## 1 Introduction
This is done within local search procedures using deterministic algorithms (critical path algorithms) in order to evaluate the neighborhood function. Satisfactory results can be obtained [10; 11]. Some of the algorithms that have applied cooperation with crossover in problems of JSSP have not given good results [11; 12; 13], this is mainly due to the fact that the methods of crossover used, are based on improving the solution with the idea of crossed neighbors in order to get better neighbors when comparing neighbors with the neighborhoods of origin, but not with the best neighbor available in the neighborhoods. The fact of not considering the best solution available for the crossover causes, that with the passage of time, the search is not directed toward a space of good solutions. Consequently, the final solution of the algorithm with cooperation generally is not satisfactory. In [14], the researchers present a hybrid genetic algorithm (GA) with parallel implementation of simulated annealing (SA) for the JSSP. The algorithm uses a GA to generate an initial population of solutions within a server machine. Every solution in the population is then distributed to a client machine. The client machine runs an SA and sends the best obtained solution to the server machine. The server again uses the GA to improve the population. This procedure GA-SA is repeated for a number of iterations. The presented results are for medium-sized benchmarks with relative errors below 3.5%. In [15], the researchers present a hybrid parallel genetic algorithm for the JSSP. The method deals with concepts of solution backbones in order to intensify the search in promising regions. They utilize path-relinking and taboo search in crossover and mutation operators. They also use the island model to store a population on each island. If after several iterations of the GA the fitness does not improve, then the subpopulations start to merge, always maintaining the size of the initial population, until in the end there is only one population. In [16], the researchers present a hybrid parallel genetic micro algorithm. The parallel implementation considers M independent GAs running M subpopulations with independent memories, genetic operations, and function evaluation (island models) in each generation. The best individualsin each subpopulation are broadcast to the other subpopulations over a communication network. Each subpopulation consists of small populations, which communicate among themselves and share information through asynchronous message passing. Although a study is presented on the efficiency (speedup) of the parallel algorithm, it appears incomplete. The study evaluates the efficiency of the parallel algorithm for each increase in the number of threads, but the efficiency is averaged and is therefore not sufficient to evaluate the algorithm. In [17], the researchers present a parallel GA for the JSSP in which active schedules are created by the priority rules of [PERSON] and [PERSON]. The model used is the master-slave model. The GA works iteratively with distributed slave populations. It does not apply cooperation between threads and sends the best results only to the master using message passing interface (MPI). The obtained results are good, and the benchmarks are of small and medium size. The cooperation with agents in SA for JSSP dynamics has also been applied, but the results in [18], show that the time consumed in communication between agents is extensive. If the existence of several agents is considered, SA works more slowly than normal when the size of the problem of JSSP is medium or bigger. Another application with agents is an agent-based parallel approach with a genetic algorithm. For this approach, the results for benchmarks of JSSP, which are small and medium, are very poor [19]. In this study, a layered architecture was used. In the lowest layer, a multi-agent system using JADE middleware was implemented which facilitated the creation of agents and their communication using MPI.