The Traveling Salesman Problem (TSP): A Spatial Navigation Task for Rats

Jena Hales Jena Hales
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Animal Cognition
Nov 2015



The Traveling Salesman Problem (TSP) is a behavioral test used to measure the efficiency of spatial navigation. It is an optimization problem, in which a number of baited targets are placed in an arena, and as the subject travels between the targets, the route is recorded and compared to chance and optimal routes. The TSP is appealing for the study of learning, memory, and executive function in nonhuman animals because the memory requirements can easily be modified with minor adjustments to task parameters. In the standard version of the task, rats are initially pre-trained to forage for bait in the arena. Once the animals consistently retrieve the bait, they are tested with a set of novel target configurations, and their behavior is recorded. The videos are then scored to produce several measures of performance.

Keywords: Spatial navigation (空间导航), Cognition (认识), Planning (规划), Working memory (工作记忆), Executive function (执行功能), Optimization (优化)


The Traveling Salesman Problem (TSP) is a spatial navigation task in which participants are asked to select the shortest possible route that visits each target in a spatial array. This task has been of interest to computer and cognitive scientists for some time (Best, 2006), but has more recently been studied from the perspective of comparative psychology (e.g., de Jong et al., 2011; Gibson et al., 2012; Baron et al., 2015). Humans are inexplicably good at finding solutions to this problem – despite its mathematical intractability, human participants can rapidly and easily produce solutions that are nearly optimal (MacGregor et al., 2000). One possible explanation for this high level of performance is that the task capitalizes on evolved processes used for natural behaviors like foraging (Blaser and Ginchansky, 2012; Blaser and Wilber, 2013). We were therefore interested in the mechanisms by which non-human animals complete the task (Bellizzi et al., 2015; Goldsteinholm and Blaser, 2015).

Although human participants typically use either a computer or paper and pencil to solve the TSP, we used the radial arm maze as a model to design a comparable task for rats (Blaser and Ginchansky, 2012). The task has not been widely used with nonhuman animals, but already several variant procedures exist. For example, Bures et al. (1992) used a TSP design in which animals were not rewarded until after all targets had been visited, with subjects trained on the same target configurations for 10 consecutive days prior to testing. Miyata et al. (2010) required pigeons to peck at a touch-screen in order to receive a food reward at the end of the test. Important variations across procedures involve whether food is available at each target or only at the end, whether animals are exposed to a specific spatial configuration more than once, and the scale of the spatial arena relative to the body size of the animal. We selected a protocol in which novel configurations are tested to reduce the degree to which performance relies on long-term spatial memory, and in which a relatively large arena encourages distance minimization.

Materials and Reagents

  1. Rats
  2. Ethanol
  3. Targets
    1. Semi-transparent purple vinyl index card dividers (Oxford Esselte, catalog number: 73153 )
    2. Rodent food dishes
    3. Sterilized bottle caps
    Targets are pieces of plastic cut into 2” diameter circles. We use semi-transparent purple vinyl index card dividers by Oxford Esselte, but in the past have successfully used both rodent food dishes and sterilized bottle caps. The flat vinyl targets are appealing because they are simple to clean, and are less attractive to the rats to explore and carry, compared to dishes or caps. Whichever targets are employed, the targets used in a single experiment should be identical to each other.
  4. Bait
    1. Froot Loops® cereal (or a generic equivalent)
    2. Fruity Pebbles® or Cocoa pebbles® (one pebble per target)
    For bait, we use Froot Loops® cereal (or a generic equivalent) broken into quarter pieces (one quarter per target), or Fruity Pebbles® or Cocoa pebbles® (one pebble per target). All work equally well.
  5. Configuration Templates
    During pre-training, targets are placed randomly and do not require templates (see Procedure). In the test trials, however, the spatial arrangement of targets is critical. For this purpose, we create a template out of posterboard which is cut to fill the entire arena floor. Holes (approx. 2.5” diameter) are cut in the posterboard where the targets will be placed. Before each trial, the template is placed in the open field, and targets are then placed in the holes. The template can then be lifted out of the open field, leaving the targets located precisely in the arena.


