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This paper analyzes the current situation of the development of tourism in Hainan and provides a new reference for the high-quality development of Hainan tourism. Firstly, the evaluation model and evaluation indexes of Hainan tourism high quality development based on a comprehensive evaluation method are constructed, the comprehensive index method is used to dimensionless process the data, and the entropy value method is used to conduct a comprehensive analysis of the quantitative relationship of selected indexes and the degree of variation to determine the index weights. Then the multi-objective linear weighting method is used to calculate the comprehensive level of Hainan tourism quality development. Then the regional difference characteristics of Hainan tourism quality development and the trend of tourism development time sequence evolution were analyzed, and finally, the path of Hainan tourism quality development was analyzed from multiple factors. On the regional difference characteristics, the northern and southern regions of Hainan have obvious advantages in terms of quality tourism development, with a comprehensive development index of 0.498 and 0.482 respectively, while the central region is relatively backward, with a development index of 0.364. The dynamics of industrial development in Hainan are relatively low, with slow and unstable growth, rising only from 0.0048 in 2013 to 0.0059 in 2018 and also showing a small downward trend in 2015 and 2016. This study has important implications for the high-quality development of tourism in Hainan.

The rational development of urban underground space resources (UUSRs) is especially crucial for alleviating “urban diseases”, and it is of great significance for exploring the appropriateness of urban underground space (UUS) development under multiple constraints for the rational use of UUSRs. This research selects the UUS in Nantong City, Jiangsu Province, as the research object, and establishes an evaluation index system for the suitability of UUS development under the perspective of sustainable development, including terrain and geomorphology, engineering geological environment, hydrogeological environment, sensitive geological factors, the regional development level, and the distribution of ecological reserve, as well as other multi-source heterogeneous data. On this basis, the relationship between the appropriateness of underground space development and the utilization and various factors was studied. We constructed a comprehensive evaluation model for the suitability of UUS using the Analytic Hierarchy Process (AHP) and the multi-objective linear weighting method. The results of the study show that ecological protection constraints and geological hazards have a greater impact on the evaluation of suitability. The suitable and secondarily suitable areas for the development of the underground space in Nantong City account for 14.74% and 30.66% of the total area, respectively. These areas are mainly distributed in Rugao City and Chongchuan District. The less suitable and unsuitable areas account for 37.17% and 17.44%, with a significant concentration in near-sea areas.

The meal delivery routing problem faced by the e-commerce platform is challenging. In order to reduce the logistics cost and meet the needs of customers, a multi-objective meal delivery routing problem is studied under the shared logistics services mode (SLSM). In the meal delivery problem, the third-party logistics providers need to arrange vehicles in the multi-depot to pick up meals from multiple food providers and deliver them to customers, so as to realize the sharing of logistics services between food providers and compare them with the traditional logistics service mode (TLSM). While realizing sharing, it is also necessary to meet customer time requirements as much as possible. In this case, a multi-objective mathematical model to minimize customer dissatisfaction and delivery cost is established, and the linear weighting method is employed to transform the model. An improved Ant Lion Optimizer (IALO) is proposed to solve the problem, and compared with other algorithms. The experiments verified the effectiveness of the proposed algorithm and show that SLSM can save logistics costs and meet customer needs more than TLSM, and provide certain reference opinions for the e-commerce platform.

The paper develops the dual equivalent linearization with one weighting coefficient to nonlinear deterministic dynamic systems. The problem of equivalent replacement of a nonlinear function by a linear function is briefly revised using the dual approach that involves two forward and backward replacements. Further selecting a weighting coefficient connecting two objective functions is investigated using a semi-analytical analysis. The dual equivalent linearization with the selected weighting coefficient is then applied to the frequency analysis of nonlinear free vibrations, and some case studies are subsequently carried out in order to verify the accuracy and influence of nonlinearities on the effectiveness of the proposed technique. It is shown that the dual equivalent linearization provides the lowest maximal errors among the solutions obtained from several approximate methods for the rather large nonlinearities considered.

Goal programming (GP) is one of the widely used and effective method of solving real-world multi-objective decision-making problems. The term “multi-objective transportation problem” (MOTP) covers a specific class of vector maximum (minimum) linear programming problem that typically has multiple, competing, and incompatible objective functions. In this article, GP and weighted goal programming (WGP) are summarized in MOTP. Furthermore, its advantages over GP are illustrated by a theorem. Additionally, by utilizing WGP, a solution procedure is articulated for MOTP. Finally, an application on screen-panels of mobile devices is presented to explore the applicability. The paper ends with a conclusion and including an outlook to future studies, whereby we address internal and external transportation, and view the internal one with a broader understanding of logistics.

Regional integrated energy site layout optimization involves multi-energy coupling, multi-data processing and multi-objective decision making, among other things. It is essentially a kind of non-convex multi-objective nonlinear programming problem, which is very difficult to solve by traditional methods. This paper proposes a decentralized optimization and comprehensive decision-making planning strategy and preprocesses the data information, so as to reduce the difficulty of solving the problem and improve operational efficiency. Three objective functions, namely the number of energy stations to be built, the coverage rate and the transmission load capacity of pipeline network, are constructed, normalized by linear weighting method, and solved by the improved p-median model to obtain the optimal value of comprehensive benefits. The artificial immune algorithm was improved from the three aspects of the initial population screening mechanism, population updating and bidirectional crossover-mutation, and its performance was preliminarily verified by test function. Finally, an improved artificial immune algorithm is used to solve and optimize the regional integrated energy site layout model. The results show that the strategies, models and methods presented in this paper are feasible and can meet the interest needs and planning objectives of different decision-makers.

