Optimality and duality for complex multi-objective programming

<p style='text-indent:20px;'>We consider a complex multi-objective programming problem (CMP). In order to establish the optimality conditions of problem (CMP), we introduce several properties of optimal efficient solutions and scalarization techniques. Furthermore, a certain parametric dual model is discussed, and their duality theorems are proved.</p>

A parametric approach to fuzzy multi-objective linear fractional program: An alpha cut based method

In the multi-objective programming problem (MOPP), finding an efficient solution is challenging and partially encompasses some difficulties in practice. This paper presents an approach to address the multi-objective linear fractional programing problem with fuzzy coefficients (FMOLFPP). In the method, at first, the concept of α - cuts is used to change the fuzzy numbers into intervals. Therefore, the fuzzy problem is further changed into an interval-valued linear fractional programming problem (IVLFPP). Afterward, this problem is transformed into a linear programming problem (LPP) using a parametric approach and the weighted sum method. It is proven that the solution resulted from the LPP is at least a weakly ɛ - efficient solution. Two examples are given to illustrate the method.

Stochastic Multi-Objective Programming Problem: A Two-Phase Weighted Coefficient Approach

This paper deals with multi-objective stochastic linear programming problem. The problem is considered by introducing the coefficients of the decision variables and the right-hand-side parameters in the constraints as normal random variables. A method for converting the problem into its deterministic problem is proposed and hence two- phase approach with equal weights is proposed for finding an efficient solution. The advantages of the approach are: as weights which is positive, not necessarily equal and generate an efficient solution. A numerical example is given to illustrate the suggested methodology.

Research on a Bi-Level Collaborative Optimization Method for Planning and Operation of Multi-Energy Complementary Systems

Multi-energy complementary systems (MCSs) are complex multilevel systems. In the process of system planning, many aspects—such as power planning, investment cost, and environmental impact—should be considered. However, different decision makers tend to have different levels of control objectives, and the multilevel problems of the system need to be solved effectively with comprehensive judgment. Therefore, based on the terminal MCS energy structure model, the optimization method of MCS planning and operation coordination, considering the influence of planning and operation in the system’s life cycle, is studied in this paper. Consequently, the research on the collaborative optimization strategy of MCS construction and operation was carried out based on the bi-level multi-objective optimization theory in this paper. Considering the mutual restraint and correlation between system construction and operation in practical engineering, a bi-level optimization model for collaborative optimization of MCS construction and operation was constructed. To solve the model effectively, the existing non-dominated sorting genetic algorithm III (NSGA-III) was improved by the authors on the basis of previous research, which could enhance the global search ability and convergence speed of the algorithm. To effectively improve and strengthen the reliability of energy supply, and increase the comprehensive energy utilization of the system, the effects of carbon transaction cost and renewable energy penetration were considered in the optimization process. Based on an engineering example, the bi-level model was solved and analyzed. It should be noted that the optimization results of the model were verified to be applicable and effective by comparison with the single-level multi-objective programming optimization. The findings of this paper could provide theoretical reference and practical guidance for the planning and operation of MCSs, making them significant for social application.

Stability of Parametric Intuitionistic Fuzzy Multi-Objective Fractional Transportation Problem

In this study, a parametric intuitionistic fuzzy multi-objective fractional transportation problem (PIF-MOFTP) is proposed. The current PIF-MOFTP has a single-scalar parameter in the objective functions and an intuitionistic fuzzy supply and demand. Based on the (α,β)-cut concept a parametric (α,β)-MOFTP is established. Then, a fuzzy goal programming (FGP) approach is utilized to obtain (α,β)-Pareto optimal solution. We investigated the stability set of the first kind (SSFK) corresponding to the solution by extending the Kuhn-Tucker optimality conditions of multi-objective programming problems. An algorithm to crystalize the progressing SSFK for PIF-MOFTP as well as an illustrative numerical example is presented.

