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Reservoir-operation optimisation is a crucial aspect of water-resource development and sustainable water process management. This study addresses bi-objective optimisation problems by proposing a novel crossover evolution operator, known as the hybrid simulated binary and improved arithmetic crossover (SBAX) operator, based on the simulated binary cross (SBX) and arithmetic crossover operators, and applies it to the Non-dominated Sorting Genetic Algorithms-II (NSGA-II) algorithm to improve the algorithm. In particular, the arithmetic crossover operator can obtain an optimal solution more precisely within the solution space, whereas the SBX operator can explore a broader range of potential high-quality solutions. Considering the advantages of both operators, this study introduces an improved arithmetic operator to reduce the risk of local convergence inherent in conventional arithmetic operators. Subsequently, two strategies for the SBAX operator are discussed: SBX operator + new arithmetic operator and new arithmetic operator + SBX operator. The convergence of the bi-objective Pareto solution set is evaluated based on the generation and inverted generational distances. This method is used for the collaborative optimisation of the water supply and ecological operation of the Fenhe Reservoir, where its effectiveness is demonstrated. A comparative analysis of the bi-objective optimisation schemes obtained using different crossover operators indicates the following: (1) the NSGA-II algorithm based on the SBAX operator achieves a convergence efficiency that is 14.25–41.95% higher than that of the conventional NSGA-II algorithm; (2) the reservoir operation indices of the scheduling scheme derived from the NSGA-II algorithm based on the SBAX operator significantly outperform those obtained using the conventional NSGA-II algorithm. The optimal strategy reduces the annual average water abandonment by 11.2–14.52 million m 3 . This study provides a novel approach for bi-objective optimisation and sustainable reservoir management.

As electric vehicles (EVs) are currently under-utilised, the features of deploying EVs as distributed energy resources (DERs), based on an EV as a service (EVaaS) framework, are exploited and a resource allocation scheme is proposed for optimum association of dispersed EVs with critical load for demand fulfilment in microgrids. The proposed approach is based on a combined economic emission (CEE) optimisation model where both energy costs and carbon emissions are taken into account. The CEE optimisation problem is then formulated as a bi-objective optimisation problem, considering a number of practical constraints, such as energy demand, cost budget, emission limit and charging station limit. Carbon price is introduced to convert the bi-objective problem into a single objective function. The authors included EV battery degradation cost to ensure EV owners are not worse off after EVaaS participation. The feasibility of the proposed model is demonstrated in simulation studies. The approach has been extended to evaluate the trade-off between EVaaS and conventional DERs. Numerical results demonstrate the efficiency of the proposed resource allocation scheme.

Modern assembly line optimization requires maximizing both productivity and quality while taking into account dynamic constraints related to operator skills, a critical challenge in today’s rapidly evolving manufacturing environments. This study introduces a new bi-objective Assembly Line Balancing (ALB) model that is capable of adapting in real time to operational changes in operator skills through continuous learning mechanisms. The model simultaneously aims to maximize production output and minimize defect rates. The proposed technique automatically updates operator skill matrices using historical performance data and real-time production feedback, creating a closed-loop improvement system. This innovative approach effectively replaces subjective supervisor decisions with systematic, data-driven resource allocation based on quantitative performance metrics. Our mathematical formulation resolves the critical gap between theoretical ALB assumptions and industrial practice by explicitly incorporating time-varying operator skills, production quality trade-offs, and demand-resource variability. The model offers manufacturers a dynamic balancing mechanism that facilitates adaptive decision-making, enhances line agility, and optimizes operational efficiency. Additionally, it contributes to the development of workforce skills.

