This paper presents the development of a multilevel optimization framework for the design and selection of departure routes, and the distribution of aircraft movements among these routes, while taking the sequence and separation requirements for aircraft on runways and along selected routes into account. The main aim of the framework is to minimize aircraft noise impact on communities around an airport, and the associated fuel consumption. The proposed framework features two consecutive steps. In the first step, for each given Standard Instrument Departure (SID), multi-objective trajectory optimization is utilized to generate a comprehensive set of possible alternative routes. The obtained set is subsequently used as input for the optimization problem in the second step. In this step, the selection of routes for each SID and the distribution of aircraft movements among these routes are optimized simultaneously. To ensure the feasibility of optimized solutions for an entire operational day, the sequence and separation requirements for aircraft on runways and along selected routes are included in this second phase. In order to address these issues, three novel techniques are developed and added to a previously developed multilevel optimization framework, viz., a runway assignment model, a conflict detection algorithm, and a rerouting technique. The proposed framework is applied to a realistic case study at Amsterdam Airport Schiphol in the Netherlands, in which 599 departure flights and 13 different SIDs are considered. The optimization results show that the proposed model can offer conflict-free solutions, one of which can lead to a reduction in the number of people annoyed of up to 21%, and a reduction in fuel consumption of 8% relative to the reference case solution.

In this article, we present the development of a two-step optimization framework to deal with the design and selection of aircraft departure routes and the allocation of flights among these routes. The aim of the framework is to minimize cumulative noise annoyance and fuel burn. In the first step of the framework, multi-objective trajectory optimization is used to compute and store a set of routes that will serve as inputs in the second step. In the second step, the selection of routes from the sets of pre-computed optimal routes and the optimal allocation of flights to these routes are conducted simultaneously. To validate the proposed framework, we also conduct an analysis involving an integrated (one-step) approach, in which both trajectory optimization and route allocation are formulated as a single optimization problem. A comparison of both approaches is then performed, and their advantages and disadvantages are identified. The performance and capabilities of the present framework are demonstrated using a case study at Amsterdam Airport Schiphol in The Netherlands. The numerical results show that the proposed framework can generate solutions which can achieve a reduction in the number of people annoyed of up to 31% and a reduction in fuel consumption of 7.3% relative to the reference case solution.

The paper first investigates the influence of daily mobility of population on evaluation of aircraft noise effects. Then, a new air traffic assignment model that considers this activity is proposed. The main objective is to reduce the number of people affected by noise via lowering as much as possible the noise exposure level L _den of individuals or groups of people who commute to the same locations during the day. It is hereby intended to reduce the noise impact upon individuals rather than to reduce the impact in particular – typically densely populated – areas. However, sending aircraft farther away from populated regions to reduce noise impact may increase fuel burn, thus affecting airline costs and sustainability. Therefore, a multi-objective optimization approach is utilized to obtain reasonable solutions that comply with overall air transport sustainability. The method aims at generating a set of solutions that provide proper balance between noise annoyance and fuel consumption. The reliability and applicability of the proposed method are validated through a real case study at Belgrade airport in Serbia. The investigation shows that there is a difference between the number of people annoyed (NPA) evaluated based on the census data and the NPA evaluated based on the mobility data. In addition, these numbers differ significantly across residential locations. The optimal results show that the proposed model can offer a considerable reduction in the NPA, and in some cases, it can gain up to 77%, while maintaining the same level of fuel consumption compared with the reference case.

This paper proposes an effective couple method for solving reliability-based multi-objective optimization problems of truss structures with static and dynamic constraints. The proposed coupling method integrates a single-loop deterministic method (SLDM) into the nondominated sorting genetic algorithm II (NSGA-II) algorithm to give the so-called SLDM-NSGA-II. Thanks to the advantage of SLDM, the probabilistic constraints are treated as approximating deterministic constraints. And therefore the reliability-based multi-objective optimization problems can be transformed into the deterministic multi-objective optimization problems of which the computational cost is reduced significantly. In these reliability-based multi-objective optimization problems, the conflicting objective functions are to minimize the weight and the displacements of the truss. The design variables are cross-section areas of the bars and contraints include static and dynamic constraints. For reliability analysis, the effect of uncertainty of parameters such as force, added mass in the nodes, material properties and cross-section areas of the bars are taken into account. The effectiveness and reliability of the proposed method are demonstrated through three benchmark-type truss structures including a 10-bar planar truss, a 72-bar spatial truss and a 200-bar planar truss. Moreover, the influence of parameters on the reliability-based Pareto optimal fronts is also carried out.