  1. Open Field Arena (Figure 1)
    The animals are tested in a 90 x 90 x 75 cm open field arena made of plywood. It is painted white, with a black grid painted on the floor. Any large standard open field should work, although the same type should be used consistently since the arena size and shape are expected to affect task performance measures.

    Figure 1. Photo of the open field arena with ten baited targets and a rat

  2. Stopwatch
    A simple stopwatch (minutes/seconds) is used to time the animals in the task.
  3. Video Camera
    A video camera recording high-definition video files to SD card is used to record all trials. The video camera resolution must be sufficient to see (1) whether a piece of bait has been removed from the target in low lighting conditions, and (2) whether the vibrissa (whiskers) of the animal contact the target.
  4. White Noise generator (e.g., HoMedics, model: SS-2000G/F-AMZ )
    We use a standard home-use white noise generator, HoMedics SS-200G/F-AMZ. Any standard model of white-noise generator designed for home or laboratory use would be appropriate. The white noise generator helps to mask any distractions due to extraneous sounds in or near the testing room, which reduces behavioral variability in the task.


  1. Handling/gentling the animals
    See Figure 2 for a schematic diagram of the entire experimental timeline. Prior to testing, the individuals that will be handling the animals in the experiment should begin to handle (pick up and hold) each animal for a few minutes each day. If the bait is a novel food for the rats, a few pieces of the cereal can also be offered each day to acclimate the rats to the food. Animals should be handled a minimum of 4 days prior to the start of pre-training, but ideally 5-7 days.

    Figure 2. Experimental Timeline. The entire experiment takes approximately 18-24 days, including handling, pre-training, and testing. The entire timeline is represented schematically in this Figure.

  2. Food deprivation
    2-3 days before pre-training, food deprivation should begin. First, the baseline weights of all animals should be recorded, and then all food (but not water) should be removed for 24 h. After 24 h, limited food (about 40 g/rat) should be provided on a daily basis. Rats should be weighed each day, and the amount of food provided each day should be adjusted so that animals maintain approximately 85-90% of their baseline weight.
  3. Habituation
    The first day of the experiment, following about 2-3 days of food deprivation, is habituation. Habituation and all other training should occur during the rats’ dark cycle, at approximately the same time (i.e., within a 2-h time window) each day.
    1. Lights in the testing room should be dimmed to the lowest level at which the video-cameras can function–if red lights are available, the experiment can be run in darkness with red lights only. The white noise generator should be on.
    2. Animals are placed individually into the open field arena, and allowed to explore for 10 min. At the end of 10 min, the animals are removed from the arena, returned to their home cage, and fed.
    3. During habituation and all pre-training and test trials, the experimenter should either leave the room (monitoring the rat via video-camera), or sit still and quietly in a location set back from the open field. There should be no food, drinks, lotions, perfumes, jewelry, music, or other distracting stimuli present in the testing room.
    4. Between rats, the arena should be wiped down with an ethanol solution to clean and disperse odor cues.
  4. Pre-training
    After one day of habituation, pre-training begins. All environmental conditions such as lighting and white noise should remain the same as during habituation. Pre-training is run in stages, with animals needing to complete each stage before moving to the next. Animals receive one trial each day for the duration of pre-training. Therefore, the time to complete pre-training may vary, with animals usually requiring approximately 10-14 days.
    1. For the first stage of pre-training, four targets are placed randomly in the arena, with one piece of bait on each target. An individual rat is placed in a designated starting point, and allowed to forage for the bait. The trial ends when the rat retrieves all four pieces of bait, or when 10 min is up, whichever happens first. Stage one of pre-training is complete when the animal successfully retrieves all four pieces of bait on two consecutive trials.
    2. For stage two, six targets are placed in the arena, each with one piece of bait. Stage two is completed when the rat successfully retrieves all six pieces on one trial.
    3. For stage three, eight targets are placed in the arena, each with one piece of bait; completion requires the successful retrieval of all eight pieces on one trial.
    4. Finally, for stage four, 10 baited targets are placed in the arena. Stage four, and pre-training, are complete when the animal successfully retrieves nine out of the 10 targets on three consecutive trials. At this point, the animal can begin the testing phase of the experiment.
  5. Testing phase
    During the testing phase, animals are observed in the arena with a specific target configuration designed to answer a particular test question.
    1. The configuration template is first placed on the arena floor, then baited targets are placed, and finally the template should be removed before the rat is placed in the arena. As in pre-training, the behavior of the rat is recorded for 10 min, or until the rat retrieves all of the bait, whichever happens first.
    2. After the trial, the rat is placed back into the home cage and fed. The specifics of the configurations (number of targets, location of targets, number of different configurations) will depend on the experimental question. Configurations used in previous research studies (e.g., Blaser and Ginchansky, 2012) may be used for reference; see Figure 3 for examples of four 10-target configurations. Unless the order of testing different configurations is determined by the experimental question, the sequence should be balanced across rats when multiple configurations are used. See Video 1 for an example of a rat’s behavior in a test trial.

