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In the area of Solid Waste Management, transportation of the collected waste is a critical aspect considering the substantial time spent by garbage trucks on public roads. Studies have reported that transporting garbage has challenges related to public exposure and aesthetics. This study presents a generalised bi-objective formulation for the optimal routing of garbage trucks from transfer stations to recycling sites/landfills considering the trade-off between public exposure and aesthetic loss and constraining the operating cost. The formulation uses the novel link capacity function to account for the delay at traffic signals and the mix of trucks and cars on link performance. The proposed formulation is solved using the weighted sum and ε-constraint methods and applied to a realistic case study of the City of Chicago, USA. The Pareto Front obtained for the bi-objective formulation offers diverse trade-off solutions catering to distinct performance metrics. The results highlight the disparity across the solutions; the solution (P0.95 on Pareto Front) for minimum operating cost (or travel time or distance travelled) is very different from the solution (P0.4 on Pareto Front) for aesthetic cost and public exposure. The parametric study indicated that a modest operating budget may suffice for achieving aesthetic benefits, but minimising public exposure requires a higher operating budget. Finally, the proposed framework is adaptable to address various challenges pertaining to waste transportation, thereby serving as a valuable tool for evaluating policies and practices geared towards sustainability objectives.

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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.

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Home health care companies provide health care services to patients in their homes. Due to increasing demand, the provision of home health care services requires effective management of operational costs while satisfying both patients and caregivers. In practice, uncertain service times might lead to considerable delays that adversely affect service quality. To this end, this paper proposes a new bi-objective optimization problem to model the routing and scheduling problems under uncertainty in home health care, considering the qualification and workload of caregivers. A mixed-integer linear programming formulation is developed. Motivated by the challenge of computational time, we propose the Adaptive Large Neighborhood Search embedded in an Enhanced Multi-Directional Local Search framework (ALNS-EMDLS). A stochastic ALNS-EMDLS is introduced to handle uncertain service times for patients. Three kinds of metrics for evaluating the Pareto fronts highlight the efficiency of our proposed method. The sensitivity analysis validates the robustness of the proposed model and method. Finally, we apply the method to a real-life case and provide managerial recommendations.

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Improving generalization ability in multi-robot formation can reduce repetitive training and calculation. In this paper, we study the multi-robot formation problem with the ability to generalize the target position. Since the generalization ability of neural network is directly proportional to spatial dimension, we adopt the strategy of using different networks to solve different objectives, so that the network learning can focus on the learning of one objective to obtain better performance. In addition, this paper presents a distributed deep reinforcement learning method based on soft actor-critic algorithm for solving multi-robot formation problem. At the same time, the formation evaluation assignment function is designed to adapt to distributed training. Compared with the original algorithm, the improved algorithm can get higher reward cumulative values. The experimental results show that the proposed algorithm can better maintain the desired formation in the moving process, and the rotation design in the reward function makes the multi-robot system have better flexibility in formation. The comparison of control signal curve shows that the proposed algorithm is more stable. At the end of the experiments, the universality of the proposed algorithm in formation maintenance and formation variations is demonstrated.

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This article proposes a benchmark instance generator for the Hop-Constrained Minimum Spanning Tree problem, the Delay-Constrained Minimum Spanning Tree problem, and their bi-objective variants. The generator is developed in C++ and does not uses external libraries, being understandable, easy-to-read, and easy-to-use. Furthermore, the generator employs five parameters that makes possible to generate personalized benchmark instances for these problems. We also describe 640 benchmark instances that were previously used in computational experiments in the literature. Lastly, we include raw results obtained from computational experiments with the described benchmark instances. We hope that the data introduced in this article can foster the development and the evaluation of new algorithms for solving constrained minimum spanning tree problems.

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[This corrects the article DOI: 10.3389/fnut.2022.1056205.].