An Extensive Study for a Wide Utilization of Green Architecture Parameters in Built Environment Based on Genetic Schemes

Recently, green structures turned into a huge path to an economic future. Green building outlines include finding the harmony between agreeable home living and a maintainable environment. Furthermore, the usage of modern technologies is seen as part of greener construction changes to make the urban environment more viable. This paper introduces an exhaustive state-of-art review and current practices to look for the ideal green arrangement’s models, procedures, and parameters utilizing the genetic algorithms innovations to help for settling on the most ideal choice from various options. The integrated Genetic Algorithm (GA) along with the Nondominated Sorting Genetic Algorithm strategy GA-NSGA-II is considered to be more accurate for predicting a viable future. The above methodology is widely relevant for its humility, ease of execution, and enormous durability. Besides other approaches, the GA was incorporated as well as the Neural Network (NN), Simulated Annealing (SA), Fuzzy Set theory, decision-making multicriteria, and multi-objective programming. The most fashionable methods are moderately the embedded GA-NSGA-II approaches. This paper gives an outline of the capability of GA-based MOO in supporting the advancement of methodologies of the techniques and parameters to find the best solution for the building decision-making cycle. The GA combined schemes can fulfill all the requirements for finding the optimality in the case of multi-objective problem-solving.

Research on Airport Scheduling of FGAP Multi-Objective Programming Model Based on Uncertainty Theory

Based on the current background of airport management and flight-gate scheduling in China, this paper takes Shanghai Pudong International Airport’s flight number of the rising and landing aircraft in a certain day as the research object, and it establishes an uncertain FGAP (Flight-Gate Assignment Problem) multi-objective programming model under the framework of uncertainty theory. Using genetic algorithm to solve the model, the specific flight-gate assignment scheduling plan is given. The research results show that the model in this paper can effectively alleviate the problems, such as unbalanced flight-gate allocation and excessive operating pressure of a single gate, in the conventional model, and make the allocation and scheduling more reasonable and efficient. Finally, we give the future application of uncertainty theory in finance and management, as well as the prospect of combining it with symmetry in physics.

An integrated approach to site selection for a big data center using PROMETHEE-MCGP methodology

In today’s economy, information technology (IT) is vitally important, and the increasing use of the Internet, telecommunications services, and internal IT networks in organizations have led to rapid growth in the demands on big data processing. In general, site selection is a fundamental part of the design of a big data center (BDC), and a poor site decision can affect the sustainability of the facility. To construct a comprehensive assessment framework for a BDC, the following three categories of indicators are determined based on the “Specification for Design of Data Center” in GB50174-2017 of China: economic factors, natural climate environment factors, and energy resources factors. After explaining the rationality of choosing these indicators in detail, an integrated method that combines the multi-criteria decision-making (MCDM) method and the multi-choice goal programming (MCGP) model is proposed. The proposed approach uses two phases to conduct the decision procedure. First, the preference ranking organization method for enrichment evaluation (PROMETHEE) method is applied to evaluate the economic factors. Then, the evaluation results are added to the MCGP model as one of the goals of multi-objective programming. Second, the remaining five sub-indicators and the evaluation results generated from the first phase are formulated as a complete MCGP model. Finally, an empirical study on the site selection for the BDC is implemented based on the proposed method. The result shows that Guiyang is the most suitable place for locating a BDC in China.

Aircraft Sequencing and Scheduling in Parallel-Point Merge Systems for Multiple Parallel Runways

The Point Merge System (PMS) is one of the approaches that offer systematic sequencing in terminal maneuver area (TMA) which was developed at the EUROCONTROL Experimental Centre in 2006. The Parallel-Point Merge System (P-PMS) is used in TMAs with high air traffic density as a combination of two PMSs with opposite directions. However, it is difficult to optimize arrival sequences in such a system because of the additional separation requirements at common points as well as at merge points. Additionally, it is important to operate at maximum efficiency with parallel runway systems when using the runway reassignment process. Reassigning arriving/departing aircraft to a different runway, however, can significantly affect delays and fuel consumption depending on the difference in taxi-in/out times. This effect is overlooked in most aircraft sequencing and scheduling optimization studies with PMS. This study proposes single and multi-objective programming models for a TMA with P-PMS to minimize total fuel consumption, total flight time, and total delay including taxi-in/out times. The models were implemented on the current layout of Istanbul Airport having two PMS with two merge points, three common points, and five parallel runways. The considered traffic scenarios included both dependent and independent runway operations for mixed arrival–departure sequences. The results revealed that arrival–departure sequencing considering taxi-in/out times resulted in shorter delays up to 77.5% and low level of fuel consumption up to 8.7%.