    Figure 3. Four example target configurations. A. Simple Baseline; B. Nearest-Neighbor Adequate; C. Cluster Approach; D. Nearest-Neighbor Inadequate. Four example configurations, all with 10 targets are provided in Figure 3. In 3A is a simple baseline configuration to determine baseline motivation and locomotor activity. In 3B is a configuration for which a simple nearest-neighbor strategy produces the optimal route. In 3C is a configuration to determine preference for target clusters. In 3D is a configuration for which the simple nearest-neighbor strategy produces a sub-optimal route.

  6. Video coding and analysis
    Once the trials are complete, the video files are coded for several behavioral measures. First, each target is given a unique number. The optimal route (shortest possible path) must also be determined for each configuration.
    Contact: Contact with a target is recorded when the whiskers, nose, or forepaw of the subject touch either the target or bait. Contact with a target by the tail or hind paws of the animal is not counted.
    Retrieval: Retrieval of bait is recorded when the subject removes the bait from the target (so all retrieval scores are automatically counted as contact with that target). These are recorded into a data file as a list of target numbers in the sequence in which they are contacted, with an additional flag (e.g., color code or highlight) to designate retrievals.

    Video 1. Video of a rat completing a test configuration

    Transitions: Transitions are calculated from the sequence of target contacts. A transition is defined as the line segment connecting two consecutive contacts. For example, if a subject contacts Target 2 then Target 4, a transition from 2 to 4 is recorded. This establishes a sequence of transitions for each animal on each trial. Optimal Transitions are the segments connecting target pairs along the optimal route. The distance between each target pair (cm) is used to calculate Total Travel Distance for each subject. Because transitions are used to calculate distance measures, these measures do not take into account deviations from the shortest path between two targets. If desired, the videos can also be played through a video-tracking program (such as Ethovision®, Anymaze®, or ViewPoint®) to establish actual travel distances as well.
    Memory Measures
    Revisits: Revisits are defined as any contact with a target after the bait from that target is retrieved.
    Omissions: Omissions are defined as any target that is not visited in the 10-min trial period.
    Span: Span is defined as the number of targets visited prior to the first revisit.
    Route Choice Measures
    Percent Above Optimal: Percent Above Optimal (PAO) is calculated as the difference between the total travel distance and the optimal route distance, divided by the optimal route distance. A lower score indicates better performance, since lower scores indicate shorter path lengths.
    Proportion of Optimal Transitions: The Proportion of Optimal Transitions is calculated as the number of transitions that fell along the optimal route, divided by the total number of transitions.
    Proportion of Distance on Optimal: The Proportion of Distance on Optimal is defined as the total distance traveled along the optimal route, divided by the total travel distance.

