Each year, a large majority of global cargo is transported via container vessels operated by liner shipping companies through networks of scheduled, weekly rotations. These networks dictate the majority of operational costs, including fuel, capital, and port fees. Because manual design is immensely complex, the Liner Shipping Network Design Problem (LSNDP) is a vital candidate for operations research. To evaluate a network's quality, one must determine how containers flow through rotations—a multicommodity flow (MCF) problem. This is solved using a heuristic because exact methods are too slow. By applying Lagrange relaxation to arc capacity constraints, capacity can be temporarily exceeded at the cost of a Lagrange multiplier. These multipliers are tuned iteratively by solving a shortest path problem for all cargo, identifying which arcs are attractive and requires higher multipliers.Because multipliers alone cannot guarantee a feasible solution, a repair algorithm is implemented to move excess containers by rerouting or rejecting cargo. When compared to exact methods, this MCF heuristic achieves an objective value within $5–6\%$ of optimal while reducing the running time to approximately $1/250$ of the original. To optimize the network, an initial starting point must be generated from scratch. This is achieved through an auxiliary network assuming direct connections between all ports. To ensure economic viability, a pricing scheme is applied where the cost is highest for the first container and decreases as volume increases, providing an incentive to use active arcs. Each container is flowed individually to adjust these costs dynamically.The resulting auxiliary flow forms the basis for serial, greedy rotation generation. The arc with the highest unserved load is selected as the starting point and expanded to neighboring arcs until a preset duration is reached. By randomly selecting these durations, the algorithm can quickly generate various networks. While these initial networks are typically of lower quality than optimized ones, they provide the necessary foundation for heuristic refinement. The optimization uses a local search procedure with six neighborhoods. Four of these use a delta evaluation procedure, which allows a move to be assessed without recalculating the entire multicommodity flow—a significant time-saver.This delta evaluation uses a subgraph covering only the modified rotation. To account for transshipments between rotations, feeder arcs are introduced to replace missing connections. While not perfectly coherent with the main graph, this approximation effectively identifies attractive moves. The local search is controlled by a Variable Neighborhood Search (VNS) metaheuristic. To escape local optima, a "shake" (a random move) is performed only after a local optimum is reached across all neighborhoods, preventing excessive randomness. Tests confirmed that all six neighborhoods contribute positively to the final objective value.Computational tests on LINER-LIB datasets compared this algorithm to the work of Brouer et al. (2014a). Out of seven instances, this thesis identified the best solution for four and provided a novel solution for the largest, all while running ten times faster per replication than the previous benchmark. A primary issue identified was the choice of sailing speed; the model often selected the minimum allowed speed because the calculation only considered direct operating costs rather than potential revenue from faster rotations. This led to capacity shortages and long transit times that exceeded LINER-LIB time limits, although these are not part of the problem definition in this research.Ultimately, the method successfully finds high-quality solutions for the LSNDP. While the speed calculation procedure requires refinement, the local search could also benefit from neighborhoods that specifically promote hub-and-spoke structures. The most critical future extension is the introduction of time constraints. This would move the model toward a more customer-oriented approach, balancing operational cost reduction with attractive, competitive travel times.