Swap Sequence Research Articles

Coordination of Cyclic crossover and Bat Algorithm for the Travelling Salesman Problems in Different Environments: A Simulation Approach

In this study, the features of cyclic crossover process and K-opt are incorporated in the bat algorithm (BA) to solve the Travelling Salesman Problems (TSP) in different environments. Swap operation and swap sequence are applied for the modification of the different operations of the BA to solve the TSPs. The cyclic crossover operation is applied in a regular interval of iterations on the best found solution and each solution of the final population of BA for the enhancement of the exploration as well as exploitation of the search process. K-Opt operation is applied on the population in each iteration of the BA with some probability for the exploitation. The algorithm is tested with a set of benchmark test instances of the TSPLIB. The algorithm produces exact results for a set of significantly large size problems. For the TSPs in fuzzy environment, a fuzzy simulation approach is proposed to deal with the fuzzy data having linear as well as non-linear membership functions. Also, a rough simulation process is proposed to deal with the TSPs in the rough environment where rough estimation can be done following any type of rough measure. The performance of the algorithm is compared with the state-of-the-art algorithms for the TSPs with crisp cost matrices using different statistical tools.

The Impact of Processing Time Variations on Swap Sequence Performance in Dual-Armed Cluster Tools

The performance of a swap sequence is analyzed by assuming cyclic scheduling in dual-armed cluster tools with processing time variations. A dual-armed cluster tool consists of multiple processing modules (PMs), one material handling robot that can hold two wafers at the same time, and loadlocks where wafer cassettes are loaded or unloaded. The swap sequence in a dual-armed cluster tool is widely used in practice and known to be optimal with deterministic processing times when the bottleneck PM’s workload is larger than the robot workload. However, in practice, processing times on a PM can have a small variation, which leads to a different processing time of each wafer on the PM. Hence, when the processing time variation is introduced, the performance of the swap sequence needs to be analyzed. This paper first defines a fundamental cycle and analyzes its cycle time. It then proposes optimality conditions of the swap sequence and performs numerical experiments to show the effectiveness of the sequence. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —A dual-armed cluster tool used for semiconductor manufacturing processes is usually operated with a swap sequence because it is simple, easy to control, and proven to be optimal with deterministic processing times. However, studies on the performance of the swap sequence are still limited with processing times varying in PMs which often occur in practice. Hence, this study shows the effectiveness of the swap sequence with the processing time variations by analyzing cycle times, optimality conditions, and performing numerical experiments.

A Multigoal Path-Planning Approach for Explosive Ordnance Disposal Robots Based on Bidirectional Dynamic Weighted-A* and Learn Memory-Swap Sequence PSO Algorithm

In order to protect people’s lives and property, increasing numbers of explosive disposal robots have been developed. It is necessary for an explosive ordinance disposal (EOD) robot to quickly detect all explosives, especially when the location of the explosives is unknown. To achieve this goal, we propose a bidirectional dynamic weighted-A star (BD-A*) algorithm and a learn memory-swap sequence particle swarm optimization (LM-SSPSO) algorithm. Firstly, in the BD-A* algorithm, our aim is to obtain the shortest distance path between any two goal positions, considering computation time optimization. We optimize the computation time by introducing a bidirectional search and a dynamic OpenList cost weight strategy. Secondly, the search-adjacent nodes are extended to obtain a shorter path. Thirdly, by using the LM-SSPSO algorithm, we aim to plan the shortest distance path that traverses all goal positions. The problem is similar to the symmetric traveling salesman problem (TSP). We introduce the swap sequence strategy into the traditional PSO and optimize the whole PSO process by imitating human learning and memory behaviors. Fourthly, to verify the performance of the proposed algorithm, we begin by comparing the improved A* with traditional A* over different resolutions, weight coefficients, and nodes. The hybrid PSO algorithm is also compared with other intelligent algorithms. Finally, different environment maps are also discussed to further verify the performance of the algorithm. The simulation results demonstrate that our improved A* algorithm has superior performance by finding the shortest distance with less computational time. In the simulation results for LM-SSPSO, the convergence rate significantly improves, and the improved algorithm is more likely to obtain the optimal path.

