# Parallelized Swarm Intelligence Approach for Solving TSP and JSSP Problems
## 1 Introduction  
Pioneering work in the area of the population-based metaheuristics included genetic algorithms (GA) [1], evolutionary computations--EC [2], particle swarm optimization (PSO) [3] and its two offspring--at colony optimization [4] and bee colony algorithms (BCA) [5]. Since the end of the last century, tremendous research effort has brought a variety of approaches and population-based metaheuristics. In 2013 [PERSON] et al. [6] proposed the classification of the population-based metaheuristics and grouped them into two broad classes. The first is evolutionary computation with subclasses, including genetic algorithms, evolution strategy, evolutionary programming, genetic programming, estimation of distribution algorithms, differential evolution, coevolutionary algorithms, cultural algorithms and scatter search and path relinking. The second class is swarm intelligence with subclasses, including ant colony optimization, particle swarm optimization, bacterial foraging optimization, bee colony optimization, artificial immune systems and biogeography-based optimization. Over the last 20 years, more than a few thousand new population-based approaches and many new subclasses have been proposed. A recent survey of the population-based techniques can be found in [7]. Judging from the number of publications appearing during the last two decades, swarm intelligence is one of the fastest-growing areas of research in the population based methods. According to [8], in the period 2001-2017 more than 3900 swarm intelligence journal publications were indexed by Web of Science. The concept introduced in 1993 by [PERSON] and [PERSON] [9] is broadly understood as the collective behavior of a decentralized, self-organized population of individuals. The structure and behavior of such a group is usually inspired by a metaphor taken from natural or artificial systems. Swarm intelligence has proven an effective tool for solving variety of difficult optimization and controlproblems. The importance of the tool in different areas of application has been highlighted in several recent surveys and reviews as, for example [10; 11; 12; 13; 14]. Researchers tackling difficult optimization problems often focus their efforts on searching for methods able to deal with two famous combinatorial optimization problems--traveling salesman (TSP) and job-shop scheduling (JSSP). Both have attracted numerous teams and labs, resulting in publications and implementations of a huge number of algorithms and approaches. Both problems are important from the point of view of the real life applications, and both belong to the NP hard class. In addition, they are in a certain sense classic, even if they still pose a challenge to researchers in the field of the OR and AI. Performance of algorithms for solving instances of the TSP and JSSP is, usually, evaluated from the point of view of two criteria--accuracy and computation time. In the quest for approaches providing optimal or near optimal solutions to TSP and JSSP in a reasonable computation time, swarm intelligence and other population-based methods play a leading role. Some well performing recent approaches to solving the TSP include a hybrid method based on particle swarm optimization, ant colony optimization and 3-opt algorithms for traveling salesman problem [15; 16], discrete bat algorithm for symmetric and asymmetric TSP [17] and a hybrid ga-PSO algorithm for solving the TSP [18]. A novel design of differential evolution for solving discrete TSP named NDDA was described in [19]. The idea is to enhance DE algorithm with several components including the enhanced mapping method transforming the randomly generated initial population with continuous variables into a discrete one. Next, an improved \(k\)-means clustering is adapted as a repairing method for enhancing the discrete solutions in the initial phase.