Mika Johnsson

An adaptive hybrid genetic algorithm for the three-matching problem

This paper presents a hybrid genetic algorithm (GA) with an adaptive application of genetic operators for solving the 3-matching problem (3MP), an NP-complete graph problem. In the 3MP, we search for the partition of a point set into minimal total cost triplets, where the cost of a triplet is the Euclidean length of the minimal spanning tree of the three points. The problem is a special case of grouping and facility location problems. One common problem with GA applied to hard combinatorial optimization, like the 3MP, is to incorporate problem-dependent local search operators into the GA efficiently in order to find high-quality solutions. Small instances of the problem can be solved exactly, but for large problems, we use local optimization. We introduce several general heuristic crossover and local hill-climbing operators, and apply adaptation to choose among them. Our GA combines these operators to form an effective problem solver. It is hybridized as it incorporates local search heuristics, and it is adaptive as the individual recombination/improvement operators are fired according to their online performance. Test results show that this approach gives approximately the same or even slightly better results than our previous, fine tuned GA without adaptation. It is better than a grouping GA for the partitioning considered. The adaptive combination of operators eliminates a large set of parameters, making the method more robust, and it presents a convenient way to build a hybrid problem solver.

ON SOLVING SINGLE MACHINE OPTIMIZATION PROBLEMS IN ELECTRONICS ASSEMBLY

This paper deals with optimization problems arising in printed circuit board (PCB) assembly. Todays automated manufacturing systems involve a large variety of special purpose robots that together form the production line. The organization of the production includes several problems to be solved, starting from top-level tactical decisions at scheduling, through product grouping and line balancing, to single machine optimization problems. The paper deals on the single machine optimization: determining the order of component insertions and scheduling the assignment of different nozzles (tools) to the printing heads. The aim is to maximize the throughput of the machine. The machine type considered is the general surface mounting (GSM) machine. The problem is solved by modeling the production situation and the machine, decomposing the arising optimization problems into hierarchical levels, and developing effective heuristics for solving them. The practical results of the new optimizing system show significant increase (5–10%) in the productivity when compared to the current state.

Scheduling Algorithms for Computer-Aided Line Balancing in Printed Circuit Board Assembly.

Generalized flexible flow line (GFFL) is a scheduling environment comprising several machine banks which the products visit in the same order but can skip some machine banks. The type of machines in a bank can differ but they are suitable for performing the same manufacturing tasks. To change one product to another demands a set-up operation of the machine. This paper describes several scheduling algorithms for the GFFL problem. The overall structure of these algorithms is similar, consisting of machine allocation and sequencing phases. The algorithms have been integrated into an interactive production scheduling system for electronics assembly. Sample cases are used to illustrate the operation of the system in practice.

Job grouping in surface mounted component printing

Abstract The arrangement of operations in a production line for mounting the surface components on a printed circuit board is discussed. The production program includes a wide range of different products, which causes frequent set-up operations. The overall efficiency of the production line depends heavily on how the printing operations are organized. Set-ups cause delays which can be cut down by selecting carefully the feeders for the components and by solving a suitable sequence for the products. We describe an integrated production management system for job grouping. The system utilizes approximate algorithms for minimizing the number of component switching instants. A discussion of the exact minimization by using mathematical 0/1 integer programming approach is also given. The revision of the production management system has had a major impact on the productivity, and an increase of ca. 58% in the number of component insertions per hour is observed.

Three Perspectives for Solving the Job Grouping Problem

The production efficiency of printed circuit board (PCB) assembly depends strongly on the organization of the component placement jobs. This is characteristic, especially in a high-mix low-volume production environment. The present study discusses the problem of arranging the jobs of one machine into groups in such a way that the job change costs will be minimized when the costs depend on the number of the job groups. This problem is motivated by the practical case where the group utilizes a common machine set-up and the number of set-up occasions is the dominating factor in the production line optimization. The problem is well known and its large instances are hard to solve to optimality. We show how real-life problem instances can be solved by three different methods: efficient heuristics, 0/1-programming, and constraint programming. The first two of these are standard approaches in the field, whereas the application of constraint programming is new for the job grouping problem. The heuristic approach turns out to be efficient: algorithms are fast and produce optimal or nearly optimal groupings. 0/1-programming is capable of finding optimal solutions to small problem instances and it therefore serves as a benchmark to approximative methods. The constraint approach solves moderately large problem instances to optimality and it has the great advantage that changing the problem formulation is relatively easy one can add new constraints or modify the details of the existing ones flexibly.