Load scheduling is a key factor in demand side management (DSM), which manages available generation capacity with regard to the required demand. In this paper, a triple-objective load scheduling optimization problem (LSOP) is formulated for achieving optimal cost and peak demand as well as minimum customer inconvenience. A Henry gas solubility optimization (HGSO) algorithm that is based on multi-objective is used for solving LSOP. The proposed HGSO offers a set of compromise solutions that represent the tradeoff between the three objectives of the formulated problem. A set of all compromise solutions from the dominant Pareto front is achieved first, and then ranked by using MCDM so as to optimally sort these solutions. An entropy weighting method (EWM) is then used for computing the weights of various criteria that dominate the LSOP and is provided as a technique for ordering preferences by similarity to achieve the ideal solution (TOPSIS) so as to rank the sorted solutions. Two types of end-users are considered so as to show the effectiveness of the proposed LSOP: non-cooperative and cooperative users. The results of the proposed load scheduling method show the significance of the proposed method for both the cooperative and non-cooperative end-users. The proposed method achieves a cost of energy of R50.62 as a total cost of energy consumed by four non-cooperative end-users. The cost of energy for the cooperative end-users is found to be R47.39. Thus, saving in the energy cost unit is found to be around 5.5% by using the proposed method; moreover, the peak demand value is reduced by 9.7% when non-cooperative end-users becomes cooperative.

Forward and reverse supply chains are one of the most important issues in supply chain management. These kinds of supply chain networks include a direct and reverse supply chain. In this paper, a multi-objective closed-loop supply chain network consisting of multi-level, multi-period, and multi-products is proposed under the set of parameter uncertainties. We formulate the problem as a mixed-integer linear programming model. The model assumes a shortage and a remaining inventory at the end of each period. The first objective function is to minimize the total costs of the network. The second one is to maximize the on-time delivery of the products purchased from suppliers to factories. The third objective is to maximize the quality according to the quality of the products produced in the forward supply chain and those that can be recovered in the reverse supply chain. Another point worth noting in this manuscript is selecting the best supplier. Because choosing the best supplier is one of the most critical decisions that purchasing managers have to make in a supply chain. It is based on different criteria, such as price, quality, customer service, and delivery, discussed in this article. Uncertainty is also considered in the model, and a scenario-based robust optimization approach is used to cope with it. Due to the problem’s multi-objective nature, four exact methods, namely LP-metric, sequential linear goal programming (SLGP), TH approach, and simple additive weighting are used to solve the objective functions. Finally, the most effective method for solving various numerical examples is selected as the best method by the least deviations compared to the other methods; in this paper, the SLGP method is chosen. To illustrate the response to a problem in more detail, some of the SLGP method outputs are presented. The results show the efficiency of the proposed model. Thus, it can be used in a variety of industries whose products are recycled and where the quality of products and the choice of appropriate suppliers are of great importance.

Climate variability and growing competition for limited water resources have made the operation of cascade reservoirs increasingly complex. This study develops a comprehensive system-based multi-objective optimization and evaluation framework that simultaneously integrates five goals: power generation, water supply, ecological protection, navigation reliability, and flood control as a constraint. The framework employs the NSGA-III evolutionary algorithm to address the high-dimensional optimization problem and combines Analytic Hierarchy Process (AHP), Entropy Weight Method, and TOPSIS to integrate subjective expertise with objective data in the evaluation of alternatives. Applied to the lower Jinsha River cascade under wet, normal, and dry hydrological scenarios, the model reveals distinct conflicts between hydropower and ecological or navigational requirements, partial synergies between hydropower and water supply, and tension between ecological and supply demands. Hydrological variability alters these relationships, with wet years intensifying conflicts and dry years heightening supply and ecological pressures. Functional differentiation among reservoirs is also evident, with Baihetan and Xiluodu showing pronounced power–ecology tensions, while Xiangjiaba primarily supports supply and navigation. The study not only advances the theory of multi-objective decision-making in water resources systems but also offers actionable guidance for sustainable reservoir governance and regional development.

Fuzzy portfolio selection has resulted in many researchers to focus on this field. Based on the risk attitudes, this study discusses the risk attitudes in a decision group for portfolio selection. Therefore, we adopt the risk attitudes to describe the experts’ risk preferences and subjective judgments, and then we suppose that the risk seeker considers a higher return for an excess investment based on the selected guaranteed rate of return; the risk averter considers a shortage in investment for the securities whose return rates are smaller than the selected guaranteed rate of return; and finally, the risk neutral pursues the regular return rate. In order to solve the multi-objective return rate functions under the corresponding investment risks, the SMART-ROC weighting method is used to hybridize the multi-objective programming model to a linear programming model for solving the portfolio selection. Finally, we illustrate a numerical example and two risk scenarios to show the optimal portfolio selection under different investment risks. The results show that the proposed model can obtain a more robust portfolio than the compared models under different risk priorities in a decision group.