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In metropolitan cities, it is very complicated to govern the optimum routes for garbage collection vehicles due to high waste production and very dense population. Furthermore, wrongly designed routes are the source of wasting time, fuel and other resources in the collection of municipal trash procedure. The Vehicle Routing Problem (VRP) published between 2011 and 2023 was systematically analysed. The majority of the surveyed research compute the waste collecting problems using metaheuristic approaches. This manuscript serves two purposes: first, categorising the VRP and its variants in the field of waste collection; second, examining the role played by most of the metaheuristics in the solution of the VRP problems for a waste collection. Three case study of Asia continent has been analysed and the results show that the metaheuristic algorithms have the capability in providing good results for large-scale data. Lastly, some promising paths ranging from highlighting research gap to future scope are drawn to encourage researchers to conduct their research work in the field of waste management route problems. [ABSTRACT FROM AUTHOR]

The slime mould algorithm may not be enough and tends to trap into local optima, low population diversity, and suffers insufficient exploitation when real-world optimization problems become more complex. To overcome the limitations of SMA, the Gaussian mutation (GM) with a novel strategy is proposed to enhance SMA and it is named as SMA-GM. The GM is used to increase population diversity, which helps SMA come out of local optima and retain a robust local search capability. Additionally, the oscillatory parameter is updated and incorporated with GM to set the balance between exploration and exploitation. By using a greedy selection technique, this study retains an optimal slime mould position while ensuring the algorithm's rapid convergence. The SMA-GM performance was evaluated by using unconstrained, constrained, and CEC2022 benchmark functions. The results show that the proposed SMA-GM has a more robust capacity for global search, improved stability, a faster rate of convergence, and the ability to solve constrained optimization problems. Additionally, the Wilcoxon rank sum test illustrates that there is a significant difference between the optimization outcomes of SMA-GM and each compared algorithm. Furthermore, the engineering problem such as industrial refrigeration system (IRS), optimal operation of the alkylation unit problem, welded beam and tension/compression spring design problem are solved, and results prove that the proposed algorithm has a better optimization efficiency to reach the optimum value. [ABSTRACT FROM AUTHOR]

This manuscript explores the Generalized Restricted Four-Body Problem within the context of radiation pressure, the albedo effect, oblateness, and a disc-like structure that orbits around the primary bodies. We have considered that one of the primaries is a bigger primary, and the rest of the two smaller primaries are of equal masses, in which one of the smaller primaries is considered as a black body. Moreover, the perturbing forces by the effect of radiation pressure and oblateness are considered in the bigger primary. The effect of albedo and oblateness due to the second smaller primary is also taken into count. This study yields nine equilibrium points corresponding to various parameter values, including three collinear and six non-collinear equilibria. We conduct an analysis of the equilibrium points, their linear stability, and the motion around them. In the context of the considered parameter set, certain collinear equilibrium points exhibit stability, while others are unstable. Additionally, most of the non-collinear equilibrium points display linear stability. We also investigate variations in Jacobi's constant and the positions of existing equilibrium points caused by the albedo and disc effects. It is found that the value of Jacobi constant C L j decreases with an increase in the mass parameter μ at the collinear points, which results in an expansion in the prohibited region. The inhibited zone of motion of the infinitesimal body is shown for different sets of parameters. [ABSTRACT FROM AUTHOR]

In this paper, we studied the oblateness and segment-length effect on the dynamics of the restricted 2+2 body problem. It consists of two primaries and two infinitesimal bodies, assuming the bigger primary is an oblate spheroid, and the smaller primary is elongated. The effect of oblateness and segment-length on the equilibrium points are discussed. Variations of equilibrium points of this model compared to the equilibrium points of the classical CRTBP with different parameters are performed. Equilibrium points of some realistic planetary systems, i.e. Jupiter-Amalthea, Pluto-Hydra and Saturn-Prometheus system, are computed. Periodic orbits and their orbital periods are discussed analytically in the Saturn-Prometheus system with binary satellites. Poincaré Surfaces of Section is depicted in the Pluto-Hydra system to elaborate the periodic orbits when the position of one infinitesimal is known. [ABSTRACT FROM AUTHOR]