A Method Based on Timing Weight Priority and Distance Optimization for Quantum Circuit Transformation

In order to implement a quantum circuit on an NISQ device, it must be transformed into a functionally equivalent circuit that satisfies the device's connectivity constraints. However, NISQ devices are inherently noisy, and minimizing the number of SWAP gates added to the circuit is crucial for reducing computation errors. To achieve this, we propose a subgraph isomorphism algorithm based on the timing weight priority of quantum gates, which provides a better initial mapping for a specific two-dimensional quantum architecture. Additionally, we introduce a heuristic swap sequence selection optimization algorithm that uses a distance optimization measurement function to select the ideal sequence and reduce the number of SWAP gates, thereby optimizing the circuit transformation. Our experiments demonstrate that our proposed algorithm is effective for most benchmark quantum circuits, with a maximum optimization rate of up to 43.51% and an average optimization rate of 13.51%, outperforming existing related methods.

Token Swapping on Trees

The input to the token swapping problem is a graph with vertices $v_1, v_2, \ldots, v_n$, and $n$ tokens with labels $1, 2, \ldots, n$, one on each vertex. The goal is to get token $i$ to vertex $v_i$ for all $i= 1, \ldots, n$ using a minimum number of swaps, where a swap exchanges the tokens on the endpoints of an edge. We present some results about token swapping on a tree, also known as "sorting with a transposition tree": 1. An optimum swap sequence may need to perform a swap on a leaf vertex that has the correct token (a "happy leaf"), disproving a conjecture of Vaughan. 2. Any algorithm that fixes happy leaves -- as all known approximation algorithms for the problem do -- has approximation factor at least $4/3$. Furthermore, the two best-known 2-approximation algorithms have approximation factor exactly 2. 3. A generalized problem -- weighted coloured token swapping -- is NP-complete on trees, even when they are restricted to be subdivided stars, but solvable in polynomial time on paths and stars. In this version, tokens and vertices have colours, and colours have weights. The goal is to get every token to a vertex of the same colour, and the cost of a swap is the sum of the weights of the two tokens involved.

Optimal Algorithms for Sorting Permutations with Brooms

Sorting permutations with various operations has applications in genetics and computer interconnection networks where an operation is specified by its generator set. A transposition tree T=(V,E) is a spanning tree over n vertices v1,v2,…vn. T denotes an operation in which each edge is a generator. A value assigned to a vertex is called a token or a marker. The markers on vertices u and v can be swapped only if the pair (u,v)∈E. The initial configuration consists of a bijection from the set of vertices v1,v2,…,vn to the set of markers (1,2,⋯,n−1,n). The goal is to sort the initial configuration of T, i.e., an input permutation, by applying the minimum number of swaps or moves in T. Computationally tractable optimal algorithms to sort permutations are known only for a few classes of transposition trees. We study a class of transposition trees called a broom and its variation a double broom. A single broom is a tree obtained by joining the centre vertex of a star with one of the two leaf vertices of a path graph. A double broom is an extension of a single broom where the centre vertex of a second star is connected to the terminal vertex of the path in a single broom. We propose a simple and efficient algorithm to obtain an optimal swap sequence to sort permutations with the transposition tree broom and a novel optimal algorithm to sort permutations with a double broom. We also introduce a new class of trees named millipede tree and prove that D* yields a tighter upper bound for sorting permutations with a balanced millipede tree compared to D′. Algorithms D* and D′ are designed previously.

Comparison of a Bat and Genetic Algorithm Generated Sequence Against Lead Through Programming When Assembling a PCB Using a Six-Axis Robot With Multiple Motions and Speeds

An optimal component feeder arrangement and robotic placement sequence are both important for improving assembly efficiency. Both problems are combinatorial in nature and known to be NP-hard. This article presents a novel discrete hybrid bat-inspired algorithm for solving the feeder slot assignment and placement sequence problem encountered when planning robotic assembly of electronic components. In our method, we use the concepts of swap operators and swap sequence to redefine position and velocity operators from the basic bat algorithm (BA). Furthermore, we propose an improved local search method based on genetic operators of crossover and mutation enhanced by the 2-opt search procedure. The algorithm is formulated with the objective of minimizing the total traveling distance of the pick-and-place device. Through numerical experiments, using a real printed circuit board (PCB) assembly scenario, we demonstrate the considerable effectiveness of the proposed discrete BA to improve the selection of feeder arrangement and placement sequence in PCB assembly operations and achieve high throughput production. The results also highlighted that even though the algorithms outperformed traditional lead through programming techniques, the programmer must consider the influence of different robot motions and speeds.