Determining the Proper Number and Price of Software Licenses

Software houses sell their products by transferring usage licenses of various software components to the customers. Depending on the kind of software, there are several different license types that allow controlled access of services. The two most popular types are the fixed license, which gives access rights for an identified workstation, and the floating license, which restricts the number of simultaneous users to a certain bound. The latter of these types is advantageous when the users do not demand full-time services and occasional lack of access is bearable. The problem of deciding the number of floating licenses is studied in the present paper. Based on the expected usage profile of the software, we calculate the minimal number of licenses that guarantees that the customers get service better than a given lower bound. The problem is studied by using certain queuing models, known as the Erlang toss system, the Erlang delay system, and the Engset model. None of these analytic models consider, however, the transient period that we analyze by means of simulation and by the so-called modified offered load approximation. We also give simple formulas presenting how the number of software licenses needed to keep the probability of nonaccess below a given blocking level grows as a function of the offered load, which is the proportion of the time used in the case that all requests were successful. Results of the study may be used for setting license prices and for determining the proper number of licenses.

Estimating printed circuit board assembly times using neural networks

Several production planning tasks in the printed circuit board (PCB) assembly industry involve the estimation of the component placement times for different PCB types and placement machines. This kind of task may be, for example, the scheduling of jobs or line balancing for single or multiple jobs. The simplest approach to time estimation is to let the production time be a linear function of the number of components to be placed. To achieve more accurate results, the model should include more parameters (e.g. the number of different component types, the number of different component shapes, the dimensions of the PCBs, etc.). In this study we train multilayer neural networks to approximate the assembly times of two different types of assembly machines based on several parameter combinations. It turns out that conventional learning methods are prone to overfitting when the number of hidden units of the network is large in relation to the number of training cases. To avoid this and complicated training and testing, we use Bayesian regularisation to achieve efficient learning and good accuracy automatically.

Selecting the nozzle assortment for a Gantry-type placement machine

Electronics manufacturing systems employ increasingly multi-head gantry machines, where several vacuum nozzles are used simultaneously in pick-and-place operations to insert components on bare PCBs. Their use includes several options that have an impact on the overall manufacturing speed of the machine. In the present paper we address the problem of selecting the nozzles for this kind of a gantry machine, which is an important subproblem of the larger scheduling problem of multi-head gantry machines. Nozzles come in different types, and different types of components may require different types of nozzles in their placing. We address first a case where a single PCB type is manufactured and the only limitation on the number of nozzles is given by the capacity of the placement head. Then we discuss the case where there is a budget limitation on the total cost of the nozzles we can buy. We show that both of these problems can be solved optimally by the means of efficient greedy algorithms. We also discuss the case of selecting nozzles when manufacturing multiple different PCB types.

Supporting Production Planning by Production Process Simulation

An interactive production planning system for electronic industry is described. PCB component printing is used as a case study, but the method can be adapted to other similar environments of generalized flexible flow line. The system simulates the production from an initial situation to a given moment in the future. The input defines the product batches, their allocation and sequence for each machine and the due dates. The output includes summaries of the production period including the lateness of the batches and machine workload charts. The user can reconsider the allocation and sequencing of the batches and repeat the simulation and update operations to find a better balancing of the workload.

Estimating the Production Times in PCB Assembly

Several control problems of PCB assembly industry involve the estimation of the component placement times for various different placement robots. A standard approach, widely used in scientic literature, is to let the time to be a linear function of the number of components. In this paper, we demonstrate that a more realistic model should include additional parameters (e.g., the number of different component types and the board size). Linear multiregression indicates that the coefficient of determination for the improved model is over 90 percent.