The main purpose of present work is to find approximated periodic solution in the compact form of the circular Sitnikov restricted four-body problem by getting liberate of the secular terms using the Multiple Scale Method. Also, we found numerical solutions of the prospective model and compared it with analytically obtained solutions for bounded small amplitude ( z (0) ≤ 0.3 ). However, its solution goes away from the actual motion when z (0) > 0.3 . We observed that the motion obtained by both methods is well ordered and periodical, whenever the infinitesimal body starts moving close to the primary's common center of mass. Whereas, the motion starts a long way from the center of mass, the second-order approximation results always give a periodic solution and numerical result may not present periodic solution for long time. The initial conditions play most important part in numerical as well as logical system. The Multiple Scale Method is more realistic and accurate than the numerical because it always provide commitment that the motion will be periodic all time. We also discussed and compared an exact solution of this problem with MacMillan problem. [ABSTRACT FROM AUTHOR]

In this paper, the effect of radiation pressure force on formation of the nominal halo orbit around the collinear point L 1 is estimated in the framework of Sun–Earth system. Using Lindstedt–Poincaré technique, the periodic solutions up to third-order approximation are computed. Further, the Fourier series solutions of nominal halo orbit are also evaluated. With considering the radiation pressure force effect, the proposed analysis in this work can be used to design a trajectory for spacecraft moving in more realistic system. [ABSTRACT FROM AUTHOR]

In this paper, we determine the effect of radiation pressure, Poynting–Robertson drag and solar wind drag on the Sun–(Earth–Moon) restricted three-body problem. Here, we take the larger body of the Sun as a larger primary, and the Earth+Moon as a smaller primary. With the help of the perturbation technique, we find the Lagrangian points, and see that the collinear points deviate from the axis joining the primaries, whereas the triangular points remain unchanged in their configuration. We also find that Lagrangian points move towards the Sun when radiation pressure increases. We have also analysed the stability of the triangular equilibrium points and have found that they are unstable because of the drag forces. Moreover, we have computed the halo orbits in the third-order approximation using the Lindstedt–Poincaré method and have found the effect of the drag forces. According to this prevalence, the Sun–(Earth–Moon) model is used to design the trajectory for spacecraft travelling under drag forces. [ABSTRACT FROM AUTHOR]

In this paper, the approximated periodic solutions of the circular Sitnikov restricted four–body problem (RFBP) were constructed using the Lindstedt–Poincaré method, by removing the secular terms, and compared with numerical solution. It can be observed that, in the numerical as well as approximated solutions patterns, the initial conditions are important. In the sense of a numerical solution, the motion is periodic in a certain interval, but beyond this interval, the motion is not periodic. But, the Lindstedt–Poincaré method constantly gives regular and periodic motion all time. Finally, we observed that the solution obtained by the Lindstedt–Poincaré method gives the true motion of the circular Sitnikov RFBP and the fourth approximate solution has more accuracy than the first, second, and third approximate solutions. [ABSTRACT FROM AUTHOR]

The relative motion of an outline of the rendezvous problem has been studied by assuming that the chief satellite is in circular symmetric orbits. The legitimacy of perturbation techniques and nonlinear relative motion are investigated. The deputy satellite equations of motion with respect to the fixed references at the center of the chief satellite are nonlinear in the general case. We found the periodic solutions of the linear relative motion satellite and for the nonlinear relative motion satellite using the Lindstedt–Poincaré technique. Comparisons among the analytical solutions of linear and nonlinear motions and the obtained solution by the numerical integration of the explicit Euler method for both motions are investigated. We demonstrate that both analytical and numerical solutions of linear motion are symmetric periodic. However, the solutions of nonlinear motion obtained by the Lindstedt–Poincaré technique are periodic and the numerical solutions obtained by integration by using explicit Euler method are non-periodic. Thus, the Lindstedt–Poincaré technique is recommended for designing the periodic solutions. Furthermore, a comparison between linear and nonlinear analytical solutions of relative motion is investigated graphically. [ABSTRACT FROM AUTHOR]

• The effect of the created perturbation by the Moon motion in the Moon perturbed Sun–Earth system are analyzed. • The Lagrangian points and zero velocity curves in the Moon perturbed Sun–Earth system are determined. • The motion of infinitesimal mass in the neighborhood of the equivalent equilibria of the triangular points are obtained. • The first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of triangular equilibrium points are estimated. In this paper, we have considered that the Moon motion around the Earth is a source of a perturbation for the infinitesimal body motion in the Sun–Earth system. The perturbation effect is analyzed by using the Sun–Earth–Moon bi–circular model (BCM). We have determined the effect of this perturbation on the Lagrangian points and zero velocity curves. We have obtained the motion of infinitesimal body in the neighborhood of the equivalent equilibria of the triangular equilibrium points. Moreover, to know the nature of the trajectory, we have estimated the first order Lyapunov characteristic exponents of the trajectory emanating from the vicinity of the triangular equilibrium point in the proposed system. It is noticed that due to the generated perturbation by the Moon motion, the results are affected significantly, and the Jacobian constant is fluctuated periodically as the Moon is moving around the Earth. Finally, we emphasize that this model could be applicable to send either satellite or telescope for deep space exploration. [ABSTRACT FROM AUTHOR]

