lines and marine terminal operators for sustainable and environmental-friendly ship schedule design

Oceangoing ships transport a significant amount of different goods across the globe. The seaborne trade is expected to continue its growth despite the COVID-19 pandemic. The International Maritime Organization considers the amount of emissions produced by oceangoing ships as substantial. Shipping lines have to explore innovative and effective alternatives to meet challenging emission reduction targets. This study proposes a new type of collaborative agreements amongst shipping lines and marine terminal operators, where the shipping line is not only able to select the marine terminal for the ship service at every port of the shipping route but also request the appropriate arrival time window and handling rate. A multi-objective mathematical model is developed to capture the proposed collaborative agreements. The first objective of the model minimizes the cost components that are mostly driven by the economic perspectives, while the second one directly captures the environmental perspectives as well. A novel customized exact multi-objective optimization method, inspired by the ε-constraint method and the goal programming method, is developed to address the problem. The computational experiments are conducted for the Europe Pakistan India Consortium 2 (EPIC-2) shipping route. The results show that the developed solution method is able to generate the Pareto Fronts with sufficient solution density. The experiments also demonstrate that the proposed multi-objective mathematical model could facilitate the analysis of trade-offs amongst the economic and environmental perspectives in the ship schedule design. Furthermore, the importance of effective collaborative agreements amongst shipping lines and marine terminal operators is showcased as well.

A multi-objective mathematical model and evolutionary algorithm for the dual-resource flexible job-shop scheduling problem with sequencing flexibility

A multi-objective mathematical model and evolutionary algorithm for the dual-resource flexible job-shop scheduling problem with sequencing flexibility

An intelligent UAV path planning optimization method for monitoring the risk of unattended offshore oil platforms

To ensure the safe operation of static and dynamic devices in a limited platform space and prevent security threats caused by accidents and external intruders, the unmanned aerial vehicle (UAV) is becoming an important tool to monitor and reduce the operational risk of unattended offshore oil platforms. However, UAVs may encounter location errors, adversely affecting patrol efficiency and accuracy. Therefore, the optimal UAV path planning is vital to ensure complete monitoring routes and reduce the risk presented by the marine environment, devices, and employees on unattended offshore platforms. This paper established a multi-objective mathematical model with the shortest flight path and minimum correction times for the intelligent UAV patrol of unattended offshore platforms. An intelligent algorithm with large-scale constraints for UAV path planning was proposed based on non-dominated sorting genetic algorithms. A flight path length of 8076.11 m and 25 correction times presented the optimal solution. The results indicated that the proposed algorithm could be used to plan an effective and accurate three-dimensional (3D) UAV flight path according to the size of the offshore oil platform. This is highly significant for the intelligent risk monitoring of unattended offshore platforms in practical engineering in the future.

Efficient multiobjective optimization for an AGV energy-efficient scheduling problem with release time

In recent years, green manufacturing has attracted wide attention from researchers. However, the energy efficiency problem in matrix manufacturing workshops is still a blank area. This paper considers a novel automatic guided vehicle (AGV) energy-efficient scheduling problem with release time (AGVEESR) to optimize the three objectives of energy consumption, number of AGVs used and customer satisfaction simultaneously. Considering the development of the AGVEESR, we extract problem-specific knowledge, establish a multiobjective mathematical model, and design a hybrid constructive heuristic. Due to the complexity of the problem, we propose an efficient multiobjective greedy algorithm (MOGA) with effective strategies such as new population initialization, greedy operation, and self-adaptive multiple neighbourhood local search. Meanwhile, an ideal-point-based construction operator in the greedy operation phase is presented to lower the computational complexity. Simulation results show that the proposed MOGA has a tremendously superior performance to the five state-of-the-art algorithms in solving the problem considered.