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The use of renewable fuels leads to reduction in the use of fossil fuels and environmental pollutants. In this study, the design and analysis of a CCPP based on the use of syngas produced from biomass is discussed. The studied system includes a gasifier system to produce syngas, an external combustion gas turbine and a steam cycle to recover waste heat from combustion gases. Design variables include syngas temperature, syngas moisture content, CPR, TIT, HRSG operating pressure, and PPTD. The effect of design variables on performance components such as power generation, exergy efficiency and total cost rate of the system is investigated. Also, through multi-objective optimization, the optimal design of the system is done. Finally, it is observed that at the final decisioned optimal point, the produced power is 13.4 MW, the exergy efficiency is 17.2%, and the TCR is 118.8 $/h.

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The hierarchical diagnosis and treatment reform of China can guide residents to seek medical treatment in an orderly manner and improve access to medical treatment. Most existing studies on hierarchical diagnosis and treatment used accessibility as the evaluation index to determine the referral rate between hospitals. However, the blind pursuit of accessibility will cause the problem of uneven utilization efficiency of hospitals at different levels. In response to this, we constructed a bi-objective optimization model based on the perspective of residents and medical institutions. This model can give the optimal referral rate for each province considering the accessibility of residents and the utilization efficiency of hospitals, to improve the utilization efficiency and equality of access for hospitals. The results showed that the applicability of bi-objective optimization model is good, and the optimal referral rate based on the model can ensure the maximum benefit of the two optimization goals. In the optimal referral rate model, residents' medical accessibility is relatively balanced overall. In terms of obtaining high-grade medical resources, the accessibility is better in the eastern and central regions, but poorer in the western China. According to the current allocation of medical resources in China, the medical tasks undertaken by high-grade hospitals account for 60%-78%, which are still the main force of medical services. In this way, there is a big gap in realizing the "serious diseases do not leave the county" goal of hierarchical diagnosis and treatment reform.

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This article presents a bi-objective mixed-integer linear model for the waste management system design. Two types of facilities, landfills and transfer stations (TSs), are identified based on two objectives: minimising the total system's costs and the total negative impact of located facilities on end users as waste generators through a defined pollution decay function. Landfills and TSs are categorised as undesirable facilities due to associated environmental risks. In this article undesirability of a located facility is defined as a two-threshold linear decreasing function of the distance between the end users and the located facility. Also, we considered additional restrictions that no two selected landfills or TSs are within a pre-specified distance from each other, limiting the superimposed pollution generated in these facilities. The model performances are tested on a real-scale example for Vojvodina (Serbia). Results showed that the proposed model has potentials and can be beneficial for government organisations, local authorities and other organisations related to waste management issues.

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When COVID-19 suddenly broke out, the epidemic areas are short of basic emergency relief which need to be transported from surrounding areas. To make transportation both time-efficient and cost-effective, we consider a multimodal hub-and-spoke transportation network for emergency relief schedules. Firstly, we establish a mixed integer nonlinear programming (MINLP) model considering multi-type emergency relief and multimodal transportation. The model is a bi-objective one that aims at minimizing both transportation time consumption and transportation costs. Due to its NP-hardness, devising an efficient algorithm to cope with such a problem is challenging. This study thus employs and redesigns Grey Wolf Optimizer (GWO) to tackle it. To benchmark our algorithm, a real-world case is tested with three solution methods which include other two state-of-the-art meta-heuristics. Results indicate that the customized GWO can solve such a problem in a reasonable time with higher accuracy. The research could provide significant practical management insights for related government departments and transportation companies on designing an effective transportation network for emergency relief schedules when faced with the unexpected COVID-19 pandemic.

