Optimising in many-objective search spaces, i.e. search spaces with more than three objectives, is a challenging task. Scalarization functions transform the multi-objective search space into a single objective search space. In order to scale-up optimisation in many-objective search spaces, we use Cartesian product of scalarization functions or simpler product functions to reduce the number of objectives of the search space. Stochastic product local search (SprLS) uses product functions to evaluate solutions within a local search run with the goal of generating the entire Pareto front. To improve the performance of SprLS algorithms: 1) we pursuit a fixed set the product function that improves the most the performance of the algorithm, or 2) we adapt the direction of the component scalarization functions using solutions in the current (possible suboptimal) Pareto front. We compare the performance of local search algorithms on many-objective quadratic assignment instances with correlated flow matrices. I. INTRODUCTION Numerous real-world applications, e.g., scheduling, investment planning, vehicle routing, can be modelled as combi-natorial optimisation problems with three or more objectives to optimise simultaneously. Efficient optimisation algorithms designed for many-objective search spaces should consider a large amount of Pareto optimal solutions. In fact, for most combinatorial optimization problems, Pareto front increases with the number of objectives. We assume that searching in multi-objective search spaces of reduced cardinality is computationally more efficient than searching directly in the many-objective search space. Local search (LS) [1] is a successful and powerful method for combinatorial optimisation problems. Local search applies an exploration strategy to iteratively move from a current to a neighbour solution that improves upon the current solution. The result of this optimisation is a single solution, and LS needs to be repeated several times with different scalarization functions in order to generate all solutions in the optimal Pareto set. Pareto local search (PLS) [2], [3] is an LS that is performed directly in the multi-objective space using dedicated dominance measures for comparing the quality of solutions. Pareto LS using an exhaustive neighbourhood function, or best improvement, stops in the maximum Pareto local optimum set that is the set of non-dominated solutions with no improving solutions in their neighbourhood. An advantage of Pareto local search is that the relationship between objectives can be directly exploited with the dominance relation. However, Pareto search does not scale well with many dimensions, because, often, there are many incomparable solutions, that are difficult to iterate and store.