The vehicle routing problem (VRP) is the problem of designing a specific number of routes to serve a given number of customers while achieving minimum total travel distance and minimum number of vehicles. VRP with time window constraints (VRPTW) restricts that the service time of each customer should start within a time window. This problem and its variations are known to be NP-hard. This paper proposes a transformation of the NP-hard problem into another. The approach is based on satisfiability modulo theories (SMT) in order to take advantage of its relative CPU time competitiveness. This poses transformability challenges in order to apply SMT solving techniques on the VRPTW. In this work, SMT is successfully applied to solve the VRPTW. The solution quality proves to be competitive to other optimization techniques since the solving time is significantly decreased opening the door to solve much larger problems. In addition, it sets a proof for using SMT efficiently as a main step for solving optimization problems.

Sketch recognition is defined as the process of identifying symbols that users draw using single or multiple strokes. Users draw strokes using a pen and the system immediately interprets their strokes as objects that can be easily manipulated. This paper uses Particle Swarm Optimization Algorithm (PSO) to divide the strokes the user draws into meaningful geometric primitives. These geometric primitives are grouped to formulate symbols which are further identified. The results show that using PSO improves segmentation results which guide the symbol recognition phase. This paper uses Support Vector Machines (SVM) classifier which further improves the final recognition accuracy.

In this paper an Incremental GA techniques is proposed tosolve the problem of small disjuncts in classification trees. It is once applied on the disjuncts sorted in ascending orderand once in descending order with respect to their coverage. Both versions of the technique have been tested using benchmark datasets and the results are compared with thoseof other hybrid techniques.