Tool Switching Problem Research Articles

Exploiting symmetry for the job sequencing and tool switching problem

The Job Sequencing and Tool Switching Problem (SSP), a well-known combinatorial optimization problem in the domain of Flexible Manufacturing Systems (FMS), is studied in this article. The aim of this research is to improve the currently known exact solution methodology for this NP-hard problem. We propose a new integer linear programming approach with symmetry-breaking and tightening cuts that provably outperformed the existing methodology described in the literature. The computational study conducted on a data set with 1,050 instances showed that the developed method can solve hard instances that were not solvable with the state-of-the-art methods presented in the literature.

Biased random-key genetic algorithm for the job sequencing and tool switching problem with non-identical parallel machines

We address the job sequencing and tool switching problem associated with non-identical parallel machines – a variation of the well-known sequencing and switching problem (SSP) better adapted to reflect the challenges in modern production environments. The NP-hard problem is approached by considering two isolated objective functions: the minimization of the makespan and the minimization of the total flow time. We present two versions of a parallel biased random-key genetic algorithm hybridized with tailored local search procedures that are organized using variable neighborhood descent. The proposed methods are compared with state-of-the-art methods by considering 640 benchmark instances from literature. For both objective functions considered, the proposed methods consistently outperform the compared methods. All known optimal values for both objectives are achieved, and a substantial gap is reported for all instance groups when compared with the best previously published solution values.

Hybridizing local searching with genetic algorithms for the job sequencing and tool switching problem with non-identical parallel machines

The job sequencing and tool switching problem (SSP) is an old and highly studied problem. However, the SSP with non-identical parallel machines (SSP-NPM) is a new generalization of this problem. Since the SSP-NPM has been very recently introduced, the number of solution methods for this problem is low. Additionally, exact solution methods are mostly insufficient to find a good solution within a reasonable computational time since this problem is NP-hard. Therefore, heuristic approaches are more appropriate, especially when solving large-size problems. Thus, this study presents a new hybrid algorithm that is a combination of a genetic algorithm (GA) and a local search (LS) technique. Both of these methods are greatly preferred by authors for solving job scheduling problems. Thereby, this study combines their strengths to solve the SSP-NPM. Two versions of the proposed method are tested with benchmark instances. These versions differ in terms of their tool optimization policies: the first uses the well-known “keep tool needed soonest” (KTNS) policy, while the second uses the “randomly remove tool” (RRT) policy. Computational experiments showed that combining some of the features of GA and LS methods for the SSP-NPM contributed greatly to the quality of the solution. Two versions of the proposed hybrid method were compared to a mixed-integer programming model and several schemes of an iterated local search algorithm. Our computational results show that both versions of the proposed hybrid method were significantly better than the other methods, and were able to find the solutions within a reasonable computational time.

Multiobjective Sequence-Dependent Job Sequencing and Tool Switching Problem

This article considers the extension of the job sequencing and tool switching problem with sequence-dependent setup times (SDSSP) and with the requirement to comply with the due date of the processed jobs. This extension is motivated by the practical application in manufacturing environment where the products manufactured may be subjected to a specific due date. This study develops a multiobjective SDSSP model (MO-SDSSP) to simultaneously minimize the total setup time of tool switches and the tardiness of the machining process. Then, a two-stage Multiobjective Adaptive Large Neighborhood Search (MOALNS) and Simulated Annealing (SA) is presented as a heuristic algorithm for the MO-SDSSP, in which the MOALNS is proposed to solve the job sequencing subproblem while the SA is used to solve the tool switching subproblem. Subsequently, the performance of MOALNS-SA is compared to several popular multiobjective optimization algorithms. Comparison on four performance criteria has shown the applicability of the MOALNS. Finally, managerial analysis is performed to analyze the relationship between the total tool setup time and the compliance of due dates.

A comparison of different mathematical models for the job sequencing and tool switching problem with non-identical parallel machines

This paper addresses the generalisation of the NP-hard job sequencing and tool switching problem with non-identical parallel machines and sequence-dependent setup times where a set of jobs is to be scheduled on unrelated parallel machines with machine-dependent processing and tool switching times. Three different mathematical models for two different objectives are presented and applied to newly generated test instances. The instances are compared and analysed using a commercial solver and an iterated local search heuristic. Overall, it is shown that the solution quality obtained by the mathematical models depends on the size of the problem instance as well as the tool requirements. The precedence-based formulation is superior in general to the position-based and time-index-based formulation for dense problem instances while the position-based formulation works well for sparse problems. With an increasing problem size, the metaheuristic requires significantly less time to find near-optimal solutions than the mathematical models.

