# Parallelized Swarm Intelligence Approach for Solving TSP and JSSP Problems
## 1 Introduction
Then, a copy of the modified discrete population is again transformed into a continuous format using the backward mapping method, thus enabling the DE to perform mutation and crossover operations in the continuous landscape. Additionally, an ensemble of DE continuous mutation operators are proposed for increasing the exploration capability of DE. An effective spider monkey optimization algorithm for TSP named DSMO was proposed in [20]. In DSMO, every spider monkey represents a TSP solution where swap sequence (SS) and swap operator (SO) based operations are employed, which enables interaction among monkeys in obtaining the optimal or close to the optimal TSP solution. Another swarm intelligence approach called a discrete symbiotic organisms search (DSOS) algorithm for finding a near optimal solution for the TSP was proposed in [21]. A very good performance in solving TSP instances achieves the approach proposed in [22]. The authors propose a genetic algorithm with an effective ordered distance vector (ODV) crossover operator, based on the ODV matrix used at the population seeding stage. With the advance of computational technologies, a number of approaches for solving TSP using parallel computations, have been proposed. One of the first was parallel GA on MapReduce framework using Hadoop cluster [23]. Another solution using the Hadoop MapReduce for parallel genetic algorithm for TSP can be found in [24]. Distributed ant colony optimization algorithm for solving the TSP was proposed in [25]. Parallel version of the population learning metaheuristic applied, among other, to TSP can be found in [26]. Research efforts on TSP have also produced numerous heuristic and local search algorithms that offer good performance and may serve as the inspiration in constructing hybrid swarm intelligence solutions. One of them is the constructive, insertion and improvement (CII) algorithm proposed in [27]. CII has three phases. The constructive heuristics of Phase 1 produces a partial tour that includes solely the points of the girding polygon. The insertion heuristic of Phase 2 transforms the partial tour of Phase 1 into a full feasible tour using the cheapest insertion strategy. The tour improvement heuristic of Phase 3 improves iteratively the tour of Phase 2 based on the local optimality conditions using two additional heuristic algorithms. Population based algorithms including swarm intelligence and evolutionary systems have proven successful in tackling JSSP--another hard optimization problem considered in this study. A state of the art review on application of the AI techniques for solving the JSSP as of 2015 can be found in [28]. Recently, several interesting swarm intelligence solutions for JSSP were published. In [29] the local search mechanism of the PSA and large-span search principle of the cuckoo search algorithm are combined into an improved cuckoo search algorithm (ICSA). A hybrid algorithm for solving JSSP integrating PSO and neural network was proposed in [30]. An improved whale optimization algorithm (IWOA) based on quantum computing for solving JSSP instances was proposed by [31]. An improved GA for JSSP [32] offers good performance. Their niche adaptive genetic algorithm (NAGA) involves several rules to increase population diversity and adjust crossover rate and mutation rate according to the performance of the genetic operators. Niche is seen as the environment permitting species with similar features to compete for survival in the elimination process. According to the authors, niche technique prevents premature convergence and improves population diversity. A discrete wolf pack algorithm (DWPA) for job shop scheduling problem was proposed in [33]. WPA is inspired by the hunting behaviors of wolves. DWPA involves 3 phases: initialization, scouting and summoning. During initialization heuristic rules are used to generate a good quality initial population. The scouting phase is devoted to the exploration while summoning takes care of the intensification.