In this paper, we have analysed the dynamical behavior of the restricted three-body problem having elongated smaller primary with disc-like structure. We discuss the zero-velocity curve, equilibrium points, and their stability by considering the different segment-length of the elongated primary and mass ratio of the primary. The impacts of disc-like structure and elongated primary body are observed on the equilibrium points and their stability analysis. We demonstrate that all collinear equilibrium points are unstable by varying the mass parameter μ and the segment length l. Further, the critical point for mass parameter μ c at non-collinear equilibrium points is calculated. Furthermore, we emphasize our discussion through an example by taking mass parameter μ = 0.01 < μ c and segment-length l = 0.01. Finally, we conclude that the proposed problem is a credible model for describing the infinitesimal body's motion in a disc-like structure with an elongated smaller primary. [ABSTRACT FROM AUTHOR]

This work investigates the dynamics of the modified circular restricted three-body problem. The triaxial shape of the massive body, a modified gravitational parameter, quantum correction effect, radiation pressure and small perturbations in the Coriolis and centrifugal forces are all taken into account. The impact of the considered parameters in the equilibrium points and their linear stability is studied. Some new significant results in the critical mass parameter, μc\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mu _c$$\end{document}, are observed in the presence of perturbing parameters. It is found that the critical mass parameter, μc\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\mu _c$$\end{document}, increases in the presence of modified gravitational potential, and it slightly decreases due to the quantum correction effect. Analytical construction of periodic orbits around the collinear equilibrium points is performed. Additionally, analysis of the impact of perturbations on the shape of these periodic orbits is conducted. [ABSTRACT FROM AUTHOR]

Due to lack of specification and solubility of drug molecules, patients have to take high doses of the drug to achieve the desired therapeutic effects for the treatment of diseases. To solve these problems, there are various drug carriers present in the pharmaceuticals, which can used to deliver therapeutic agents to the target site in the body. Mesoporous silica materials become known as a promising candidate that can overcome above problems and produce effects in a controllable and sustainable manner. In particular, mesoporous silica nanoparticles (MSNs) are widely used as a delivery reagent because silica possesses favorable chemical properties, thermal stability, and biocompatibility. The unique mesoporous structure of silica facilitates effective loading of drugs and their subsequent controlled release of the target site. The properties of mesoporous, including pore size, high drug loading, and porosity as well as the surface properties, can be altered depending on additives used to prepare MSNs. Active surface enables functionalization to changed surface properties and link therapeutic molecules. They are used as widely in the field of diagnosis, target drug delivery, bio-sensing, cellular uptake, etc., in the bio-medical field. This review aims to present the state of knowledge of silica containing mesoporous nanoparticles and specific application in various biomedical fields. [ABSTRACT FROM AUTHOR]

• The properties of Sitnikov motion are analyzed. • The multiple scales method is used to remove secular terms. • The periodic solution of the circular Sitnikov problem is found. • Comparisons among a numerical solution and the solutions provide by the multiple scales method are investigated. The objective of this paper is to find periodic solutions of the circular Sitnikov problem by the multiple scales method which is used to remove the secular terms and find the periodic approximated solutions in closed forms. Comparisons among a numerical solution (NS), the first approximated solution (FA) and the second approximated solution (SA) via multiple scales method are investigated graphically under different initial conditions. We observe that the initial conditions play a vital role in the numerical and approximated solutions behaviour. The obtained motion is periodic, but the difference of its amplitude is directly proportional with the initial conditions. We prove that the obtained motion by the numerical or the second approximated solutions is a regular and periodic, when the infinitesimal body starts its motion from a nearer position to the common center of primaries. Otherwise when the start point distance of motion is far from this center, the numerical solution may not be represent a periodic motion for along time, while the second approximated solution may present a chaotic motion, however it is always periodic all time. But the obtained motion by the first approximated solution is periodic and has regularity in its periodicity all time. Finally we remark that the provided solutions by multiple scales methods reflect the true motion of the Sitnikov restricted three–body problem, and the second approximation has more accuracy than the first approximation. Moreover the solutions of multiple scales technique are more realistic than the numerical solution because there is always a warranty that the motion is periodic all time. [ABSTRACT FROM AUTHOR]