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Combinatorial optimization problems are often considered NP-hard problems in the field of decision science and the industrial revolution. As a successful transformation to tackle complex dimensional problems, metaheuristic algorithms have been implemented in a wide area of combinatorial optimization problems. Metaheuristic algorithms have been evolved and modified with respect to the problem nature since it was recommended for the first time. As there is a growing interest in incorporating necessary methods to develop metaheuristics, there is a need to rediscover the recent advancement of metaheuristics in combinatorial optimization. From the authors’ point of view, there is still a lack of comprehensive surveys on current research directions. Therefore, a substantial part of this paper is devoted to analyzing and discussing the modern age metaheuristic algorithms that gained popular use in mostly cited combinatorial optimization problems such as vehicle routing problems, traveling salesman problems, and supply chain network design problems. A survey of seven different metaheuristic algorithms (which are proposed after 2000) for combinatorial optimization problems is carried out in this study, apart from conventional metaheuristics like simulated annealing, particle swarm optimization, and tabu search. These metaheuristics have been filtered through some key factors like easy parameter handling, the scope of hybridization as well as performance efficiency. In this study, a concise description of the framework of the selected algorithm is included. Finally, a technical analysis of the recent trends of implementation is discussed, along with the impacts of algorithm modification on performance, constraint handling strategy, the handling of multi-objective situations using hybridization, and future research opportunities.

NOMENCLATURE A z launch azimuth (deg) d T distance of thrust location from vehicle longitudinal axis (m) h Altitude of separation (km) I Inertia tensor (kg-m 2 ) l CG distance of CG from nose tip along longitudinal axis (m) l T distance of thrust location from nose tip along longitudinal axis(m) m M , m S mass of the ongoing and spent bodies (kg) m propellant mass flow rate (kgs -1 ) R E , R P , R S Earth's equatorial radius, polar radius, radius at the surface (km) r, q, p body angular rates yaw, pitch and roll (deg/s) r I position vector in ECI frame (X I , Y I , Z I ) (m) r CG position vector of the body CG offset (m) r s spring location from CG (m) r T distance of thrust location from main body CG (m) t time (s) T thrust (N) v velocity in the body frame (ms -1 ) X, Y, Z body axes yaw, pitch and roll δ spring mounting azimuth angle (deg) ABSTRACTThis paper presents a systematic formulation for the simulation of rigid body dynamics, including the short period dynamics, inherent to stage separation and jettisoning parts of a satellite launcher. This also gives a review of various types of separations involved in a launch vehicle. The problem is sufficiently large and complex; the methodology involves iterations at successively lower levels of abstraction. The best choice to tackle such problems is to use stateof-the-art programming technique known as object oriented programming. The necessary classes have been identified to represent various entities in the launch vehicle separation process (e.g., gravity, aerodynamics, propulsion and separation mechanisms etc.). Simple linkages are modelled with suitable objects. This approach helps the designer to simulate a launch vehicle separation dynamics and also to analyse separation system performance. To examine the influence of the design variables on the separating bodies, statistical analyses have been performed on the upper stage separation process and pull out of ongoing stage nozzle from the spent stage of a multistage rocket carrier using retro rockets.

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