Multicriteria Scheduling Problems Research Articles

Multi-criteria Scheduling in Parallel Environment with Learning Effect

Abstract This paper is devoted to the study of a multi-criteria scheduling problem on unrelated processors with machines’ learning effect, with the goal of minimizing makespan, machine cost and maximal flow-time simultaneously, which is an NP-hard problem. An improved particle swarm optimization algorithm equipped with the overloaded operators, as well as a procedure of Levy flight, is proposed to generate the Pareto-optimal solutions. The experimental results show that the Levy flight strategy can effectively improve the performance of the algorithm, which can generate more non-dominated solutions, and slightly reduce the execution time of the process.

Bi-objective flexible job shop scheduling on machines considering condition-based maintenance activities

This paper investigates multi-objective flexible job shop scheduling considering maintenance activities. The condition-based maintenance strategy is used to reduce machines breakdown. After maintenance activities are completed, the machine degradation model’s parameters are updated using Bayesian inference to make it more realistic. A novel multi-objective evolutionary algorithm is designed to address the multi-criteria scheduling problem. An innovative insertion algorithm is proposed in this paper to balance production plan and maintenance activities. According to the experimental results, the designed evolutionary algorithm performs better than the other two traditional algorithms, and the insertion approach can reduce the impact of maintenance activities on production plan by up to 200%.

Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early

Algorithms for Multicriteria Scheduling Problems to Minimize Maximum Late Work, Tardy, and Early

Integration of Discrete Simulation, Prediction, and Optimization Methods for a Production Line Digital Twin Design

The integration of discrete simulations, artificial intelligence methods, and the theory of probability in order to obtain a high flexibility of the production system is crucial. In this paper, the concept of a smart factory operation is proposed along with the idea of data exchange architecture, simulation creation, performance optimization, and predictive analysis of the production process conditions. A Digital Twin for a hybrid flow shop from the automotive industry is presented as a case study. In the paper, the Ant Colony Optimization (ACO) algorithm is developed for multi-criteria scheduling problems in order to obtain a production plan without delays and maximum resource utilization. The ACO is compared to the immune algorithm and genetic algorithm. The best schedules are achieved with low computation time for the Digital Twin. By predicting the reliability parameters of the limited resources of the Digital Twin, stable deadlines for the implementation of production tasks are achieved. Mean Time To Failure and Mean Time of Repair are predicted for a real case study of an electric steering gear production line. The presented integration and data exchange between the elements of the smart factory: a Digital Twin, a computing module including an optimization, prediction, and simulation methods fills the gap between theory and practice for Industry 4.0. The paper presents measurable benefits of integration of discrete simulation tools, historical data analysis, and optimization methods.

A heuristic approach to minimize three criteria using efficient solutions

In <span>optimization, scheduling problems is concerning allocations of some resources which are usually limited. These allocations are done in order to fulfil some criterion by performing some tasks or jobs to optimize one or more objective functions. Simultaneous multi-criteria scheduling problem is known as np-hard optimization problem. Here, we consider three criteria for scheduling a number of jobs on a single machine. The problem is to minimize the sum of total completion time, maximum earliness and maximum tardiness. Every job is to be processed without interruption and becomes available for processing at time zero. The aim is to find a processing order of the jobs to minimize three-objective functions simultaneously. We present a new heuristic approach to find a best overall solution (accepted) of the problem using efficient solutions of one of the other related criteria. We establish a result to restrict the range of the optimal solution, and the lower bound depends on the decomposition of the problem into three subproblems. The approach is tested on a set of problems of different number of jobs. Computational results demonstrate the efficiency of the proposed approach.</span>

Search method for solving multicriteria scheduling problem

Our research includes studying the case $ 1 // F(sum U_i ,sum Ti ,T_{max})$ minimized the cost of a three-criteria objective function on a single machine for scheduling n jobs. and divided this into several partial problems and found simple algorithms to find the solutions to these partial problems and compare them with the optimal solutions. This research focused on one of these partial problems to find minimize a function of sum cost of $ (sum U_i) $ sum number of late job and $ (sum Ti) $ sum Tardiness and $ (T_{max} ) $ the Maximum Tardiness for n job on the single machine, which is NP-hard problem, first found optimal solutions for it by two methods of Complete Enumeration technique(CEM) and Branch and Bounded ((BAB)). Then use some Local search methods(Descent technique(DM), Simulated Annealing (SA) and Genetic Algorithm (GA)), Develop algorithm called ((A)) to find a solution close to the optimal solution. Finally, compare these methods with each other.

