#combinatorial

In theoretical computer science, combinatorial optimization problems are about finding an optimal item from a finite set of objects. Combinatorial optimization is the process of searching for maxima or minima of an unbiased function whose domain is a discrete and large configuration space. It often involves determining the way to efficiently allocate resources used to find solutions to mathematical problems. Applications for combinatorial optimization include determining the optimal way to deliver packages in logistics applications, determining taxis best route to reach a destination address, and determining the best allocation of jobs to people. Some common problems involving combinatorial optimizations are the Knapsack problem, the Job Assignment problem, and the Travelling Salesman problem. This paper proposes three new optimized algorithms for solving three combinatorial optimization problems namely the Knapsack problem, the Job Assignment problem, and the Traveling Salesman respectively. The Knapsack problem is about finding the most valuable subset of items that fit into the knapsack. The Job Assignment problem is about assigning a person to a job with the lowest total cost possible. The Traveling Salesman problem is about finding the shortest tour to a destination city through travelling a given set of cities. Each problem is to be tackled separately. First, the design is proposed, then the pseudo code is created along with analyzing its time complexity. Finally, the algorithm is implemented using a high level programming language. As future work, the proposed algorithms are to be parallelized so that they can execute on multiprocessing environments making their execution time faster and more scalable.