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การประชุมวิชาการดานการวิจัยดําเนินงานแหงชาติ ประจําป 2554
วันที่
8-9 กันยายน 2554 ณ โรงแรม เอส ดี อเวนิว กรุงเทพฯ
Interaction of Crossover and Mutation Operations for Designing Non-rotatable Machine Layout
Srisatja Vitayasak 1 and Pupong Pongcharoen 2
Department of Industrial Engineering, Faculty of Engineering, Naresuan University, Pitsanulok 65000, Thailand.
Corresponding e-mail addresses: pupongp@nu.ac.th and srisatjav@nu.ac.th
Abstract
The design task on machine layout problem involves the
arrangement of machines into shop floor area to optimise performance
measures such as minimising the total handling distances of materials
and/or parts to be performed on a predefined sequence of machines
located in a specified area. Shorten total handing distance leads to the
efficiency of productivity and it related costs. Machine Layout Design
(MLD) problem is classified as Non-deterministic Polynomial-time
hard problem, which means that the amount of computation required to
find solutions increases exponentially with problem size. Solving this
kind of problem by full numerical methods especially for the large size
can be computationally expensive. The objectives of this paper were to
i) describe the application of Genetic Algorithm (GA) for designing
non-rotatable machine layout in a multiple-row environment aiming to
minimise the total material handling distance and ii) investigate genetic
operators (including sixteen crossover and eight mutation operators),
that have an influence on the solution quality. An automated machine
layout designing tool has been coded in modular style using a general
purpose programming language called Tcl/Tk. The computational
experiment was designed using four MLD benchmarking datasets
adopted from literature and conducted with five replicates on each
combination. A total of 2,560 computational runs were carried out. The
analysis on the results obtained from computational experiments
suggested that the proposed algorithm performed distinctively on each
problem size when adopting different crossover and mutation operator.
The best crossover and mutation operators for MLD problem were
statistically compared and reported.
Keyword: Multiple rows, Machine layout design, Genetic Algorithm,
Crossover, Mutation.
1. Introduction
Genetic Algorithm (GA) introduced by Holland [1] and
Goldberg [2] is biologically-based stochastic search algorithm for
approximating optimal solution in a search space and therefore gained
more interest during the last few decades [3]. GA starts with an initial
population of random solution called chromosome. Chromosome
representation deals with a coding of problem which has been used in a
variety of approaches (binary digits, lists of integers, floating points and
strings) depending on the nature of the problem. Each approach yields
differently good solution [4]. GA uses probabilistic (non-deterministic)
transition rules to guide a highly exploitative search and also performs a
multiple directional search by maintaining a population of potential
solutions. In each iteration of the search process (generation), GA
exploits the best solution within the population and also explores
different parts of solution space simultaneously [3]. This mechanism
can be adjusted for helping to escape from local optimal. Therefore, a
number of GA applications have increased in the last few decades and
can be found in the production and operations management literature [4,
5]. GA has widely been applied to the area of industrial engineering
such as machine layout design, scheduling, transportation and many
other combinatorial optimisation problems.
The genetic operations, including crossover and mutation,
are the process to create new offspring in each generation. Crossover
operator helps GA move towards a local optimum. Mutation operator is
the exploration operator which tends to move the search to a new
neighbourhood [6]. A number of new offspring were based on the
probabilities of crossover and mutation. A variety of new offspring
depends on crossover and mutation mechanisms. Sixteen crossover and
eight mutation operations have been described by Pongcharoen [7].
They were used for scheduling the production of complex products in
the capital good industry. Genetic operators have also been investigated
in flow shop scheduling [8], travelling salesman problem [9], facility
layout problem [10, 11] and communication network design [12].