## Optimization of single-objective job-shop scheduling problem

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Cost minimization for processing a set of independent orders on a set of distinct parallel machines

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This suite can be used to evaluate the performance of single objective unconstrained optimization techniques for integer variables and can be used as black-box optimization problems.

Some of the features of the problem are
(i) A machine can process multiple orders whereas an individual order cannot be processed on multiple machines.

(ii) A machine can process only one order at a given point of time.

(iii) The processing cost and time of an order are machine dependent.

(iv) Every order is associated with a release and due date. The processing of the order can be performed on or after the release date but has to be completed on or before the due date.

There are ten minimization optimization problems in this suite (P1S1.p, P1S2.p, P2S1.p, P2S2.p, P3S1.p, P3S2.p, P4S1.p, P4S2.p, P5S1.p and P5S2.p). Each of them has the following format

[F] = P1S1(X);

Input: population (or solution, denoted by X)
Output: the objective function value of the population (F).

The file ProblemDetails.p can be used to determine the lower and upper bounds along with the function handle for each of the cases. The format is

[lb,ub,fobj] = ProblemDetails(n);

Input: n is an integer from 1 to 10.
Output: (i) the lower bound (lb),
(ii) the upper bound (ub), and
(iii) function handle (fobj).

The file Script.m shows how to use the inbuilt ga function of MATLAB.

The file plotgc.p is used to plot the Gantt Chart from the solution of the optimization problem

The dimension of the problems are

P1S1 & P1S2: 06 integer variables
P2S1 & P2S2: 14 integer variables
P3S1 & P3S2: 24 integer variables
P4S1 & P4S2: 30 integer variables
P5S1 & P5S2: 40 integer variables

Additional details, with respect to solving using computational intelligence techniques, on the problem can be obtained from

(a) https://www.worldscientific.com/doi/abs/10.1142/9789814299213_0018 (only P1S1, P1S2, P4S1, P4S2, P5S1 and P5S2 are solved with GA)

(b) doi: 10.1007/978-981-10-8968-8_5 (Uses GWO and JAYA algorithms)

(c) Scheduling of Jobs on Dissimilar Parallel Machine using Computational Intelligence Algorithms (uses GA, DNLPSO, s-TLBO, MPEDE, ABC)
Metaheuristic Optimization Methods: Algorithms and Engineering Applications, Eds. Fouad Bennis, Rajib K Bhattacharjya, 2019

### 引用

SKS Labs (2022). Optimization of single-objective job-shop scheduling problem (https://github.com/SKSLAB/Optimization-of-single-objective-job-shop-scheduling-problem), GitHub. 取得済み .

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