Data analysis

Most commonly, the behavioral measures can be compared between two experimental groups using a t-test (if only two groups), or an ANOVA (if multiple groups or repeated testing is needed). We typically use the standard definition of an outlier as a subject who scores at least 2 standard deviations above the mean–these are excluded from analysis.


The original inspiration for this line of research was from discussions with Dr. Ed Chronicle, to whom I am most grateful. The recent work has been supported by the University of San Diego Faculty Research Grants. The author has no conflicts of interest to declare.


  1. Baron, D. M., Ramirez, A. J., Bulitko, V., Madan, C. R., Greiner, A., Hurd, P. L. and Spetch, M. L. (2015). Practice makes proficient: pigeons (Columba livia) learn efficient routes on full-circuit navigational traveling salesperson problems. Anim Cogn 18(1): 53-64.
  2. Best, B. J. (2006). Cognitive Approaches to the Traveling Salesperson Problem: Perceptual Complexity that Produces Computational Simplicity. AAAI Spring Symposium: Between a Rock and a Hard Place: Cognitive Science Principles Meet AI-Hard Problems.
  3. Blaser, R. E. and Wilber, J. (2013). A comparison of human performance in figural and navigational versions of the traveling salesman problem. Psychol Res 77(6): 761-772.
  4. Blaser, R. E. and Ginchansky, R. R. (2012). Route selection by rats and humans in a navigational traveling salesman problem. Anim Cogn 15(2): 239-250.
  5. Bellizzi, C., Goldsteinholm, K. and Blaser, R. E. (2015). Some factors affecting performance of rats in the traveling salesman problem. Anim Cogn 18(6): 1207-1219.
  6. Bures, J., Buresová, O. and Nerad, L. (1992). Can rats solve a simple version of the traveling salesman problem? Behav Brain Res 52(2): 133-142.
  7. de Jong, L. W., Gereke, B., Martin, G. M. and Fellous, J. M. (2011). The traveling salesrat: insights into the dynamics of efficient spatial navigation in the rodent. J Neural Eng 8(6): 065010.
  8. Gibson, B., Wilkinson, M. and Kelly, D. (2012). Let the pigeon drive the bus: pigeons can plan future routes in a room. Anim Cogn 15(3): 379-391.
  9. MacGregor, J. N., Ormerod, T. C. and Chronicle, E. P. (2000). A model of human performance on the traveling salesperson problem. Mem Cognit 28(7): 1183-1190.
  10. Miyata, H. and Fujita, K. (2010). Route selection by pigeons (Columba livia) in "traveling salesperson" navigation tasks presented on an LCD screen. J Comp Psychol 124(4): 433-446.


旅行推销员问题(TSP)是用于测量空间导航效率的行为测试。 这是一个优化问题,其中将许多诱饵目标放置在竞技场中,并且当目标在目标之间传播时,记录路线并将其与机会路线和最佳路线进行比较。 TSP对非人类动物的学习,记忆和执行功能的研究具有吸引力,因为通过对任务参数进行微小调整,可以轻松修改记忆需求。 在标准版本的任务中,老鼠最初被预先训练去在场地中寻找诱饵。 一旦动物持续检索诱饵,就会用一组新颖的目标配置进行测试,并记录它们的行为。 然后对这些视频进行评分,以产生若干性能指标。

【背景】旅行推销员问题(TSP)是一项空间导航任务,参与者被要求选择访问空间阵列中每个目标的最短路线。这项任务一段时间以来一直受到计算机和认知科学家的关注(Best,2006),但最近从比较心理学的角度研究(例如,de Jong et al。 ,2011; Gibson et al。,2012; Baron et al。,2015)。人类在找到解决这个问题的方法时非常好 - 尽管数学难以处理,但人类参与者能够快速且容易地生成接近最佳的解决方案(MacGregor et al。 2000>)。这种高水平表现的一个可能的解释是,该任务利用了用于觅食等自然行为的进化过程(Blaser和Ginchansky,2012; Blaser and Wilber,2013)。因此,我们对非人类动物完成任务的机制感兴趣(Bellizzi等人,2015; Goldsteinholm和Blaser,2015)。

