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Network mobility (NEMO) handles mobility of a set of mobile nodes in an aggregate way using one or more mobile routers. NEMO introduces several advantages, such as reduced signaling, increased manageability, reduced power consumption and conservation of bandwidth when compared to individual host mobility. NEMO Basic Support Protocol (BSP), the IETF standard for NEMO, suffers from a number of limitations, like inefficient route and increased handoff latency. Most of the recent research efforts on NEMO have concentrated on solving the problem of inefficient route resulting in several route optimization schemes to solve the problem. To choose a route optimization scheme, it is very important to have a quantitative comparison of the available route optimization schemes. The objective of this article is to survey, classify and compare the route optimization schemes proposed in the literature over the last five years. We classify the schemes based on the basic approach for route optimization, and compare the schemes based on protocol overhead, such as header overhead, amount of signalling, and memory requirements. We conclude that performance of the classes of schemes has to be evaluated under criteria such as available bandwidth, topology of the mobile network and mobility type.