This paper addresses a supply chain situation, in which a company distributes commodities over a selected subset of customers while a manufacturer produces the commodities demanded by the customers. The distributor company has two objectives: the maximization of the profit gained by the distribution process and the minimization of CO2 emissions. The latter is important due to the regulations imposed by the government. A compromise between both objectives exists, since profit maximization only will attempt to include as many customers as possible. But, longer routes will be needed, causing more CO2 emissions. The manufacturer aims to minimize its manufacturing and shipping costs. Since a predefined hierarchy between both companies exists in the supply chain, a bi-level programming approach is employed. This problem is modelled as a bi-level programming problem with two objectives in the upper level and a single objective in the lower level. The upper level is associated with the distributor, while the lower level is associated with the manufacturer. Due to the inherent complexity to optimally solve this problem, a heuristic scheme is proposed. A nested bi-objective tabu search algorithm is designed to obtain non-dominated bi-level feasible solutions regarding the upper level. Considering simultaneously both objectives of the distributor allow us to focus on the minimization of CO2 emissions caused by the supply chain, but bearing in mind the distributor’s profit. Numerical experimentation shows that the Pareto frontiers obtained by the proposed algorithm provide good alternatives for the decision-making process and also, some managerial insights are given.

In the last decades, Reconfigurable Manufacturing Systems (RMSs) rose as an emerging manufacturing strategy matching the modern industrial and market requirements asking for a wide variety of products in flexible batches. A traditional reconfigurable manufacturing environment consists of dynamic cells, called Reconfigurable Machine Cells (RMCs), including a set of machines called Reconfigurable Machine Tools (RMTs). Such machines are characterized by fixed elements, i.e., basic modules, and dynamic elements, i.e., auxiliary modules, allowing them to perform different operations. Despite their automation level, these systems require the intervention of the human operators in performing specific tasks, e.g., handling of the auxiliary modules from the warehouse to the RMTs and their assembly/disassembly to/from the RMTs. This issue rises relevant ergonomic and safety questions due to the human–machine collaboration. Following this stream, this paper proposes and applies a bi-objective optimization model for the design and management of RMSs. The technical objective function minimizes the reconfiguration time, i.e., the time needed to equip the RMTs with the required auxiliary modules, and the part and auxiliary module travel time among the RMCs. The ergonomic objective function minimizes the repetitive movements performed by the human operators during the working activities according to the ISO 11228-3 standard. Results show the existence of a good trade-off between the two objective functions, proving the possibility to improve the ergonomic conditions of the human operators without excessively increasing the total time needed for RMTs reconfiguration and for part and auxiliary module travelling.

This paper presents a bi-objective solution approach to address the production scheduling challenge encountered by manufacturers in a shared manufacturing environment. In such scenarios, manufacturers are required to manage orders received through a cloud platform (referred to as cloud orders) while simultaneously fulfilling orders from their long-term and regular clients (local orders). The problem is to efficiently coordinate the production of both types of orders within shared manufacturing facilities. We formulate the problem into a bi-objective mixed integer programming model aimed at simultaneously minimizing the delivery time of cloud orders and mitigating the disruptions to local order production caused by cloud orders. This solution approach comprises three key components: computation of cloud orders’ starting times, construction of available time intervals of manufacturing facilities, and a bi-objective heuristic. This heuristic combines an enhanced hybrid discrete differential evolution with a modified forward–backward earliest starting time algorithm. We introduce an advanced population initialization technique, a novel individual update strategy, and an adaptive local search mechanism based on Pareto-dominance principles to improve the search capabilities of the algorithm towards discovering Pareto non-dominated solutions. Computational results show that the proposed approach outperforms the existing algorithm in most test instances in terms of five common metrics. Insights are discussed, highlighting the practical implications and potential benefits of the proposed approach for shared manufacturing scheduling.

In the presence of uncertainties in the parameters of a mathematical model, optimal solutions using nominal or expected parameter values can be misleading. In practice, robust solutions to an optimization problem are desired. Although robustness is a key research topic within single-objective optimization, little attention is received within multi-objective optimization, i.e. robust multi-objective optimization.This work builds on recent work within robust multi-objective optimization and presents a new robust efficiency concept for bi-objective optimization problems with one uncertain objective. Our proposed concept and algorithmic contribution are tested on a real-world multi-item capacitated resource planning problem, appearing at a large aerospace company manufacturing high precision engine parts. Our algorithm finds all the robust efficient solutions required by the decision-makers in significantly less time than the approach of Kuhn et al. (Eur J Oper Res 252(2):418–431, 2016) on 28 of the 30 industrial instances.