虽然人类参与者通常使用计算机或纸和铅笔来解决TSP,但我们使用径向臂迷宫作为模型来设计大鼠的可比较任务(Blaser和Ginchansky,2012)。该任务尚未广泛用于非人类动物,但已有多种变种程序。例如,Bures等人(1992)使用TSP设计,其中在所有目标已被访问之前动物未被奖励,在测试之前连续10天以相同目标配置训练受试者。 Miyata等人(2010年)要求鸽子在触摸屏上啄食,以便在测试结束时获得食物奖励。不同程序的重要变化涉及每个目标是否有食物,或只有最后一个,动物是否暴露于特定的空间配置不止一次,以及空间竞技场相对于动物体型的规模。我们选择了一种协议,其中测试新配置以降低性能依赖于长期空间记忆的程度,并且其中相对较大的舞台鼓励距离最小化。

关键字:空间导航, 认识, 规划, 工作记忆, 执行功能, 优化


  1. 大鼠
  2. 乙醇
  3. 目标

    1. 半透明紫色乙烯基索引卡分隔符(Oxford Esselte,目录号:73153)
    2. 啮齿类食物
    3. 无菌瓶盖
    目标是切成2“直径圆形的塑料片。我们使用Oxford Esselte提供的半透明紫色乙烯基索引卡分隔器,但过去已成功使用了啮齿动物食物盘和消毒瓶盖。平坦的乙烯基靶材具有吸引力,因为它们易于清洁,并且相比于盘子或帽子,对老鼠来说探索和携带的吸引力较小。无论使用哪个目标,单个实验中使用的目标都应该彼此相同。
    1. Froot Loops 麦片(或普通的等同物)
    2. 果味卵石®或可可卵石(每个目标一颗卵石)
    对于诱饵,我们使用Froot Loops 谷物(或通用等价物),分成四分之一块(每个目标四分之一),或者Fruity Pebbles ®或Cocoa pebbles ®(每个目标一颗卵石)。所有的工作同样好。
  4. 配置模板


  1. Open Field Arena(图1)
    这些动物在胶合板制成的90 x 90 x 75厘米开阔场地中进行测试。它被涂成白色,地板上画着黑色的格子。任何大型标准露天场地都应该有效,不过应该一致地使用相同类型的场地,因为场地的大小和形状预计会影响任务绩效指标。


  2. 秒表
  3. 摄像机
  4. 白噪声发生器(例如,HoMedics,型号:SS-2000G / F-AMZ)
    我们使用标准家用白噪声发生器HoMedics SS-200G / F-AMZ。设计用于家庭或实验室使用的任何标准型号的白噪声发生器都是合适的。白噪声发生器有助于掩盖任何由于测试室内或附近的外部声音而造成的干扰,从而减少任务中的行为变化。


