零工式生產排程問題(Job-Shop Scheduling Problem, JSP)在過去的數十年被大量研究。許多學者以各式各樣的方法研究此問題，都有良好的成效，啟發式演算法被大量應用於此問題。常見的啟發式演算法在求解組合最佳化方面的問題(combinatorial optimization problems)為基因演算法(Genetic Algorithm, GA)、塔布搜尋法(Tabu Search Approach)、蟻族最佳化演算法(Ant Colony Optimization, ACO)、模擬退火法(Simulated Annealing, SA)以及粒子群最佳化演算法 (Particle Swarm Optimization, PSO)等等，且往往都能在有限的時間內求得近似的最佳解。
隨著科技的進步與演化，傳統的零工式生產排程已經不足以應付少量多樣式的生產型態。企業處於在競爭激烈的製造業中，為了降低生產成本，有效利用產能，提高競爭力，而衍生出更具彈性且更具複雜度的彈性零工式生產排程問題 (Flexible Job-Shop Scheduling Problem, FJSP)。傳統的零工式生產問題，只針對每個加工作業進行排程，然而由其衍生出來的彈性零工式生產問題，不但要決定每個加工作業的排程，也要決定每個加工作業所需加工的機台，因此本研究的問題比傳統的零工式生產排程的問題更加的複雜且艱澀。對於彈性零工式生產排程問題，要在可以合理的時間內找出最佳解是相當困難的。
本篇論文裡，我們採用改良簡化群體演算法 (improved simplified swarm optimization, iSSO)來解決彈性零工式生產排程問題，並與幾個著名的啟發式演算法進行比較。

The job-shop scheduling problem (JSP) has been studied extensively in the past years. Many scholars have used various methods to study this problem and have obtained excellent results, in which heuristic algorithms are often applied.
There are many famous heuristic algorithms that can generate approximate solutions close to the optimum with less computational time in combinational optimization problem, such as Genetic Algorithm (GA), Tabu Search Approach, Ant Colony Optimization (ACO), Simulated Annealing (SA) and Particle Swarm Optimization (PSO).
Because of the development and progress of the technology, small batch number and variety of production methods have been different from the job shop problem. In the manufacturing industry, companies must reduce production costs and increase production capacity to improve competitiveness and develop more flexible and complex problem, called flexible job-shop scheduling problem (FJSP).
Since more complicated constraints, the flexible job-shop scheduling problem is regarded as more difficult problem than the job-shop scheduling problem, which is hard to find the best solution within a reasonable time.
In this paper, we use the improved simplified swarm optimization (iSSO) to solve the flexible job-shop scheduling problem and compare it with several famous heuristic algorithms.

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