Zhao-hong Jia

A meta-heuristic to minimize makespan for parallel batch machines with arbitrary job sizes

We consider the problem of scheduling a set of n jobs with arbitrary job sizes on a set of m identical and parallel batch machines so as to minimize the makespan. Motivated by the computational complexity of the problem, we propose a meta-heuristic based on the max–min ant system method. Computational experiments are performed with randomly generated test data. The results show that our algorithm outperforms several of the previously studied algorithms.

An improved meta-heuristic for makespan minimization of a single batch machine with non-identical job sizes

We consider the problem of minimizing the makespan on a single batch machine with non-identical job sizes, where several jobs can be simultaneously processed as a batch. We formulate makespan minimization as a problem of minimizing the wasted space. Applying a candidate set strategy to narrow the search space, combined with a wasted-space-based heuristic to update the pheromone information, an improved max-min ant system algorithm is presented. A specific local search method is incorporated to gain better performance. Appropriate parameter settings in the proposed algorithm are determined by extensive experiments. The experimental results show that the proposed algorithm outperforms several previously studied algorithms.

An ACO algorithm for makespan minimization in parallel batch machines with non-identical job sizes and incompatible job families

Graphical abstractDisplay Omitted HighlightsScheduling N jobs with non-identical job sizes from F families on M parallel BPMs is considered.The objective is to minimize the makespan.A meta-heuristic based on MMAS combined with the Multi-Fit algorithm is presented.The performance of the algorithm is compared with several previously studied algorithms.Our results show that the proposed algorithm outperforms the previously studied algorithms. We study the problem of scheduling a set of N jobs with non-identical job sizes from F different families on a set of M parallel batch machines; the objective is to minimize the makespan. The problem is known to be NP-hard. A meta-heuristic based on Max-Min Ant System (MMAS) is presented. The performance of the algorithm is compared with several previously studied algorithms by computational experiments. According to our results, the average distance between the solutions found by our proposed algorithm and the lower bounds is about 4% less than that of the best of all the compared algorithms, demonstrating that our algorithm outperforms the previously studied algorithms.

Fast approximation algorithms for bi-criteria scheduling with machine assignment costs

We consider parallel machine scheduling problems where the processing of the jobs on the machines involves two types of objectives. The first type is one of two classical objective functions in scheduling theory: either the total completion time or the makespan. The second type involves an actual cost associated with the processing of a specific job on a given machine; each job-machine combination may have a different cost. Two bi-criteria scheduling problems are considered: (1) minimize the maximum machine cost subject to the total completion time being at its minimum, and (2) minimize the total machine cost subject to the makespan being at its minimum. Since both problems are strongly NP-hard, we propose fast heuristics and establish their worst-case performance bounds.

Integrated production and delivery on parallel batching machines

We consider the problem of scheduling a set of n jobs on m identical and parallel batching machines. The machines have identical capacities equal to K and the jobs have identical processing times equal to p. Job j has a size sj, a due date dj and a profit Rj. Several jobs can be batched together and processed by a machine, provided that the total size of the jobs in the batch does not exceed the machine capacity K. The company will earn a profit of Rj dollars if job j is delivered by time dj; otherwise, it earns nothing. A third party logistic (3PL) provider will be used to deliver the jobs. The 3PL provider picks up the jobs at times T1 < T2 < ⋅⋅⋅ < Tz, and vk (1 ≤ k ≤ z) vehicles will be provided for delivery at time Tk. The vehicles have identical capacities equal to C. The objective is to find a production and delivery schedule so as to maximize the total profit that the company can earn. We show that the problem is solvable in polynomial time if the jobs have identical sizes, but it becomes unary NP-hard if the jobs have different sizes. We propose heuristics for various NP-hard cases and analyze their performances.