  1. 处理/控制动物


  2. 剥夺食物
    在培训前2-3天,应开始剥夺食物。首先记录所有动物的基线重量,然后将所有食物(但不包括水)移走24小时。 24小时后,应每日提供有限的食物(约40克/只)。应该每天对大鼠称重,每天提供的食物量应该调整,以便动物维持大约85-90%的基准体重。
  3. 习惯
    在大约2-3天的食物剥夺之后,实验的第一天就是习惯化。习惯和所有其他训练应在大鼠的黑暗周期中进行,每天大约在同一时间(即在2小时的时间窗内 , )。
    1. 测试室内的灯光应该变暗至视频摄像机可以工作的最低级别 - 如果有红灯可用,则实验可以在黑暗中用红灯运行。白噪声发生器应该打开。
    2. 将动物单独放入开阔场地,并允许探索10分钟。在10分钟结束时,将动物从竞技场中移出,返回到它们的笼子并喂食。
    3. 在习惯化和所有预培训和测试试验期间,实验者应该离开房间(通过摄像机监视大鼠),或者静静地坐在远离旷野的位置。测试室内不应有食物,饮料,乳液,香水,珠宝,音乐或其他令人分心的刺激物。
    4. 在老鼠之间,应该用乙醇溶液擦拭竞技场以清洁和分散气味线索。
  4. 预培训
    1. 对于预训练的第一阶段,四个目标随机放置在竞技场,每个目标上有一个诱饵。将一只老鼠放置在指定的起点,并且允许捕获诱饵。试验结束时,大鼠取回所有四个诱饵,或10分钟时,以先发生者为准。
    2. 对于第二阶段,六个目标被放置在舞台上,每个都有一个诱饵。
    3. 第三阶段,八个目标放在竞技场内,每个目标都有一个诱饵;完成要求在一次试验中成功检索所有八个部分。
    4. 最后,在第四阶段,将10个诱饵目标放置在竞技场中。当动物连续三次试验成功地从十个目标中检索出九个时,第四阶段和预先训练完成。此时,动物可以开始实验的测试阶段。
  5. 测试阶段
    1. 首先将配置模板放置在竞技场地板上,然后放置诱饵目标,最后在将老鼠放入竞技场之前将模板移除。如在训练前一样,记录大鼠的行为10分钟,或者直到大鼠找回所有诱饵,以先发生者为准。
    2. 试验后,将老鼠放回家笼中喂食。配置的细节(目标数量,目标位置,不同配置的数量)将取决于实验问题。在以前的研究中使用的配置(例如,Blaser和Ginchansky,2012)可以用作参考;有关四个10目标配置的示例,请参见图3。除非测试不同配置的顺序由实验问题确定,否则当使用多种配置时,应该在大鼠之间平衡序列。

    图3.四个示例目标配置。 A.简单基线; B.最近邻居充分; C.分组方法; D.最近邻居不足。图3提供了四个示例配置,所有配置都有10个目标。在3A中,确定基线动机和运动活动的简单基准配置。在3B中,简单最近邻策略产生最佳路线的配置。在3C中是确定目标集群偏好的配置。在3D中,简单最近邻策略产生次优路线。

  6. 视频编码和分析

    转场: 转场是根据目标联系人序列计算的。转换定义为连接两个连续联系人的线段。例如,如果主题联系目标2和目标4,则会记录从2到4的转换。这为每个试验的每只动物建立了一系列转换。最佳过渡是沿着最佳路线连接目标对的区段。每个目标对之间的距离(厘米)用于计算每个主题的总行程距离。因为过渡用于计算距离度量,所以这些度量不考虑两个目标之间最短路径的偏差。如果需要,还可以通过视频跟踪程序(如Ethovision ®,Anymaze ®或ViewPoint ®)播放视频至建立实际的行程距离。


最常见的情况是,行为测量可以在两个实验组之间进行比较,如果只使用两个组,或者使用ANOVA(如果需要多个组或重复测试)。我们通常使用异常值的标准定义作为一个主体,他们的平均值至少高于2个标准偏差 - 这些都被排除在分析之外。


这一系列研究的最初灵感来自与Ed Chronicle博士的讨论,我非常感谢他。最近的工作得到了圣地亚哥大学教授研究基金的支持。作者没有利益冲突要申报。


  1. Baron,D.M.,Ramirez,A.J.,Bulitko,V.,Madan,C.R.,Greiner,A.,Hurd,P.L。和Spetch,M.L。(2015)。 练习使精通:鸽子( Columba livia )全程学习高效路线 - 电路导航旅行销售人员问题。 Anim Cogn 18(1):53-64。
  2. Best,B. J.(2006)。旅行商问题的认知方法:产生计算简单性的感知复杂性。 AAAI春季研讨会:在一块岩石和一块坚硬的地方:认知科学原理遇到AI难题。
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引用:Blaser, R. E. (2018). The Traveling Salesman Problem (TSP): A Spatial Navigation Task for Rats. Bio-protocol 8(11): e2870. DOI: 10.21769/BioProtoc.2870.