A Multi-Objective Optimization Approach for Multi-Head Beam-Type Placement Machines

This paper addresses a highly challenging scheduling problem in the field of printed circuit board (PCB) assembly systems using Surface Mounting Devices (SMD). After describing some challenging optimization sub-problems relating to the heads of multi-head surface mounting placement machines, we formulate an integrated multi-objective mathematical model considering of two main sub-problems simultaneously. The proposed model is a mixed integer nonlinear programming one which is very complex to be solved optimally. Therefore, it is first converted into a linearized model and then solved using an efficient multi-objective approach, i.e., the augmented epsilon constraint method. An illustrative example is also provided to show the usefulness and applicability of the proposed model and solution method.PCB assembly. Multi-head beam-type placement machine. Multi-objective mathematical programming. Augmented epsilon-constraint method

A note on a motion control problem for a placement machine.

Assembling printed circuit boards effciently using automated placement machines is a challenging task. Here, we focus on a motion control problem for a specific type of placement machines. More specifically,the problem is to establish movement patterns for the robot arm, the feeder rack,and -when appropriate- the work table, of a sequential, pick-and-place machine. In this note we show that a (popular) greedy strategy may not always yield an optimum solution. However, under the Tchebychev metric, as well as under the Manhattan metric, we can model the problem as a linear program, thereby establishing the existence of a polynomial time algorithm for this motion control problem. Finally, we give experimental evidence that computing optimal solutions to this motion control problem can yield significantly better solutions than those found by a greedy method.Algorithms; Computational complexity; Control; Printed circuit boards;

Algorithmic Solutions for Combinatorial Problems in Resource Management of Manufacturing Environments

This thesis studies the use of heuristic algorithms in a number of combinatorial problems that occur in various resource constrained environments. Such problems occur, for example, in manufacturing, where a restricted number of resources (tools, machines, feeder slots) are needed to perform some operations. Many of these problems turn out to be computationally intractable, and heuristic algorithms are used to provide efficient, yet sub-optimal solutions. The main goal of the present study is to build upon existing methods to create new heuristics that provide improved solutions for some of these problems. All of these problems occur in practice, and one of the motivations of our study was the request for improvements from industrial sources. We approach three different resource constrained problems. The first is the tool switching and loading problem, and occurs especially in the assembly of printed circuit boards. This problem has to be solved when an efficient, yet small primary storage is used to access resources (tools) from a less efficient (but unlimited) secondary storage area. We study various forms of the problem and provide improved heuristics for its solution. Second, the nozzle assignment problem is concerned with selecting a suitable set of vacuum nozzles for the arms of a robotic assembly machine. It turns out that this is a specialized formulation of the MINMAX resource allocation formulation of the apportionment problem and it can be solved efficiently and optimally. We construct an exact algorithm specialized for the nozzle selection and provide a proof of its optimality. Third, the problem of feeder assignment and component tape construction occurs when electronic components are inserted and certain component types cause tape movement delays that can significantly impact the efficiency of printed circuit board assembly. Here, careful selection of component slots in the feeder improves the tape movement speed. We provide a formal proof that this problem is of the same complexity as the turnpike problem (a well studied geometric optimization problem), and provide a heuristic algorithm for this problem.Siirretty Doriast

A Multi-Exchange Neighborhood Search Heuristic for an Integrated Clustering and Machine Setup Model for PCB Manufacturing

In the manufacture of printed circuit boards, electronic components are attached to a blank board by one or more pick-and-place machines. Frequent machine setups, though time consuming, can reduce overall processing time. We consider the Integrated Clustering and Machine Setup (ICMS) model, which incorporates this tradeoff between processing time and setup time and seeks to minimize the sum of the two. Solving this model to optimality is intractable for very large-scale instances. We show that ICMS is NP-hard and consequently propose and test a heuristic based on multi-exchange neighborhood search structures. Initial numerical results are very encouraging. Keywords: Printed circuit board assembly, feeder slot assignment, product clustering, integer programming, computational complexity, heuristics

Comparison of a bat and genetic algorithm generated sequence against lead through programming when assembling a PCB using a 6 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 paper 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. 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 PCB assembly scenario, we demonstrate the considerable effectiveness of the proposed discrete Bat Algorithm (BA) to improve selection of feeder arrangement and placement sequence in PCB assembly operations and achieve high throughput production. The results also highlighted that the even though the algorithms out performed traditional lead through programming techniques, the programmer must consider the influence of different robot motions

Setup Optimization in High-Mix Surface Mount PCB Assembly

Siirretty Doriast