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Objective. Proton arc therapy (PAT) is a new delivery technique that exploits the continuous rotation of the gantry to distribute the therapeutic dose over many angular windows instead of using a few static fields, as in conventional (intensity-modulated) proton therapy. Although coming along with many potential clinical and dosimetric benefits, PAT has also raised a new optimization challenge. In addition to the dosimetric goals, the beam delivery time (BDT) needs to be considered in the objective function. Considering this bi-objective formulation, the task of finding a good compromise with appropriate weighting factors can turn out to be cumbersome.Approach. We have computed Pareto-optimal plans for three disease sites: a brain, a lung, and a liver, following a method of iteratively choosing weight vectors to approximate the Pareto front with few points. Mixed-integer programming (MIP) was selected to state the bi-criteria PAT problem and to find Pareto optimal points with a suited solver.Main results. The trade-offs between plan quality and beam irradiation time (staticBDT) are investigated by inspecting three plans from the Pareto front. The latter are carefully picked to demonstrate significant differences in dose distribution and delivery time depending on their location on the frontier. The results were benchmarked against IMPT and SPArc plans showing the strength of degrees of freedom coming along with MIP optimization.Significance. This paper presents for the first time the application of bi-criteria optimization to the PAT problem, which eventually permits the planners to select the best treatment strategy according to the patient conditions and clinical resources available.

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The thought to put forward a queuing model proposed in this work was its pertinence in everyday life wherever we can see the uses of computing and networking systems. Industrial software developers and system managers can consider the results of the model to evolve their system for better results. Here we present a novel queueing model having erratic server with delayed repair and balking. Two distinct breakdowns i.e. active and passive breakdown for the system are also considered with their respective amendments. This model is closely related with the smooth functioning of the system during some internal faults (virus attack, electricity failures etc.). The performance indicators which are utilized in enhancing the service standards are obtained using supplementary variable technique. Using ANFIS soft computing technique we have compared the analytical results with those of neuro fuzzy results. Furthermore single and bi-objective minimization problems are considered and minima is obtained using particle swarm optimization and multi objective genetic algorithm respectively. Also, the minimization problems are shown as a convex programming problem to ensure the global optimality of the result. The proposed approach makes it conceivable to accomplish a relevant harmony between operational expenses and administration quality.

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This paper investigates control and design-for-control strategies to improve the resilience of sectorized water distribution networks (WDN), while minimizing pressure induced pipe stress and leakage. Both evolutionary algorithms (EA) and gradient-based mathematical optimization approaches are investigated for the solution of the resulting large-scale non-linear (NLP) and bi-objective mixed-integer non-linear programs (BOMINLP). While EAs have been successfully applied to solve discrete network design problems for large-scale WDNs, gradient-based mathematical optimization methods are more computationally efficient when dealing with large search spaces associated with continuous variables in optimal network control problems. Considering the advantages of each method, we propose a sequential hybrid method for the optimal design-for-control of large-scale WDNs, where a refinement stage relying on gradient-based mathematical optimization is used to solve continuous optimal control problems corresponding to design solutions returned by an initial EA search. The proposed method is applied to compute the Pareto front of a bi-objective design-for-control problem for the operational network BWPnet, where we consider reopening closed connections between isolated supply areas. The results show that the considered design-for-control strategy increases the resilience of BWPnet while minimizing pressure induced leakage. Moreover, the refinement stage of the proposed hybrid method efficiently improves the coarse approximation computed by the initial EA search, returning a continuous and even Pareto front approximation.

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Sedimentation affects the normal function of reservoirs and is a decisive factor in the reservoir's service life. Flushing sediment during reservoir operation is an effective non-engineering measure to alleviate reservoir sedimentation; however, lowering water level to discharge more flow conflicts with hydropower generation. In this study, reservoir management software is developed to simultaneously optimise sediment discharge and hydropower generation with the reservoir discharge as the decision variables. The sediment transport rate is calculated by an integral of the vertical distribution of suspended load concentration and flow velocity instead of empirical formulas. The model is solved by the most widely used multi-objective optimisation algorithm NSGA-II, resulting in the optimal schedule corresponding to the maximal sediment discharge and hydropower generation, which can be displayed graphically in the software. The software was developed in MATLAB with a Graphical User Interface (GUI) and applied to a large reservoir and can be generalised to other reservoirs. The results show that within the recommended discharge variation of 5%, the sediment release can be increased by 2.07 × 106 t as a reduction of per 1010 kW h in annual power generation. Compared with the original scheme, sediment release can be increased most by 3.31% at the cost of 0.03% loss of power generation. Moreover, the dual objective in the flood season was optimised by 7.30% and 3.92%, respectively.