Disassembly Sequence Planning for Intelligent Manufacturing Using Social Engineering Optimizer

Product disassembly and recycling are important issues in green design. Disassembly sequence planning (DSP) is an important problem in the product disassembly process. The core idea is to generate the best or approximately optimal disassembly sequence to reduce disassembly costs and time. According to the characteristics of the DSP problem, a new algorithm to solve the DSP problem is proposed. Firstly, a disassembly hybrid graph is introduced, and a disassembly constraint matrix is established. Secondly, the disassembling time, replacement frequency of disassembly tool and replacement frequency of disassembly direction are taken as evaluation criteria to establish the product fitness function. Then, an improved social engineering optimizer (SEO) method is proposed. In order to enable the algorithm to solve the problem of disassembly sequence planning, a swap operator and swap sequence are introduced, and steps of the social engineering optimizer are redefined. Finally, taking a worm reducer as an example, the proposed algorithm is used to generate the disassembly sequence, and the influence of the parameters on the optimization results is analyzed. Compared with several heuristic intelligent optimization methods, the effectiveness of the proposed method is verified.

Wafer Delay Analysis and Workload Balancing of Parallel Chambers for Dual-Armed Cluster Tools With Multiple Wafer Types

We examine a scheduling problem for a dual-armed cluster tool that processes multiple similar wafer types concurrently. It has been recently proved that the well-known swap sequence, which is widely used for single wafer type processing, also minimizes the cycle time for concurrent processing. In this article, we wish to minimize wafer delays in a process chamber, which are critical to wafer quality degradation, while maintaining the minimum cycle time. In particular, we show that concurrent processing of wafers with different processing times complicates the analysis of wafer delays significantly, and the wafer delays can be remarkably reduced by finding a proper cycle plan which is the release sequence of different wafer types. We first characterize wafer delays for a given cycle plan by analyzing the circuits of the timed event graph (TEG) model. From this, we prove that concurrent processing of wafers may cause a significant workload imbalance between parallel chambers of a process step, and hence the wafer delays increase substantially. We present that the wafer delays are minimized by a cycle plan that evenly balances workloads between parallel chambers. We also propose how wafer loading task at each process step has to be postponed to meet wafer delay constraints while maintaining the minimum cycle time. Note to Practitioners —Wafer quality control has become an essential fab operational problem in semiconductor manufacturing industry. In cluster tools, which are dominantly being used for diverse wafer fabrication stages, it has been proven that the wafer delays within process chambers have a crucial impact on the wafer quality. Accordingly, modern fabs have introduced stringent quality control to regulate wafer delays in cluster tools. In this research, we propose a scheduling strategy to minimize the wafer delays when a cluster tool concurrently processes multiple wafer types. We first show that the release sequence of different wafer types significantly impacts the wafer delays under concurrent processing, and we then propose how these wafer delays can be minimized by finding the optimal wafer release sequence.

Scheduling of Dual-Gripper Robotic Cells With Reinforcement Learning

A dual-gripper robotic cell consists of multiple processing machines and one material handling robot, which can perform an unloading or a loading task one at a time but can hold two parts at the same time. We address a scheduling problem of the robotic cell that determines a robot task sequence when two part types are processed in a different set of machines and all machines have variable processing times within a given interval. The objective is to minimize the makespan. This study proposes a learning-based method, i.e., a reinforcement learning (RL) approach, for the first time, to address a dual-gripper robotic cell scheduling problem. The problem is modeled with a Petri net, a graphical and mathematical modeling tool, which is used as an environment in RL. The states, actions, and rewards are defined by using flow shop scheduling properties, features from a Petri net, and knowledge from previous studies of scheduling robotized tools. Then, the RL approach is compared to the first-in-first-out (FIFO) rule, which is generally used in practice, a swap sequence, which is widely used for cyclic scheduling of dual-gripper robotic cells, and a lower bound. The extensive experiments show that the proposed method performs better than FIFO and the swap sequence; moreover, the gap between the makespan of the proposed method and the lower bound is not large. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —We address a scheduling problem of dual-gripper robotic cells with two-part types when all machines have processing time variations. We propose an RL approach to obtain an efficient robot task sequence in order to minimize makespan. The proposed method is performed offline, and a robot task sequence is then obtained instantaneously. The proposed method performs better than the FIFO rule used in practice and the swap sequence used for cyclic scheduling of robotic cells. It can be easily extended for scheduling other configurations of robotic cells.