Environmental and social implications of incorporating carpooling service on a customized bus system

This study addresses one of the most challenging issues in designing a sustainable and efficient ride-sharing service. This paper uses an extensive computational study to quantify the behavior of carpooling in customized bus routing problems. This mechanism allows organizations to draw on the potential of their employees’ private cars to provide convenient alternative rides for other employees, thereby reducing air pollution and greenhouse gas emissions as well as increasing overall satisfaction with the transportation system offered. The objective functions minimize: (i) total transportation costs and incentives paid to drivers of private cars, (ii) dissatisfaction as determined by staff walking distance, travel time, and delays in arriving at work, and (iii) total carbon emissions generated by commuting. We propose a resolution algorithm based on Pareto Strength Ant Colony Optimization (PSACO) as an effective meta-heuristic method for solving the multi-objective mathematical model and compare it with the results obtained by an exact method. The effectiveness and applicability of the proposed problem have been evaluated by performing computational experiments on a real case study in Paris using a number of comparative metrics with appropriate assumptions. Different parameters affecting the performance of the algorithm are also investigated. The concluding section presents a comparison of the results achieved. The test outcomes confirm that the formulation and the solution methods can be useful references for practice. The insights obtained from the research could provide the basis for designing incentive schemes and information campaigns aimed at making ride-sharing systems more successful and improving their performance.

Multiobjective Mathematical Optimization Model for Municipal Solid Waste Management with Economic Analysis of Reuse/Recycling Recovered Waste Materials

Municipal solid waste management in developing countries like Nigeria did not consider benefits from reuse/recycling recovered waste materials during solid waste evacuation and disposal. The benefits from recovered waste materials mostly go to informal waste vendors and scavengers. This study developed a multiobjective mathematical programming model for waste evacuation and disposal, considering the benefits of reuse/recycling recovered waste materials. Data were collected from the Abuja environmental protection board (AEPB), personal interviews, and other stakeholders. The formulated model was solved using spreadsheet solver version 14.0. The study uses various daily budgetary provisions for solid waste evacuation and disposal at a 15% recovery level of solid waste materials to observe the responses of the model. The solution shows that at 71.5% recovery of reuse/recycling recovered waste material; no budgetary provision is required to evacuate and dispose of the waste at the collection centers. Benefits realized from recovered waste materials are sufficient to evacuate and dispose of the wastes. After a 71.5% level of recovery, the net benefit of $1,108.17 from recovered waste materials starts to accrue until the percentage recovery level reaches 100%. The volume of waste shifted to the disposal sites was reduced to 74.5 tons (i.e., unrecoverable waste material) which is 16.82% of the total waste generated per day, and 368.33 tons (83.18%) of waste materials were recovered. The study will give the policymakers viable information to aid proper planning while budgeting and controlling solid-waste-associated problems in the Abuja municipal area in particular and the country as large.

Multi-objective low-carbon hybrid flow shop scheduling via an improved teaching-learning-based optimization algorithm

In this article, for achieving an effective and environmental-friendly production scheduling, we investigate a multi-objective low-carbon hybrid flow shop scheduling problem (MLHFSP) with the consideration of machines with varied energy usage ratios. The problem is formulated by a multi-objective mathematical model with two optimization objectives, i.e., minimizing total carbon emission (TCE) and makespan (Cmax). We primarily analyse on the formation of TCE and derive its mathematical expression. MLHFSP is NP-hard, therefore, to tackle the model, an improved multi-objective teaching-learning-based optimization (ITLBO) algorithm is proposed. The ITLBO algorithm mainly contains global search based teaching phase and local search based learning phase. In ITLBO, a solution is represented by two vectors, i.e., job sequence vector and machine assignment vector. Sigma method is utilized to quantify each individual, and to avoid local optimum, sequential neighbourhood search (SNS) method is also adopted. Experimental results validate the feasibility and effectiveness of proposed ITLBO in addressing MLHFSP. The research findings help manufacturing engineers to seek a sophisticated balance between carbon emission reduction and makespan reduction.

Production planning optimisation in a sustainable hybrid manufacturing remanufacturing production system

In this study, we investigate a production planning problem in hybrid manufacturing remanufacturing production system. The objective is the determine the best mix between the manufacturing of new products, and the remanufacturing of recovered products, based on economic and environmental considerations. It consists to determine the best manufacturing and remanufacturing plans to minimising the total economic cost (start-up and production costs of new and remanufactured products, storage costs of new and returned products and disposal costs) and the carbon emissions (new products, remanufactured products and disposed products). The hybrid system consists of a set of machines used to produce new products and remanufactured products of different grades (qualities). We assume that remanufacturing is more environmentally efficient, because it allows to reduce the disposal of used products. A multi-objective mathematical model is developed, and a non dominated sorting genetic algorithm (NSGA-II) based approach is proposed. Numerical experience is presented to study the impact of carbon emissions generated by new, remanufactured and disposed products, over a production horizon of several periods.

