An heterogeneous sensor network (hSN) consists of different types of sensor nodes with varying coverage capability, range, and sensing quality. hSNs are used by military and other defense organizations for a number of purposes such as monitoring critical facilities, surveilling an area of interest, tracking enemies, or protecting borders. Therefore, the deployment problem of such networks to form an effective coverage and surveillance is of high importance. In this study, we consider the problem of locating an hSN along a two-dimensional belt-shaped border region which includes a number of critical facilities that need protection against intruders. Assuming a hub-spoke location topology, we allow the use of cooperative and gradual covering, multiple types of sensors, critical facilities and intruders. We developed two competing multi-objective mixed integer non-linear program formulations as well as their equivalent mixed integer linear program (MILP) reformulations which adopt a goal programming approach. The MILP formulations are then solved by a commercial optimizer for a set of problem instances using the branch-and-cut (B&C) procedure with various branching and node selection strategies as well as different user defined optimality gap and goal settings. Our results indicate that the performance of formulations are significantly affected by the B&C variable selection strategy as well as the goal levels determined by the decision-makers. We also observe that, using proper settings, the majority of the problem instances can be solved within a maximum of 10% optimality gap in reasonable computing times.

异构传感器网络（h SN）由不同类型的传感器节点组成，具有不同的覆盖能力，范围和传感质量。h SN被军事和其他防御组织用于许多目的，例如监视关键设施，监视目标区域，跟踪敌人或保护边界。因此，这种网络的形成问题以形成有效的覆盖和监视是非常重要的。在这项研究中，我们考虑了定位h沿二维带状边界区域的SN，其中包括许多需要防御入侵者的关键设施。假设使用中心辐射状的位置拓扑，我们允许使用协作式和渐进式覆盖，多种类型的传感器，关键设施和入侵者。我们开发了两种竞争的多目标混合整数非线性程序公式，以及它们的等效混合整数线性程序（MILP）格式，它们采用了目标编程方法。然后，由商业优化器使用分支剪切（B＆C）程序，各种分支和节点选择策略以及不同的用户定义的最优差距和目标设置，针对一组问题实例对MILP公式进行求解。我们的结果表明，配方的性能受到B＆C变量选择策略以及决策者确定的目标水平的显着影响。我们还观察到，使用适当的设置，大多数问题实例都可以在合理的计算时间内在最大10％的最优间隙内得到解决。