Multi-objective traveling salesman problem: an ABC approach

Using the concept of swap operation and swap sequence on the sequence of paths of a Traveling Salesman Problem(TSP) Artificial Bee Colony (ABC) algorithm is modified to solve multi-objective TSP. The fitness of a solution is determined using a rule following the dominance property of a multi-objective optimization problem. This fitness is used for the selection process of the onlooker bee phase of the algorithm. A set of rules is used to improve the solutions in each phase of the algorithm. Rules are selected according to their performance using the roulette wheel selection process. At the end of each iteration, the parent solution set and the solution sets after each phase of the ABC algorithm are combined to select a new solution set for the next iteration. The combined solution set is divided into different non-dominated fronts and then a new solution set, having cardinality of parent solution set, is selected from the upper-level non-dominated fronts. When some solutions are required to select from a particular front then crowding distances between the solutions of the front are measured and the isolated solutions are selected for the preservation of diversity. Different standard performance metrics are used to test the performance of the proposed approach. Different sizes standard benchmark test problems from TSPLIB are used for the purpose. Test results show that the proposed approach is efficient enough to solve multi-objective TSP.

Scheduling dual-arm cluster tools with multiple wafer types and residency time constraints

Accompanying the unceasing progress of integrated circuit manufacturing technology, the mainstream production mode of current semiconductor wafer fabrication is featured with multi-variety, small batch, and individual customization, which poses a huge challenge to the scheduling of cluster tools with single-wafer-type fabrication. Concurrent processing multiple wafer types in cluster tools, as a novel production pattern, has drawn increasing attention from industry to academia, whereas the corresponding research remains insufficient. This paper investigates the scheduling problems of dual-arm cluster tools with multiple wafer types and residency time constraints. To pursue an easy-to-implement cyclic operation under diverse flow patterns, we develop a novel robot activity strategy called multiplex swap sequence. In the light of the virtual module technology, the workloads that stem from bottleneck process steps and asymmetrical process configuration are balanced satisfactorily. Moreover, several sufficient and necessary conditions with closed-form expressions are obtained for checking the system's schedulability. Finally, efficient algorithms with polynomial complexity are developed to find the periodic scheduling, and its practicability and availability are demonstrated by the offered illustrative examples.

Discrete Spider Monkey Optimization for Travelling Salesman Problem

Meta-heuristic algorithms inspired by biological species have become very popular in recent years. Collective intelligence of various social insects such as ants, bees, wasps, termites, birds, fish, has been investigated to develop a number of meta-heuristic algorithms in the general domain of swarm intelligence (SI). The developed SI algorithms are found effective in solving different optimization tasks. Travelling Salesman Problem (TSP) is the combinatorial optimization problem where a salesman starting from a home city travels all the other cities and returns to home city in the shortest possible path. TSP is a popular problem due to the fact that the instances of TSP can be applied to solve real-world problems, implication of which turns TSP into a standard test bench for performance evaluation of new algorithms. Spider Monkey Optimization (SMO) is a recent addition to SI algorithms based on the social behaviour of spider monkeys. SMO implicitly adopts grouping and regrouping for the interactions to improve solutions; such multi-population approach is the motivation of this study to develop an effective method for TSP. This paper presents an effective variant of SMO to solve TSP called discrete SMO (DSMO). 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 TSP solution. The SOs are generated using the experience of a specific spider monkey as well as the experience of other members (local leader, global leader, or a randomly selected spider monkey) of the group. The performance and effectiveness of the proposed method have been verified on a large set of TSP instances and the outcomes are compared to other well-known methods. Experimental results demonstrate the effectiveness of the proposed DSMO for solving TSP.