Approximation Solutions For Multicriteria Scheduling Problems

This paper presents local search algorithms for finding approximation solutions of the multicriteria scheduling problems within the single machine context, where the first problem is the sum of maximum tardiness and maximum late work and the second problem is the sum of total late work and maximum late work. Late work criterion estimates the quality of a schedule based on durations of late parts of jobs. Local search algorithms (descent method (DM), simulated annealing (SA) and genetic algorithm (GA))are implemented. Based on results of computational experiments, conclusions are formulated on the efficiency of the local search algorithms.

Solving a multicriteria scheduling problem using a genetic algorithm

The work is devoted to the multiobjective task of scheduling, in which a given set of works must be performed by several performers of different productivity. A certain number of bonuses is accrued for the work performed by the respective executor, which depends on the time of work performance. The criteria for evaluating the schedule are the total time of all jobs and the amount of bonuses spent. In the research the main approaches to solving multiobjective optimization problems were analyzed, based on which the Pareto approach was chosen. The genetic algorithm was chosen as the algorithm. The purpose of this work is to increase the efficiency of solving multicriteria optimization problems by implementing a heuristic algorithm and increase its speed. The tasks of the work are to determine the advantages and disadvantages of the approaches used to solve multicriteria optimization problems, to develop a genetic algorithm for solving the multicriteria scheduling problem and to study its efficiency. Operators of the genetic algorithm have been developed, which take into account the peculiarities of the researched problem and allow to obtain Pareto solutions in the process of work. Due to the introduction of parallel calculations in the implementation of the genetic algorithm, it was possible to increase its speed compared to the conventional version. The developed algorithm can be used in solving the problem of optimal allocation of resources, which is part of the system of accrual of bonuses to employees.

Exact and Local Search Algorithms to Minimize Multicriteria Scheduling Problem

In this article , we consider the Multicriteria scheduling problem on a single machine for minimizing the sum of total completion time (∑Cj) with the total tardiness (∑Tj) and maximum earliness (Emax). We propose a branch and bound (BAB) algorithm to find the optimal solution for the problem. In this BAB algorithm, a lower bound (LB) based on the decomposition property of the Multicriteria problem is used. Two local search algorithms, descent method (DM) and simulated annealing (SA) are applied for the problem. The algorithms DM and SA are compared with the BAB algorithm in order to evaluate effectiveness of the solution methods. Conclusions are formulated on the efficiency of the algorithms, Based on findings of computational experiments.

Single machine multi-criteria scheduling problem: total completion time, maximum lateness, and maximum earliness performance measures

This paper considers the multi-criteria scheduling problem with total completion time, maximum lateness, and maximum earliness as the objectives. The problem is a minimisation problem; the total completion time, a MIN-SUM problem, the maximum earliness, a MIN-MAX problem, and the maximum lateness, a MIN-MAX problem. Though, the problem is NP-hard, shortest processing time (SPT) rule, yields optimal for total completion time while early due date rule (EDD) is the optimal solution for maximum lateness and maximum earliness if each criterion were to be considered separately. Two heuristics, named SOL I and SOL II were proposed and the results for each of the criteria were compared to the optimal of the sub-problems. Results of the computational experiment on small job-sizes (5 ≤ n ≤ 30) and large job-sizes (40 ≤ n ≤ 100) show that the two heuristics results are not significantly different from the optimal at 99% significant level for total completion time and maximum lateness performance measures. However, for maximum earliness, the optimal solutions are significantly better than the two proposed heuristics.

Single machine multi-criteria scheduling problem: total completion time, maximum lateness, and maximum earliness performance measures

Single machine multi-criteria scheduling problem: total completion time, maximum lateness, and maximum earliness performance measures

Using Heuristic and Branch and Bound Methods to Solve a Multi-Criteria Machine Scheduling Problem

In this paper, we investigate some methods to solve one of the multi-criteria machine scheduling problems. The discussed problem is the total completion time and the total earliness jobs To solve this problem, some heuristic methods are proposed which provided good results. The Branch and Bound (BAB) method is applied with new suggested upper and lower bounds to solve the discussed problem, which produced exact results for in a reasonable time.