Bi-criteria ant colony optimization algorithm for minimizing makespan and energy consumption on parallel batch machines

Graphical abstractDisplay Omitted HighlightsWe consider the problem of scheduling n jobs on m batch-processing machines.The goal is to minimize a bi-criteria objective: makespan and electric power cost.We formulate the problem as a mixed integer programming problem.We propose a meta-heuristic, PACO, and compare with NSGA-II and SPEA2.Experimental results show that PACO outperforms NSGA-II and SPEA2. We investigate the problem of minimizing the makespan and the total electric power cost simultaneously on a set of parallel identical batch-processing machines, where the jobs with non-identical sizes dynamically arrive. To address the bi-criteria problem, a Pareto-based ant colony optimization (PACO) algorithm is proposed. Depending on whether the current batch being delayed after the job is added into, two candidate lists are constructed to narrow the search space. Moreover, heuristic information is designed for each candidate list to guide the search. In addition, the objective-oriented local optimization methods are applied to improve the solution quality. Finally, the proposed algorithm is compared with existing multi-objective algorithms through extensive simulation experiments. The experimental results indicate that the proposed algorithm outperforms all of the compared algorithms, especially for large-scale problems.

Integrated production and transportation on parallel batch machines to minimize total weighted delivery time

Abstract This paper considers a production-distribution scheduling problem on parallel batch processing machines (BPMs) with multiple vehicles. In the production stage, the jobs with non-identical sizes and equal processing time are grouped into batches, which are processed on BPMs. In the distribution stage, there are vehicles with identical capacity arriving regularly to transport the batches to the customers. The objective is to minimize the total weighted delivery time of the jobs. A method of computing a lower bound is given to evaluate the proposed algorithms. To tackle this NP-hard problem, a deterministic heuristic (Algorithm H) and two hybrid meta-heuristic algorithms based on ant colony optimization (HACO, MMAS) are proposed, respectively. Through analyzing the property of the investigated problem, the heuristic information and the pheromone trails are defined. Incorporated with a local optimization strategy, the ant colony constructs the schedule first. Then, a heuristic is designed to transport the batches that have been processed. The performance of the proposed algorithms are compared with each other through testing on randomly generated problem instances. It is shown that the proposed MMAS algorithm slightly beats the HACO algorithm, which can find the better solutions than the H algorithm in a reasonable amount of time.

A meta-heuristic for minimizing total weighted flow time on parallel batch machines

Abstract To address the problem of minimizing the total weighted completion time on parallel batch processing machines with identical machine capacities, non-identical job sizes and unequal weights, an effective meta-heuristic based on ant colony optimization is proposed. After presenting a mathematic model of the problem, we provide an algorithm to calculate the lower bound. Then, a meta-heuristic is proposed to solve the problem. The heuristic information is defined with consideration of job weights and job sizes. Meanwhile, a candidate set for constructing the solution is used to narrow the search space. Additionally, to improve the solution quality, a local optimization strategy is incorporated. Simulation results show that the proposed algorithm is able to obtain a high-quality solution within a reasonable time, and outperforms the compared algorithms.

Multi-objective ACO algorithms to minimise the makespan and the total rejection cost on BPMs with arbitrary job weights

ABSTRACT In this paper, we investigate the batch-scheduling problem with rejection on parallel machines with non-identical job sizes and arbitrary job-rejected weights. If a job is rejected, the corresponding penalty has to be paid. Our objective is to minimise the makespan of the processed jobs and the total rejection cost of the rejected jobs. Based on the selected multi-objective optimisation approaches, two problems, P1 and P2, are considered. In P1, the two objectives are linearly combined into one single objective. In P2, the two objectives are simultaneously minimised and the Pareto non-dominated solution set is to be found. Based on the ant colony optimisation (ACO), two algorithms, called LACO and PACO, are proposed to address the two problems, respectively. Two different objective-oriented pheromone matrices and heuristic information are designed. Additionally, a local optimisation algorithm is adopted to improve the solution quality. Finally, simulated experiments are conducted, and the comparative results verify the effectiveness and efficiency of the proposed algorithms, especially on large-scale instances.

Minimizing makespan for arbitrary size jobs with release times on P-batch machines with arbitrary capacities

Abstract We consider the problem of scheduling a set of arbitrary size jobs with dynamic arrival times on a set of parallel batch machines with arbitrary capacities; our goal is to minimize the makespan. We first give a mathematical model of the problem, and provide a lower bound for the objective function value. Based on different rules of batching the jobs and scheduling the batches on the machines, two meta-heuristics based on Ant Colony Optimization (ACO) are proposed to solve the problem. The performance of the proposed algorithms is evaluated and compared with existing heuristics by computational experiments. Our results show that one of the ACO algorithms consistently finds better solutions than all the others in a reasonable amount of time.