This paper presents a new multi-objective optimization formulation for the design and allocation of optimal aircraft departure routes. In the considered problem – besides two conventional objectives based on cumulative noise criteria and fuel burn – a new objective considering the flight frequency is introduced. Moreover, to take advantage of the combination of designing new routes and allocating flights to these routes, two different routes are considered simultaneously, and the distribution of flights over these two routes is addressed in parallel. Then, a new version of the so-called MOEA/D optimization algorithm is developed to solve the formulated optimization problem. Two different case studies, one at Rotterdam The Hague Airport and one at Amsterdam Airport Schiphol in The Netherlands, are carried out to evaluate the reliability and applicability of the proposed approach. The obtained results reveal that the proposed approach can provide solutions which can balance more effectively the concerned metrics such as the number of annoyed people, fuel burn, number of people exposed to certain noise levels, and number of aircraft movements which people are subjected to.

The multi-objective evolutionary algorithm based on decomposition (MOEA/D) has been recognized as a promising method for solving multi-objective optimization problems (MOPs), receiving a lot of attention from researchers in recent years. However, its performance in handling MOPs with complicated Pareto fronts (PFs) is still limited, especially for real-world applications whose PFs are often complex featuring, e.g., a long tail or a sharp peak. To deal with this problem, an improved MOEA/D (named iMOEA/D) that mainly focuses on bi-objective optimization problems (BOPs) is therefore proposed in this paper. To demonstrate the capabilities of iMOEA/D, it is applied to design optimization problems of truss structures. In iMOEA/D, the set of the weight vectors defined in MOEA/D is numbered and divided into two subsets: one set with odd-weight vectors and the other with even-weight vectors. Then, a two-phase search strategy based on the MOEA/D framework is proposed to optimize their corresponding populations. Furthermore, in order to enhance the total performance of iMOEA/D, some recent developments for MOEA/D, including an adaptive replacement strategy and a stopping criterion, are also incorporated. The reliability, efficiency and applicability of iMOEA/D are investigated through seven existing benchmark test functions with complex PFs and three optimal design problems of truss structures. The obtained results reveal that iMOEA/D generally outperforms MOEA/D and NSGA-II in both benchmark test functions and real-world applications.

Parametric studies on the optimization of baffles on vibration suppression of partially filled tanks coupled by structure have been widely conducted in literature. However, few studies focus on the effect of the position of the baffles on fluid flow stratification and dampening the motion. In the present study, a numerical investigation, an engineering analysis, and optimal design study were performed to determine the effect of external flow on circular obstacle baffles performance on suppressing the vibrations of coupled structure in a closed basin. The single degree of freedom model (mass-spring-damper) is used to model the structure that holds the tank. The coupled system is released from an initial displacement without a velocity. The governing mass, turbulent Navier-Stokes momentum, volume of fluid, and one degree of freedom structure equations are solved by the Pressure-Implicit with Splitting of Operators algorithm in fluids and Newmark method in structure. Based on a detailed study of transient structure motion coupled with sloshing dynamics, the optimal baffle location was achieved. Optimal position of the baffle and its width are systematically obtained with reference to the quiescent free surface.

The paper deals with the multi-objective optimization problems of laminated composite beam structures. The objective function is to minimize the weight of the whole laminated composite beam and maximize the natural frequency. In particular, the simultaneous use of all the design variables such as fiber volume fractions, thickness and fiber orientation angles of layers is conducted, in which the fiber volume fractions are taken as continuous design variables with the constraint on manufacturing process while the thickness and fiber orientation angles are considered as discrete variables. The beam structure is subjected to the constraint in the natural frequency which must be greater than or equal to a predetermined frequency. For free vibration analysis of the structure, the finite element method is used with the two-node Bernoulli-Euler beam element. For solving the multi-objective optimization problem, the nondominated sorting genetic algorithm II (NSGA-II) is employed. The reliability and effectiveness of the proposed approach are demonstrated through three numerical examples by comparing the current results with those of previous studies in the literature.

A cell-based smoothed discrete shear gap method (CS-DSG3) based on the first-order shear deformation theory was recently proposed for static and dynamics analyses of Mindlin plates. In this paper, the CS-DSG3 is extended for analysis and active vibration control of the functionally graded material (FGM) plates integrated with piezoelectric sensors and actuators. In the piezoelectric FGM plates, the properties of core material are assumed to be graded through the thickness by the power law distribution while the electric potential is assumed to be a linear function through the thickness of each piezoelectric sub-layer. A closed-loop control algorithm based on the displacement and velocity feedbacks is used to control static deflection and active vibration of piezoelectric FGM plates. Several numerical examples are conducted to demonstrate the reliability and accuracy of the proposed method compared to other available numerical results.