A two-stage heuristic for the sequence-dependent job sequencing and tool switching problem

The job sequencing and tool switching problem is a combinatorial optimization problem that commonly happens in a flexible manufacturing system environment. In this type of environment, a set of flexible manufacturing machines can be configured with various tools to process different jobs and the requirement to switch tools may correspond to a reduction of productivity. Consequently, research on the job sequencing and tool switching problem has been concentrated on minimizing the number of tools switches. This paper discusses the sequence-dependent job sequencing and tool switching problem. The sequence-dependent job sequencing and tool switching problem extends the standard model by considering non-uniform setup times since industrial applications indicate that a tool setup time might be influenced by the previously installed tool at the same magazine slot. A two-stage heuristic procedure is developed here. In the first stage, an adaptive large neighborhood search is deployed for finding the near-optimal job sequence. Then, in the second stage, a combination of the Keep Tool Needed Soonest policy and simulated annealing is proposed for the tooling sub-problem. Comprehensive computational experiments are carried out to demonstrate the efficacy and robustness of the proposed method for solving the sequence-dependent job sequencing and tool switching problem.

An iterated local search procedure for the job sequencing and tool switching problem with non-identical parallel machines

In this paper, a new generalization of the uniform job sequencing and tool switching problem is presented. It considers non-identical parallel machines, which differ in tool magazine capacity and setup times. Applications of the problem can be found in the metal working or semiconductor manufacturing industries when the jobs require different tool sets for processing. The paper provides a Mixed Integer Programming formulation for the job sequencing and tool switching problem with machine-dependent processing and tool switching times under the consideration of three conflicting objectives (minimizing the total flowtime, minimizing the makespan and minimizing the total number of tool switches). Different efficient construction heuristics and Iterated Local Search methods are proposed and evaluated, using 640 new and publicly available instances. The results of the construction heuristics, the Iterated Local Search schemes and a Mixed Integer Programming Solver are discussed. The extensive computational experiments show the merit of the perturbation strategy in order to overcome local optima. It is shown that certain methods are more or less suitable depending on the objective function.

The job sequencing and tool switching problem with sequence-dependent set-up time

Job sequencing and tool switching (SSP) is a well-known combinatorial optimization problem that aims to minimize the number of tool switches. The problem mainly arises in a flexible manufacturing system, in which machines can be configured with various tools to process different jobs and tool switches will reduce productivity. While the general studies assume uniform set-up time for tool switching, applications in the industries indicate that the set-up time of a tool might depend on the previously installed tool of the same slot. Therefore, this article proposes two integer linear programming models for the sequence-dependent SSP, namely, the five-index formulation and the multicommodity flow formulation. Experimental tests are executed to compare the sequence-dependent SSP with the uniform SSP, and the results show the effectiveness of multicommodity flow formulation. Finally, several managerial discussions are derived from the results.

A simple and effective hybrid genetic search for the job sequencing and tool switching problem

The job Sequencing and tool Switching Problem (SSP) has been extensively studied in the field of operations research, due to its practical relevance and methodological interest. Given a machine that can load a limited amount of tools simultaneously and a number of jobs that require a subset of the available tools, the SSP seeks a job sequence that minimizes the number of tool switches in the machine. To solve this problem, we propose a simple and efficient hybrid genetic search based on a generic solution representation, a tailored decoding operator, efficient local searches and diversity management techniques. To guide the search, we introduce a secondary objective designed to break ties. These techniques allow to explore structurally different solutions and escape local optima. As shown in our computational experiments on classical benchmark instances, our algorithm significantly outperforms all previous approaches while remaining simple to apprehend and easy to implement. We finally report results on a new set of larger instances to stimulate future research and comparative analyses.

A new multicommodity flow model for the job sequencing and tool switching problem

In this paper a new multicommodity flow mathematical model for the Job Sequencing and Tool Switching Problem (SSP) is presented. The proposed model has an LP relaxation lower bound equal to the number of tools minus the tool machine's capacity. Computational tests were performed comparing the new model with the models of the literature. The proposed model performed better, both in execution time and in the number of instances solved to optimality.

