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A stochastic algorithm for obtaining feasible initial populations to the Vehicle Routing Problem with Time Windows is presented. The theoretical formulation for the Vehicle Routing Problem with Time Windows is explained. The proposed method is primarily divided into a clustering algorithm and a two-phase algorithm. The first step is the application of a modifiedk-means clustering algorithm which is proposed in this paper. The two-phase algorithm evaluates a partial solution to transform it into a feasible individual. The two-phase algorithm consists of a hybridization of four kinds of insertions which interact randomly to obtain feasible individuals. It has been proven that different kinds of insertions impact the diversity among individuals in initial populations, which is crucial for population-based algorithm behavior. A modification to the Hamming distance method is applied to the populations generated for the Vehicle Routing Problem with Time Windows to evaluate their diversity. Experimental tests were performed based on the Solomon benchmarking. Experimental results show that the proposed method facilitates generation of highly diverse populations, which vary according to the type and distribution of the instances.

In this paper, a solution is presented to the unrelated parallel machines problem that minimizes the total weighted completion time ( ∑ i kC ). Simulated annealing is applied to the problem, which is modeled as a Weighted Bipartite Matching Problem. Experimental results with benchmarks are presented, evaluating the efficiency and efficacy of the algorithm. It is then compared with an exact algorithm that solves the pondered model of Integer Linear Programming. The results demonstrate that Simulated Annealing Algorithm has high performance because for all the evaluated instances, it finds the optimum global solution.

This paper proposes a real mathematical constraint satisfaction model which defines the timetabling problem in the Faculty of Chemical Sciences and Engineering (FCSE) at the Autonomous University of Morelos State, Mexico. A Constructive Approach Algorithm (CAA) is used to obtain solutions in the proposed model. A comparison is made between the CAA’s results and the schedule generated by the FCSE administration. Using the constraint satisfaction model, it is possible to improve the allocation of class hours in the FCSE so that classroom use is more efficient.

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