Multi-objective production planning of new and remanufactured products in hybrid production system

In this study, we address the production planning problem within a hybrid manufacturing remanufacturing system. This system is composed of a single machine that can work in two modes: the first one that produces new products from raw materials and the second one that produces remanufactured products from returned used products. Our study is based on economic and environmental considerations where the goal is to determine the best manufacturing and remanufacturing plan that satisfies the demand for new and remanufactured products and simultaneously minimizes the total costs included (start-up, production, storage and disposal costs) as well as the minimization of the CO2 emissions generated by the new, remanufactured and disposed of products. A multi-objective mathematical model is established, and an approach based on a non-dominated genetic sorting algorithm (NSGA-II) is introduced; in addition, a technique of order performance by similarity to the ideal solution (TOPSIS) is used to find the best compromise solution among the pareto front obtained by the NSGA-II algorithm. Finally, a computational experiment is implemented to study the influence of carbon emissions from new, remanufactured and discarded items over a production horizon.

Selection of green suppliers with the approach of integrating economic, environmental and social decisions (Case study of Sazeh Gostar Saipa Photovoltaic Company)

Supply chain network design is one of the key issues in strategic chain planning that refers to the supply chain network configuration and as an infrastructure issue in its management, will have lasting effects on other tactical and operational decisions. In other words, the proper design of the supply chain network leads to the achievement of an optimal structure, which makes effective and competitive supply chain management possible. In this study, a problem of selecting a green supplier in terms of sustainability, under uncertainty based on three economic, environmental and social responsibility dimensions are studied by a case study of Sazeh Gostar Saipa Photovoltaic Company active in the pv industry. One of the environmental dimensions of the problem is the design of an efficient and flexible model for evaluating and selecting suppliers based on environmental indicators. One of the features of the proposed model is the use of environmental criteria in the process of selecting a green supplier and also the flexibility of the model in the number of sub-criteria. In this research, the theory of Rough sets has been used to find the weight of sub-environmental criteria. The obtained results confirm the efficiency of the multi-objective mathematical planning model in this research in evaluating suppliers and also using the theory of Rough sets to weight environmental indicators to achieve the above objectives.

Novel Concentric Hexagonal-Shaped RFID Tag Antenna With T-Shaped Stub Matching

In Mobile Wireless Sensor Networks there could be scenarios where absolutely all network nodes (including the base station) are mobile, becoming a very hard task to find a communication path between a sensor node and the base station due to many network variables are changing at each moment. In addition, there are delay-sensitive applications that require establishing communication paths as soon as possible to mitigate low network performance in terms of end-to-end delay, reducing, at the same time, the energy consumption of the network. For this reason, we propose a multiobjective mathematical optimization model for finding the optimal communication path between a source node and a sink (base station) considering hard scenarios where all network nodes are mobile and minimizing end-to-end delay and energy consumption. This mathematical model would offer significant advantages to evaluate new algorithms due to we could know how far or close are the algorithm results from the optimal values given by the mathematical model. In addition, we propose a prediction distributed routing algorithm based on Markov Chains that takes into account the network mobility in order to find as fast as possible a communication path between a source node and a sink with minimal energy consumption. We also propose a deep learning approach to predict future nodes’ distances in a mobile network to determine if future movements of nodes will cause communication disruptions in paths. Significant findings were obtained when the Markov Chains and Deep Learning approaches were compared in terms of predicting nodes mobility and reducing the delay and the energy consumption in the network. The performance of our prediction algorithms (Markov Chains and Deep Learning approaches) is evaluated against the mathematical model to determine how good it is. Finally, to analyze our prediction algorithms considering real online scenarios, we compared it against typical routing algorithms, obtaining promising results in terms of delay and energy consumption in all mobile node scenarios.