Deep memetic models for combinatorial optimization problems: application to the tool switching problem

Memetic algorithms are techniques that orchestrate the interplay between population-based and trajectory-based algorithmic components. In particular, some memetic models can be regarded under this broad interpretation as a group of autonomous basic optimization algorithms that interact among them in a cooperative way in order to deal with a specific optimization problem, aiming to obtain better results than the algorithms that constitute it separately. Going one step beyond this traditional view of cooperative optimization algorithms, this work tackles deep meta-cooperation, namely the use of cooperative optimization algorithms in which some components can in turn be cooperative methods themselves, thus exhibiting a deep algorithmic architecture. The objective of this paper is to demonstrate that such models can be considered as an efficient alternative to other traditional forms of cooperative algorithms. To validate this claim, different structural parameters, such as the communication topology between the agents, or the parameter that influences the depth of the cooperative effort (the depth of meta-cooperation), have been analyzed. To do this, a comparison with the state-of-the-art cooperative methods to solve a specific combinatorial problem, the Tool Switching Problem, has been performed. Results show that deep models are effective to solve this problem, outperforming metaheuristics proposed in the literature.

A hybrid method of 2-TSP and novel learning-based GA for job sequencing and tool switching problem

One of the well-known problems in single machine scheduling context is the Job Sequencing and Tool Switching Problem (SSP). The SSP is optimally sequencing a finite set of jobs and loading restricted subset of tools to a magazine with the aim of minimizing the total number of tool switches. It has been proved in the literature that the SSP can be reduced to the Job Sequencing Problem (JSeP). In the JSeP, the number of tool switches from the currently processed job to the next job depends on the sequencing of all predecessors. In this paper, the JSeP is modeled as a Traveling Salesman Problem of Second Order (2-TSP). We call the induced JSeP by 2-TSP as the Job Sequencing Problem of Second Order (2-JSeP) with a different objective function formulation from JSeP and prove that 2-JSeP is NP-hard. Then the Assignment Problem of Second Order (2-AP) and Karp-Steele patching heuristic are incorporated to solve 2-JSeP. The obtained solution, however, does not guarantee the optimal sequence and are used to seed a Dynamic Q-learning-based Genetic Algorithm (DQGA) to improve the solution quality. Q-learning, which is a kind of reinforcement learning method, is used to learn from the experience of selecting the order of mutation and crossover operators in each generation of the genetic algorithm. The computational results on 320 benchmark instances show that the proposed DQGA is comparable to the state-of-the-art methods in the literature. The DQGA even outperforms the existing methods for some instances, as could improve the reported “best-known solutions” in notably less time. Finally, through the statistical analysis, the performance of DQGA is compared with those of non-learning genetic algorithms.

Order picking along a crane-supplied pick face: The SKU switching problem

This paper treats an order picking system where a crane continuously relocates stock keeping units (SKUs) in a high-bay rack subdivided into the bottommost picking level and the upper reserve area. The capacity of the pick face is not large enough to store all SKUs, so that the crane has to ensure that all SKUs demanded by a current picking order are timely provided and picker idle time is avoided. We aim at a processing sequence of picking orders and a SKU switching plan, i.e., an instruction when to exchange which SKUs in the picking level, such that an unobstructed order picking is enabled. Our problem is closely related to the tool switching problem of flexible manufacturing. Here, each job requires a subset of tools to be loaded into the tool magazine (with limited capacity) of a single flexible machine. We, however, show that an alternative objective function, i.e., minimizing the maximum number of switches between any successive job pair, is better suited in the warehouse context and even better results can be obtained by a multi-objective approach. Elementary complexity proofs as well as suited solution procedures are provided and we also address managerial aspects, such as the sizing of the pick face.

An algorithmic framework for tool switching problems with multiple objectives

The tool switching problem is a classical and extensively studied problem in flexible manufacturing systems. The standard example is a CNC machine with a limited number of tool slots to which tools for drilling and milling have to be assigned, with the goal of minimizing the number of necessary tool switches and/or the number of machine stops over time. In this work we present a branch-and-bound based algorithmic framework for a very general and versatile formulation of this problem (involving arbitrary setup and processing times) that allows addressing both of these objectives simultaneously (or only of them), and that improves over several known approaches from the literature. We demonstrate the usefulness of our algorithm by rigorous theoretical analysis and by experiments with both large real-world and random instances.