A Hybrid PSO-GA Algorithm for Traveling Salesman Problems in Different Environments

In this study particle swarm optimization (PSO) is modified and hybridised with genetic algorithm (GA) using one’s output as the other's input to solve Traveling Salesman Problem(TSP). Here multiple velocity update rules are introduced to modify the PSO and at the time of the movement of a solution, one rule is selected depending on its performances using roulette wheel selection process. Each velocity update rule and the corresponding solution update rule are defined using swap sequence (SS) and swap operation (SO). K-Opt operation is applied in a regular interval of iterations for the movement of any stagnant solution. GA is applied on the final output swarm of the PSO to search the optimal path of the large size TSPs. Roulette wheel selection process, multi-point cyclic crossover and the K-opt operation for the mutation are used in the GA phase. The algorithm is tested in crisp environment using different size benchmark test problems available in the TSPLIB. In the crisp environment the algorithm gives approximately 100% success rate for the test problems up to considerably large sizes. Efficiency of the algorithm is tested with some other existing algorithms in the literature using Friedman test. Some approaches are incorporated with this algorithm for finding solutions of the TSPs in imprecise (fuzzy/rough) environment. Imprecise problems are generated from the crisp problems randomly, solved and obtained results are discussed. It is observed that the performance of the proposed algorithm is better compared to the some other algorithms in the existing literature with respect to the accuracy and the consistency for the symmetric TSPs as well as the Asymmetric TSPs.

Adaptive Scheduling of Cluster Tools With Wafer Delay Constraints and Process Time Variation

A cluster tool consists of several single-wafer processing chambers and a wafer-handling robot. Cluster tools are widely used for wafer fabrication in semiconductor manufacturing fabs. As the circuit width shrinks down to below 20 or even several nanometers, wafer waiting within a chamber after processing becomes more critical to wafer quality due to residual gases and heat. Conventional tool scheduling rules, such as the swap sequence and the backward sequence, may not satisfy strict upper limits on wafer delays, especially when process times fluctuate randomly. We examine a scheduling problem for cluster tools with strict upper limits on wafer delays under process time variation. We propose a new class of schedules, which not only keeps timing patterns steady as possible but also adapts timing of tasks in response to process time variation so as to satisfy wafer delay constraints robustly. We also derive conditions for which there exists such a schedule. We develop a mixed-integer programming model to find an optimal schedule among such adaptive schedules. By numerical experiments, we show that the proposed scheduling method can effectively cope with tight wafer delay constraints even under large process time variations. Note to Practitioners —As the circuit widths shrink down, residual gases and particles within chambers after processing wafers become more critical to wafer quality. In fact, leading fabs are now cleaning a chamber for each new wafer in order to reduce such quality risk. We propose a new practical method for scheduling tools that can significantly reduce such quality risk caused by wafer waiting within chambers after processing.

Scheduling Dual-Armed Cluster Tools for Concurrent Processing of Multiple Wafer Types With Identical Job Flows

As the order size for modern fabs tends to be smaller, fabs wish to process a class of similar wafer lots at a tool concurrently to reduce the work-in-progress lots as well as the total manufacturing lead time. We examine a scheduling problem for a dual-armed cluster tool that simultaneously produces multiple wafer types with identical wafer flow patterns but different process times. We prove that the conventional swap sequence, which is optimal and prevalently being used for single-wafer-type processing, is also optimal for such concurrent processing. We then propose a way of determining a release sequence of wafer types into the tool, called cycle plan , that maximizes the utilization of parallel chambers and hence increases the tool throughput rate. We present conditions for which the parallel chambers are shared by all wafer types and their workloads are evenly balanced so as to maximize the throughput rate. We also report the experimental results. Note to Practitioners —This paper suggests how to operate cluster tools for concurrent processing of similar wafer types. The results ensure that the conventional swap sequence is still effective for concurrent processing. We also provide a simple strategy of mixing different wafer types and the optimal release sequence for the wafers. We confirm that the tool throughput can be significantly improved when the release sequence of wafers is properly determined.

