## 1 Introduction  
Spectrum is generally regulated by governments via a command and control approach. However, this approach has led to underutilization of a spectrum in vast temporal and geographic dimensions as shown in the survey made by the Federal Communications Commission (FCC) [1]. Motivated by this observation, cognitive radio (CR) has been proposed to improve spectrum utilization by dynamically accessing spectrum \"white spaces\" (_i.e._, spectrum holes) without causing harmful interference to primary users [2]. In this dynamic spectrum access framework, CRs are considered as secondary users (SUs) of the spectrum. When a primary user (licensed user) reappears on the current channel, the CRs need to vacate the channel and reestablish a communications link on some other channel to avoid interference to primary users. This process is referred to as spectrum handoff [3]. Target channels play an important role in spectrum handoff design because target channels are the hopes that SUs can resume their unfinished transmissions.  
Based on the decision timing for selecting target channels for spectrum handoff, the target channel selection approaches can be categorized into two kinds: on-demand channel selection for reactive-decision spectrum handoff and predetermined channel selection for proactive-decision spectrum handoff [4]. On-demand channel selection searches target channels after spectrum handoff [5; 6; 7]. This may result in long spectrum handoff delay because an available channel needs to be searched in a wide frequency range. Predetermined channel selection determines target channels before spectrum handoff based on the long-term history information on channel status. It can save spectrum sensing time. This paper focuses on predetermined channel selection. Most prior work on predetermined channel selection selected a single target channel based on some objective, for instance, maximum spectrum lifetime [8], maximum residual idle time [9], maximum idle probability [10], and minimum waiting time [11]. However, in a dynamic spectrum environment, as the pre-selected channel may no longer be available, relying on a single target channel may result in low probability of link maintenance. A better mechanism is to select multiple target channels and try each target channel sequentially. The visiting order of these target channels is crucial to spectrum handoff. In our prior work [12], we designed a target channel visiting order which can realize the minimum probability of spectrum handoff failure. In this paper, we consider spectrum handoff delay as the objective for target channel visiting order design. We propose to use particle swarm optimization (PSO) to solve this combinatorial problem. PSO is an intelligent bio-inspired optimization algorithm that has shown its effectiveness for spectrum sensing, spectrum allocation and link adaptation in cognitive radio in our prior work [13; 14; 15]. To the best of our knowledge, this paper applies PSO for target channel visiting order design for spectrum handoff for the first time. Simulations are conducted to validate the effectiveness of the proposed PSO based algorithm in determining the target channel visiting order in this paper.  
The rest of the paper is organized as follows. In Section 2, we formulate the target channel visiting order design problem for spectrum handoff as a combinatorial optimization problem which aims to minimize spectrum handoff delay. In Section 3, we propose PSO for solving the problem. In Section 4, simulation results are provided and finally in Section 5, conclusions are made.