Operating Room Scheduling Optimization Based on a Fuzzy Uncertainty Approach and Metaheuristic Algorithms

Today, planning and scheduling problems are the most significant issues in the world and make a great impact on improving organizational productivity and serving systems such as medical and healthcare providers. Since operating room planning is a major problem in healthcare organizations, the optimization of medical staff and equipment plays an essential role. Thus, this study presents a multi-objective mathematical model with a new categorization (preoperative, intraoperative, and postoperative) to minimize operating room scheduling and the risk of using equipment. Time constraints in healthcare systems and medical equipment limited capacity are the most significant considered limitation in the present study. In this regard, since the duration of patient preparation and implementation of treatment processes occur in three states of optimistic, pessimistic, and normal, the introduced parameters are examined relying on a fuzzy uncertainty analysis of the problem. Hence, the model is measured in a real numerical solution sample in a medical center to evaluate and confirm the proposed mathematical model. Then, two meta-heuristic algorithms (NRGA and NSGAII) are implemented on the mathematical model to analyze the proposed model. Finally, the research results indicate that the NSGA-II is more efficient in the operating room scheduling problem.

Research on the Scheduling of Mobile Robots in Mixed-Model Assembly Lines Considering Workstation Satisfaction and Energy Consumption

With the intensification of the global energy crisis, the production costs of manufacturing companies have increased significantly. To reduce the production energy consumption and costs in mixed-model assembly lines while improving efficiency and workstation satisfaction, novel line-integrated supermarkets and mobile robots are introduced. Considering the split delivery caused by workstation satisfaction and the mobile robot’s energy limitation, a multiobjective mathematical model of mobile robot scheduling in a mixed-model assembly line with a fuzzy time window is presented with the goal of maximizing workstation satisfaction while minimizing energy consumption. On this basis, according to the problem’s characteristics, a nondominated sorting genetic algorithm II with variable neighborhood search (VNSGA-II) is developed that constructs the initial solution using a heuristic method, improves crossover operation, and performs neighborhood search using three operators: exchange, insertion, and 2-opt to improve the solution’s quality. Finally, two numerical experiments are used to validate the model and algorithm. The results demonstrate that: (1) The scheduling model for mobile robots in a mixed-model assembly line that allows for spilt delivery and uses a normal fuzzy membership function to characterize workstation satisfaction is more in line with production practice. (2) The VNSGA-II algorithm can quickly establish a reasonable scheduling scheme for mobile robots in a mixed-model assembly line, and provide managers with a basis for making scientific decisions. Compared to MOPSO and NSGA-II, workstation satisfaction has improved by 0.91% and 1.12%, respectively, and mobile robots’ energy consumption has decreased by 12.53% and 13.66%, respectively.

A Multi-Objective Mathematical Model for Real-Time Employee Assignment in the Service Industry

A Multi-Objective Mathematical Model for Real-Time Employee Assignment in the Service Industry

Unveiling a novel model for promoting mobile phone waste management with a social media data analytical approach

With the enormous growth of the population, the intense improvement of the electronic industry, and the ever-incrementing use of mobile phones in today's life, the proper disposal of waste mobile phones has been of paramount importance. Consequently, the tremendous volume of end-of-life (EOL) mobile phones worldwide calls for a sustainable management system to decide on waste mobile phone recovery to minimize the cost and environmental impact. This paper presented a decision problem, namely, EOL option determination, to decrease mobile phone waste. Thus, this study suggests a decision support system (DSS) for the iPhone mobile phone (a subset of the electronics industry) in the EOL phase. Customers’ pervading use of social media has led to these platforms being used as a rich data source to extract information. Thus, the proposed DSS analyzes the Twitter databases, collecting mobile phone defect information from the customers. We suggest an ontology-based text mining and a data mining-based technique through the self-organizing map (SOM) for information discovery from the Twitter data. Finally, a multi-objective mathematical model based on sustainability dimensions is developed to correct EOL decisions based on the defective mobile phone components analyzed from Twitter data. The proposed DSS helps manufacturers when a product is returned and decide for proper EOL processes. This study provides a novel insight and can serve as a valuable reference for solving waste management problems using social media data.