Robotic-cell scheduling with pick-up constraints and uncertain processing times

Technological developments have propelled the deployment of robots in many applications, which has led to the trend to integrate an increasing number of uncertain processes into robotic and automated equipment. We contribute to this domain by considering the scheduling of a dual-gripper robotic cell. For systems with one potential bottleneck, we determine conditions under which the widely used swap sequence does not guarantee optimality or even feasibility and prove that optimal schedules can be derived under certain conditions when building on two types of slack we introduce. With the addition of a third type of slack and the concept of fixed partial schedules, we develop an offline-online scheduling approach that, in contrast with previous work, is able to deal with uncertainty in all process steps and robot handling tasks, even under pick-up constraints. The approach can deal with single- or multiple-bottleneck systems, and is the first approach that is not restricted to a single predefined sequence such as the swap sequence. Our approach is well suited for real-world applications, since it generates cyclic schedules and allows integration into commonly-used frameworks for robotic-cell scheduling and control.We demonstrate the applicability of our approach to cluster tools in semiconductor manufacturing, showing that our approach generates feasible results for all tested levels of uncertainty and optimal or near-optimal results for low levels of uncertainty. With additional symmetry-breaking constraints, the model can be efficiently applied to industrial-scale test instances. We show that reducing uncertainty to below 10% of the processing time would yield significantly improved cycle lengths and throughput. We also demonstrate that the widely used swap sequence only finds solutions for less than 1% of the instances when strict pick-up constraints are enforced and processing times are heterogeneous. As our approach finds feasible solutions to all of these instances, it enables the application of robotic cells to a significantly broader application environment.

A swap sequence based Artificial Bee Colony algorithm for Traveling Salesman Problem

Abstract In this research paper, Artificial Bee Colony algorithm is modified with multiple update rules and K-opt operation to solve the Traveling Salesman Problem. Here the features of swap sequences and swap operations on the sequence of cities (solution/path) of the problem are used to create different solution (path) update rules of the algorithm. Eight different rules are proposed to update solutions in the algorithm. Updation of a solution by an employed bee or by an onlooker bee is done by a randomly selected rule from the rule set using Roulette Wheel selection process. In the scout bee phase of the algorithm, the perturbation technique, K-opt operation is applied on any stagnant solution for a fixed number of times for the possible improvement of it. The K-opt operation is again used at the end of the search process to improve the quality of the final solution (if possible). Proposed method is tested with a set of benchmark test problems from TSPLIB and it is observed that the efficiency of the algorithm is adequate with respect to the accuracy and the consistency for solving standard TSPs (Symmetric as well as Asymmetric) compared to the existing algorithms in the literature.

Modified Discrete Firefly Algorithm Combining Genetic Algorithm for Traveling Salesman Problem

The Firefly Algorithm (FA) has a few disadvantages in solving the constrained global optimization problem, including that it is difficult to produce initial population, the size of relative attractiveness has nothing to do with the absolute brightness of fireflies, the inertia weight does not take full advantage of the information of objective function, and it cannot better control and constrain the mobile distance of firefly. In this paper, we propose a novel method based on discrete firefly algorithm combining genetic algorithm for traveling salesman problem. We redefine the distance of firefly algorithm by introducing swap operator and swap sequence to avoid algorithm easily falling into local solution and accelerate convergence speed. In addition, we adopt dynamic mechanism based on neighborhood search algorithm. Finally, the comparison experiment results show that the novel algorithm can search perfect solution within a short time, and greatly improve the effectiveness of solving the traveling salesman problem, it also significantly improves computing speed and reduces iteration number.

Research on Intelligent Welding Robot Path Optimization Based on GA and PSO Algorithms

To make the welding robot more reasonable and furthermore improve the productivity and reduce costs, two intelligent algorithms for welding path optimization, genetic algorithm (GA) and discrete particle swarm optimization, are proposed to optimize the welding robot path. Through the improved selection of the operator, the GA achieves the fastest iterative efficiency. By introducing the “swap operator” and “swap sequence” in the particle swarm optimization algorithm, the PSO algorithm is improved for the solution of the discrete problem (welding robot path planning) which is superior to the continuous optimization problem. Besides, for the better iterative efficiency of PSO, the parameters of traditional inertia weight are determined by a linear inertia weigh, which can improve the convergence performance of the algorithm. The modeling and solutions of the two algorithms are discussed in detail to illustrate the applications in the welding robot path optimization. In order to compare the pros and cons of the two algorithms, the same welding tasks are presented, and Matlab simulation is carried out. The simulation results show that both genetic algorithm and particle swarm optimization algorithm can obtain the optimal or near-optimal welding path by iterative calculations.