Scheduling identical parallel machines with tooling constraints

We model and solve the problem of sequencing a set of jobs with specified processing times and tool requirements on a set of identical parallel machines. Decisions concern the assignment of jobs to machines, their sequencing, and the allocation of tools on each machine. The objective function minimizes the makespan. We propose two mathematical formulations of the problem and an adaptive large neighborhood search metaheuristic in which the destroy and repair operators exploit the structures of two well-known and related combinatorial optimization problems, namely the parallel machine scheduling problem and the job sequencing and tool switching problem on a single machine. Computational experiments conducted on two data sets of 1440 instances show that our algorithm produces excellent results and outperforms existing heuristics.

Minimizing tool switching and indexing times with tool duplications in automatic machines

Minimization of nonmachining time is a crucial issue for effective and profitable utilization of automatic machining centers. Most of the automatic machining centers contain an automatic tool changer (ATC) for holding multiple cutting tools. Effective operation of ATC in relation to the parts assigned for machining is critical in minimizing nonmachining times. There are actually two main operations on ATCs which can be reduced by making use of suitable optimization procedures. These operations are known as “ATC indexing problem” and “tool switching problem (ToSP).” These problems are separately addressed as NP-hard problems in the literature and mostly solved independently so far. In the present work, we made an attempt to solve these problems simultaneously by making use of a simulated annealing (SA) algorithm with novel solution coding/encoding strategies. The results are compared with the lower bounds obtained by a method proposed in the present work. Promising findings are expected to contribute to the possible future work of this research field.

Minimizing the number of switch instances on a flexible machine in polynomial time

We revisit the tool switching problem on a flexible manufacturing machine. We present a polynomial algorithm for the problem of finding a switching plan that minimizes the number of tool switch instances on the machine, given a fixed job sequence. We prove tight hardness results for the variable sequence case with the same objective function, as well as a new objective function naturally arising in multi-feeder mailroom inserting systems.

Scheduling multi-colour print jobs with sequence-dependent setup times

In this paper, a scheduling problem is considered which arises in the packaging industry. Plastic and foil wrappers used for packaging candy bars, crisps and other snacks typically require overlay printing with multiple colours. Printing machines used for this purpose usually accommodate a small number of colours which are loaded into a magazine simultaneously. If two consecutively scheduled print jobs require significantly different colour overlays, then substantial down times are incurred during the transition from the former magazine colour configuration to the latter, because ink cartridges corresponding to colours not required for the latter job have to be cleaned after completion of the former job. The durations of these down times are therefore sequence dependent (the washing and refilling time is a function of the number of colours in which two consecutive printing jobs differ). It is consequently desirable to schedule print jobs so that the accumulated down times associated with all magazine colour transitions are as short as possible for each printing machine. We show that an instance of this scheduling problem can be modelled as the well-known tool switching problem, which is tractable for small instances only. The problem can, however, be solved rather effectively in heuristic fashion by decomposing it into two subproblems: a job grouping problem (which can be modelled as a unicost set covering problem) and a group sequencing problem (which is a generalisation of the celebrated travelling salesman problem). We solve the colour print scheduling problem both exactly and heuristically for small, randomly generated test problem instances, studying the trade-off between the time efficiency and solution quality of the two approaches. Finally, we apply both solution approaches to real problem data obtained from a printing company in the South African Western Cape as a special case study.

The modular tool switching problem

This article analyzes the complexity of the modular tool switching problem arising in flexible manufacturing environments. A single, numerically controlled placement machine is equipped with an online tool magazine consisting of several changeable tool feeder modules. The modules can hold a number of tools necessary for the jobs. In addition to the online modules, there is a set of offline modules which can be changed to the machine during a job change. A number of jobs are processed by the machine, each job requiring a certain set of tools. Tools between jobs can be switched individually, or by replacing a whole module containing multiple tools. or a whole module, containing multiple tools can be replaced. We consider the complexity of the problem of arranging tools into the modules, so that the work for module and tool loading is minimized. Tools are of uniform size and have unit loading costs. We show that the general problem is NP-hard, and in the case of fixed number of modules and fixed module capacity the problem is solvable in polynomial time.

Cross entropy-based memetic algorithms: An application study over the tool switching problem

Abstract This paper presents a parameterized schema for building memetic algorithms based on cross-entropy (CE) methods. This novel schema is general in nature, and features multiple probability mass functions and Lamarckian learning. The applicability of the approach is assessed by considering the Tool Switching Problem, a complex combinatorial problem in the field of Flexible Manufacturing Systems. An exhaustive evaluation (including techniques ranging from local search and evolutionary algorithms to constructive methods) provides evidence of the effectiveness of CE-based memetic algorithms.