As an emerging computer technology with numerous bits, bit-wise allocation, and extensive parallelism, the ternary optical computer (TOC) will play an important role in platforms such as cloud computing and big data. Previous studies on TOC in handling computational request tasks have mainly focused on performance enhancement while ignoring the impact of performance enhancement on power consumption. The main objective of this study is to investigate the optimization trade-off between performance and energy consumption in TOC systems. To this end, the service model of the TOC is constructed by introducing the M/M/1 and M/M/c models in queuing theory, combined with the framework of the tandem queueing system, and the optimization problem is studied by adjusting the processor partitioning strategy and the number of small TOC (STOC) in the service process. The results show that the value of increasing active STOCs is prominent when system performance significantly depends on response time. However, marginal gains decrease as the number of STOCs grows, accompanied by rising energy costs. Based on these findings, this paper constructs a bi-objective optimization model using response time and energy consumption. It proposes an optimization strategy to achieve bi-objective optimization of performance and energy consumption for TOC by identifying the optimal partitioning strategy and the number of active small optical processors for different load conditions.

In natural disasters, having a capable network of collecting and distributing crucial items such as blood is one of the major concerns. However, due to damage to the infrastructure after disasters, mobile blood collecting facilities (blood mobiles) are usually required. This paper aims to decide the locations of mobile facilities in each period for collecting donated blood, plan the blood distribution from the fixed and mobile facilities to the main blood centers, as well as from blood centers to the hospitals and field-hospitals, under uncertain conditions. To do so, a multi-period, bi-objective mixed-integer mathematical model is developed under a multiple-scenario, aiming to minimize the unsatisfied blood demand as well as the total cost of the network. In the proposed model, the blood group compatibility matrix, failure rate of the facilities, and patients’ urgency levels are considered. An augmented ε-constraint method is applied to solve this bi-objective model. Due to the complex nature of the proposed blood supply chain model, the Lagrangian relaxation approach is used to solve the proposed model. An expected Istanbul earthquake is considered, and the blood supply planning through the Red Crescent’s European branch is performed utilizing the proposed model to examine its validity. According to the numerical results, the mobile facilities' locations in each period under each scenario are determined, the unsatisfied demand in each hospital and field-hospital for each blood type are reported, and the tradeoff between the supply chain costs and unsatisfied demand are discussed in detail. Finally, to illustrate the robustness of the proposed model, a detailed sensitivity analysis is performed. According to the study results, opening new blood centers near the high-demand sub-districts for faster testing and supply, increasing the hospitals' capacities, and usage of drones and helicopters for blood distribution are suggested can be considered as managerial insights.

Current static evacuation path planning methods are unable to meet the demands of real-time changes in fire scenarios. Therefore, a bi-objective dynamic planning (BODP) method for fire evacuation paths is proposed not only to minimize evacuation time but also reduce the thermal radiation dose received by personnel during the evacuation process. The BODP method includes both an equivalent rule proposed for the first time based on the linear weighting method, and an improved Dijkstra algorithm designed in this paper. Because of them, the BODP method can normalize evacuation time and thermal radiation dose to the same degree and perform multi-sink dynamic planning on a hexagonal grid map, in order to find the optimal evacuation path with the lowest equivalent cost in the event of a tank farm fire. This method accounts for changing fire scenarios and avoids potentially high-risk paths. Finally, a case study of a chemical plant tank farm is conducted to demonstrate the effectiveness of the method. The results indicate that the BODP method is better suited for evacuation path planning in complex and dynamic fire scenarios. The BODP method resolves the issue found in static path planning: the first-degree burn probabilities derived from estimated thermal radiation doses are 34% lower than those derived from actual thermal radiation doses, potentially resulting in unnecessary casualties. Additionally, the BODP method is also applicable to scenarios involving domino effects triggered by fire incidents. This method provides scientific and reliable technical support for emergency evacuation in tank farm fires, greatly contributing to the safety and protection of personnel.