A Simple and Effective Approach for Tackling the Permutation Flow Shop Scheduling Problem

Abstract

In this research, a new approach for tackling the permutation flow shop scheduling problem (PFSSP) is proposed. This algorithm is based on the steps of the elitism continuous genetic algorithm improved by two strategies and used the largest rank value (LRV) rule to transform the continuous values into discrete ones for enabling of solving the combinatorial PFSSP. The first strategy is combining the arithmetic crossover with the uniform crossover to give the algorithm a high capability on exploitation in addition to reducing stuck into local minima. The second one is re-initializing an individual selected randomly from the population to increase the exploration for avoiding stuck into local minima. Afterward, those two strategies are combined with the proposed algorithm to produce an improved one known as the improved efficient genetic algorithm (IEGA). To increase the exploitation capability of the IEGA, it is hybridized a local search strategy in a version abbreviated as HIEGA. HIEGA and IEGA are validated on three common benchmarks and compared with a number of well-known robust evolutionary and meta-heuristic algorithms to check their efficacy. The experimental results show that HIEGA and IEGA are competitive with others for the datasets incorporated in the comparison, such as Carlier, Reeves, and Heller.

A Local Search-Based Generalized Normal Distribution Algorithm for Permutation Flow Shop Scheduling

“…In our experiments, the proposed algorithms are extensively validated on three benchmarks commonly used in the literature: (1) the first dataset is called the Carlier dataset, having eight instances with a number of jobs ranging between 7 and 14, and a number of machines at the interval between 4 and 9 [39]; (2) the second is the Reeves dataset with 21 instances, where the number of machines and the number of jobs ranges between 20 and 75, and 5 and 20, respectively [40]; and (3) finally, the third one is known as the Heller and involves two instances with a number of jobs ranging between 20 and 100, and a number of machines of 10, respectively [41]. Those datasets are taken from [42] with…”

“…In our experiments, the proposed algorithms are extensively validated on three benchmarks commonly used in the literature: (1) the first dataset is called the Carlier dataset, having eight instances with a number of jobs ranging between 7 and 14, and a number of machines at the interval between 4 and 9 [39]; (2) the second is the Reeves dataset with 21 instances, where the number of machines and the number of jobs ranges between 20 and 75, and 5 and 20, respectively [40]; and (3) finally, the third one is known as the Heller and involves two instances with a number of jobs ranging between 20 and 100, and a number of machines of 10, respectively [41]. Those datasets are taken from [42] with some characteristics about the number of jobs and machines, and the best-known makespan z * in Table 3. Furthermore, the proposed algorithms are extensively compared with a number of the well-established optimization algorithms: sine cosine algorithm (SCA) [43], slap swarm algorithm (SSA) [44], whale optimization algorithm (WOA) [34], genetic algorithm (GA), equilibrium optimization algorithm (EOA) [45], marine predators optimization algorithm (MPA) [42], and a hybrid tunicate swarm algorithm (HTSA) [46] integrated with the local search strategy to ensure a fair comparison and verify their efficacy in terms of six performance metrics: average relative error (ARE), worst relative error (WRE), best relative error (BRE), an average of makespan (Avg), standard deviation (SD), and computational cost (Time in milliseconds (ms)).…”

“…Those datasets are taken from [42] with some characteristics about the number of jobs and machines, and the best-known makespan z * in Table 3. Furthermore, the proposed algorithms are extensively compared with a number of the well-established optimization algorithms: sine cosine algorithm (SCA) [43], slap swarm algorithm (SSA) [44], whale optimization algorithm (WOA) [34], genetic algorithm (GA), equilibrium optimization algorithm (EOA) [45], marine predators optimization algorithm (MPA) [42], and a hybrid tunicate swarm algorithm (HTSA) [46] integrated with the local search strategy to ensure a fair comparison and verify their efficacy in terms of six performance metrics: average relative error (ARE), worst relative error (WRE), best relative error (BRE), an average of makespan (Avg), standard deviation (SD), and computational cost (Time in milliseconds (ms)). BRE indicates how far the best-obtained solution Z B is close to the best-known solution and is formulated using the following formula: Meanwhile, WRE calculated using the next equation is a metric used to assess the remoteness between the worst-obtained makespan Z w and the best known.…”

“…The algorithms used in our experiments after integrating local search are named a hybrid SCA (HSCA) [43], a hybrid SSA (HSSA) [44], a hybrid WOA (HWOA) [34], a hybrid GA (HGA), a hybrid EOA (HEOA) [45], a hybrid MPA (HMPA) [42], and a hybrid TSA (HTSA) [46]. Regarding the parameters of those algorithms, they were assigned after extensive experiments.…”

One-Machine Scheduling with Time-Dependent Capacity via Efficient Memetic Algorithms

“…Local search methods have been successfully combined with other metaheuristics as genetic algorithms, resulting in so-called memetic algorithms (MAs). These algorithms have been shown to achieve a proper balance between the exploration and exploitation of the search space, what makes them more effective at solving different scheduling problems, as one-machine [18] or flow shop scheduling problems [19].…”