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This paper develops an approach to optimize a vaccine distribution network design through a mixed-integer nonlinear programming model with two objectives: minimizing the total expected number of deaths among the population and minimizing the total distribution cost of the vaccination campaign. Additionally, we assume that a set of input parameters (e.g., death rate, social contacts, vaccine supply, etc.) is uncertain, and the distribution network is exposed to disruptions. We then investigate the resilience of the distribution network through a scenario-based robust-stochastic optimization approach. The proposed model is linearized and finally validated through a real case study of the COVID-19 vaccination campaign in France. We show that the current vaccination strategies are not optimal, and vaccination prioritization among the population and the equity of vaccine distribution depend on other factors than those conceived by health policymakers. Furthermore, we demonstrate that a vaccination strategy mixing the population prioritization and the quarantine restrictions leads to an 8.5% decrease in the total number of deaths.

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This paper proposes an approach for medical resource allocation among hospitals under public health emergencies based on data envelopment analysis (DEA). First, the DEA non-regressive production technology is adopted to ensure that the DMU can always refer to the most advanced production technology throughout all production periods. Based on the non-regressive production technology, two efficiency evaluation models are presented to calculate the efficiencies of DMUs before and after resource allocation. Our theoretical analysis shows that all the DMUs can be efficient after medical resource allocation, and thus a novel resource allocation possibility set is developed. Further, two objectives are considered and a bi-objective resource allocation model is developed. One objective is to maximize the output target realizability of the DMUs, while the other is to ensure the allocated resource to each DMU fits with its operation size, preperformance, and operation practice (i.e., proportion of critically ill patients). Additionally, a trade-off model is proposed to solve the bi-objective model to obtain the final resource allocation results. The proposed approach contributes by ensuring that the medical resources are allocated in such a way that they can all be efficiently used as well as considering multiple objectives and practical constraints that make the approach more fitted with the practical application scenarios. Finally, a case study of 30 hospitals in Wuhan during the COVID-19 epidemic is applied to illustrate the proposed approach.

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Multicomponent adsorption processes are affected by both mixture and process variables viz. feed composition, pH, adsorbent dosage, and adsorbent type. Optimization of multicomponent adsorption processes with multiple objectives is challenging. It is important to accurately identify possible solutions and select the compromise solution that best satisfies the different objectives. Conventional algorithms, when applied to multicomponent adsorption, were found to identify the Pareto front less accurately, thereby necessitating the need for a reliable method. The steep portion of the Pareto front was especially not captured satisfactorily by the different conventional algorithms such as pattern search (PS), Non-dominated Sorting Genetic Algorithm (NSGA-II), and Epsilon-Constraint (EC). This portion assumes importance, if the compromise solution occurs in its vicinity. To address these challenges, a novel bi-objective optimization technique termed as elliptical method (EM) was developed and described in this work. It involves an exhaustive search, provides a well distributed Pareto front, and clearly delineates the steep region. After validating with benchmark problems, EM was applied to batch multi-component adsorption. The two objectives optimized simultaneously were adsorbent loading and percentage removal of the different solutes. The Pareto front and the compromise solution involving the best combination of the two objectives were significantly superior in the elliptical method when compared to those obtained from typical algorithms including epsilon-constraint (EC) method. The Pareto front was also well defined by the elliptical method without discontinuities near the extreme and steep regions. The number of points found by EM in the steeper region for the grade II adsorbent was 10 times greater than those found by the EC method while the PS and NSGA could not delineate this portion. The average time taken (considering both adsorbents) for EM per solution was 0.17 s which was at least 30.6% faster than the other methods. The compromise solution with the elliptical method was superior to the other methods. For instance, with grade II adsorbent, the compromise solution from the elliptical method suggested operating conditions that led to a total adsorbent loading and percentage removal of 333.4 mg/g and 56.0%. On the other hand, pattern search gave 324.1 mg/g and 56.5%, whereas the NSGA-II method gave 321.9 mg/g and 53.3%. For this adsorbent, elliptical method's compromise solution was 50% and 20% closer in terms of the Euclidean distance to the utopia point than NSGA and PS methods, respectively. The elliptical method will facilitate reliable wastewater tertiary treatment taking into cognizance the utilization of the adsorbent as well as the percentage purity requirement.

