In this work, it is investigated whether the predict+optimize framework could be utilized for combinatorial optimization problems with a linear objective that have uncertainty in the constraint parameters, such that it outperforms prediction-error-based training. To this end, a predict+optimize formulation of the 0-1 knapsack problem is used, which is an NP-hard combinatorial optimization problem. This formulation was chosen because it has many real-world applications where the constraint parameters are uncertain. In this instance, the challenge is to predict the weights of knapsack items based on feature data and then use these predictions to solve the knapsack problem. The key is that the item weights are uncertain
and thus must be estimated, but the quality of the solution is evaluated with respect to the true weights. This uncertainty in the weights can lead to infeasible solutions when evaluated on the true weights. Standard predict+optimize techniques do not account for such infeasibility of candidate solutions, which makes them mostly inapplicable for solving problems with uncertainty in the constraint parameters. To
overcome this shortcoming of standard predict+optimize techniques, several correction methods for the evaluation of infeasible solutions during training are compared. Crucially these correction methods can be varied between training and evaluation. By penalizing infeasible solutions linear in the weight of the overweight items during training, predict+optimize is able to outperform standard prediction-error-based techniques. This performance increases to an extent with increased penalization factors, leading to more stable, more optimal results on the validation set.

Wisdom of the crowds is the idea that groups of people can collectively make wise decisions. Research suggests that these crowds can even outsmart experts. To gather the wisdom of the crowds, this project utilizes a prediction market. To successfully gather the wisdom of the crowds, a predictionmarket has to overcome serious challenges, such as gathering a large and active user base, and deciding on a fair initialmarket value. The main goal of the project is to create a prediction market that can overcome these challenges and successfully gather the wisdom of the crowds. Research has been done in the field of prediction markets. This process started with researching the theory behind prediction markets, the wisdom of the crowds. After that evaluating existing prediction markets and reviewing literature related to those markets was useful. Before and during the research phase, clear goals were set for the project, together with a clear set of requirements. These goals can be divided into: leveraging the wisdomof the crowd, solving problems associated with predictionmarkets and developing a product that is easily maintainable. The final product reaches the goals of the project and meets the requirements. The prediction market correctly aggregates the estimations of users on the market, and provides probabilities on real-world events. These probabilities are contained in the values on the market. The prediction markets solves the problems encountered on other prediction markets. The project makes use of gamification, an automated marketmaker and a reward system to correctly initialise market values. The system was thoroughly tested and developed with maintainability in mind.