Acoustic surveillance of oceans is of great interest for monitoring both wildlife and anthropogenic activities. In this paper, we focus on passive, non-communicating sonar systems that are suitable for efficiently monitoring the marine environment. With such a network, no live tracking is possible; instead, we aim to record activities in the most discreet manner for surveillance purposes. General guidelines can be established to assist in designing a network of underwater acoustic sensors. These guidelines serve as both objectives and constraints, such as sensor detection capabilities, deployment area alternatives, acoustic propagation properties, and potential noise source areas. The optimization of network design, in terms of the distribution and locations of sensors (or groups of sensors physically stacked on a mooring line, for example, and referred to as anchors ), involves trade-offs between network cost, coverage of the targeted marine area, network redundancy, and localization capabilities. In this paper, we propose several approaches to address these various constraints and optimization objectives. These approaches rely on numerical simulations of underwater acoustic propagation, which allow accounting for environmental characteristics such as bathymetry, sea floor properties, and sound speed profiles. A discretized model of the network design problem is presented. It relies on a grid representation of anchor locations, and a complete Integer Programming formulation of the problem is defined. The model is used to identify sets of solutions that represent trade-offs among the different optimization criteria. Both exact and heuristic multi-objective approaches are proposed to exploit the model. The former are applicable to smaller sets of instances and optimization objectives than the latter. However, the exact approaches enable the derivation of precise bounds on the optimized criteria, as well as initial solutions that can enhance heuristic multi-objective methods based on evolutionary multi-objective optimization frameworks. This supports the designer’s choice of the final network configuration. Numerical experiments conducted on a set of sixteen semi-synthetic test cases, as well as on an actual network deployed at sea, demonstrate that an exact -constraint method is applicable to industrial-scale instances involving up to 2000 monitoring points. It provides the complete Pareto set for the coverage vs. cost problem in a few minutes. One of the proposed heuristic methods yields, in less than a second, sets of solutions with a loss of quality below 1% for the same design problem. When the triangulation capabilities of the network are optimized as a complementary objective for noise source localization, hybrid heuristic approaches are able to improve the results of the basic algorithm by up to 156% on average. • a modelling of the design of UWASN as a Multi Objective optimization problem. • 4 different optimization criteria, 2 exact methods, 2 ad-hoc heuristics and 2 meta-heuristics for solving the problem. • 4 experiments to compare exact and reference methods to approximate approaches. • 16 testcases used and a mixed approach for efficiently extending an existing real-life network.