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The aim of the bi-objective multimodal car-sharing problem (BiO-MMCP) is to determine the optimal mode of transport assignment for trips and to schedule the routes of available cars and users whilst minimizing cost and maximizing user satisfaction. We investigate the BiO-MMCP from a user-centred point of view. As user satisfaction is a crucial aspect in shared mobility systems, we consider user preferences in a second objective. Users may choose and rank their preferred modes of transport for different times of the day. In this way, we account for, e.g., different traffic conditions throughout the planning horizon. We study different variants of the problem. In the base problem, the sequence of tasks a user has to fulfil is fixed in advance and travel times as well as preferences are constant over the planning horizon. In variant 2, time-dependent travel times and preferences are introduced. In variant 3, we examine the challenges when allowing additional routing decisions. Variant 4 integrates variants 2 and 3. For this last variant, we develop a branch-and-cut algorithm which is embedded in two bi-objective frameworks, namely the ϵ -constraint method and a weighting binary search method. Computational experiments show that the branch-and cut algorithm outperforms the MIP formulation and we discuss changing solutions along the Pareto frontier.

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In many real-world optimization problems, more than one objective plays a role and input parameters are subject to uncertainty. In this paper, motivated by applications in disaster relief and public facility location, we model and solve a bi-objective stochastic facility location problem. The considered objectives are cost and covered demand, where the demand at the different population centers is uncertain but its probability distribution is known. The latter information is used to produce a set of scenarios. In order to solve the underlying optimization problem, we apply a Benders' type decomposition approach which is known as the L-shaped method for stochastic programming and we embed it into a recently developed branch-and-bound framework for bi-objective integer optimization. We analyze and compare different cut generation schemes and we show how they affect lower bound set computations, so as to identify the best performing approach. Finally, we compare the branch-and-Benders-cut approach to a straight-forward branch-and-bound implementation based on the deterministic equivalent formulation.

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INTRODUCTION: Natural deep eutectic solvents (NaDESs) are green and effective solvents that are used to extract 3 flavonoids from Yangyin Yiqi Huoxue prescription, a traditional Chinese prescription. METHODS: A total of 6 types of NaDESs were systematically screened and evaluated for the total extraction yield of puerarin, calycosin, and formononetin by high-performance liquid chromatography. Then, a 4-factor-three-level experimental scheme designed by the Box-Benhnken Design was applied on the basis of a single experiment to determine the extraction yield and the antioxidant property. Finally, the extraction process was optimized through response surface methodology (RSM) and the genetic neural network (GNN), respectively. RESULTS: The use of betaine-lactic acid as an extractant displayed significant advantages in the screening process. The optimum extraction parameters provided by GNN were as follows: water content 25% (v/v), liquid to material ratio 190 mg/ml, extraction time 37 min, and extraction temperature 63 °C. Under this condition, the average experimental comprehensive evaluation values of the extraction yield and antioxidant properties were 3.12 mg/g and 86.27%, and the relative deviations to the predicted values were 0.30% and 1.44%, respectively. In addition, the experimental results of GNN were better than those of RSM (p < 0.01). CONCLUSIONS: We found the application of GNN to be effective and credible for bi-objective optimization of extraction yields and antioxidant activity in this study. Moreover, our results provide a reference and a theoretical basis for experimental and future industrial extraction for multi-objective situations.

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