Special Issue on Exact and Heuristic Scheduling Algorithms

This special issue of Algorithms is a follow-up issue of an earlier one, entitled ‘Algorithms for Scheduling Problems’. In particular, the new issue is devoted to the development of exact and heuristic scheduling algorithms. Submissions were welcome both for traditional scheduling problems as well as for new practical applications. In the Call for Papers, we mentioned topics such as single-criterion and multi-criteria scheduling problems with additional constraints including setup times (costs), precedence constraints, batching (lot sizing), resource constraints as well as scheduling problems arising in emerging applications.

ERPOT: A Quad-Criteria Scheduling Heuristic to Optimize Execution Time, Reliability, Power Consumption and Temperature in Multicores

We investigate multi-criteria optimization and Pareto front generation. Given an application modeled as a Directed Acyclic Graph (DAG) of tasks and a multicore architecture, we produce a set of non-dominated (in the Pareto sense) static schedules of this DAG onto this multicore. The criteria we address are the execution time, reliability, power consumption, and peak temperature. These criteria exhibit complex antagonistic relations, which make the problem challenging. For instance, improving the reliability requires adding some redundancy in the schedule, which penalizes the execution time. To produce Pareto fronts in this 4-dimension space, we transform three of the four criteria into constraints (the reliability, the power consumption, and the peak temperature), and we minimize the fourth one (the execution time of the schedule) under these three constraints. By varying the thresholds used for the three constraints, we are able to produce a Pareto front of non-dominated solutions. We propose two algorithms to compute static schedules. The first is a ready list scheduling heuristic called Execution time, Reliability, POwer consumption and Temperature (ERPOT). ERPOT actively replicates the tasks to increase the reliability, uses Dynamic Voltage and Frequency Scaling to decrease the power consumption, and inserts cooling times to control the peak temperature. The second algorithm uses an Integer Linear Programming (ILP) program to compute an optimal schedule. However, because our multi-criteria scheduling problem is NP-complete, the ILP algorithm is limited to very small problem instances. Comparisons showed that the schedules produced by ERPOT are on average only 10 percent worse than the optimal schedules computed by the ILP program, and that ERPOT outperforms the PowerPerf-PET heuristic from the literature on average by 33 percent.

A Sort & Search method for multicriteria optimization problems with applications to scheduling theory

AbstractThis paper focuses on the Sort & Search method to solve a particular class of single criterion optimization problems called multiple constraints problems. This general method enables to derive exponential‐time algorithms for ‐hard optimization problems. In this paper, this method is further extended to the class of multicriteria multiple constraints problems for which the set of Pareto optima is enumerated. Then, the application of this new method on some multicriteria scheduling problems is proposed, leading to new exponential‐time algorithms for those problems.

Local Search Algorithms for Multi-criteria Single Machine Scheduling Problem

Real life scheduling problems require the decision maker to consider a number of criteria before arriving at any decision. In this paper, we consider the multi-criteria scheduling problem of n jobs on single machine to minimize a function of five criteria denoted by total completion times (∑), total tardiness (∑), total earliness (∑), maximum tardiness () and maximum earliness (). The single machine total tardiness problem and total earliness problem are already NP-hard, so the considered problem is strongly NP-hard.
 We apply two local search algorithms (LSAs) descent method (DM) and simulated annealing method (SM) for the 1// (∑∑∑) problem (SP) to find near optimal solutions. The local search methods are used to speed up the process of finding a good enough solution, where an exhaustive search is impractical for the exact solution. The two heuristic (DM and SM) were compared with the branch and bound (BAB) algorithm in order to evaluate effectiveness of the solution methods.
 Some experimental results are presented to show the applicability of the (BAB) algorithm and (LSAs). With a reasonable time, (LSAs) may solve the problem (SP) up to 5000 jobs.

Impact of Number of Interactions, Different Interaction Patterns, and Human Inconsistencies on Some Hybrid Evolutionary Multiobjective Optimization Algorithms*

ABSTRACTWe investigate the impact of the number of human–computer interactions, different interaction patterns, and human inconsistencies in decision maker responses on the convergence of an interactive, evolutionary multiobjective algorithm recently developed by the authors. In our context “an interaction” means choosing the best and worst solutions among a sample of six solutions. By interaction patterns we refer to whether preference questioning is more front‐, center‐, rear‐, or edge‐loaded. As test problems we use two‐ to four‐objective knapsack problems, multicriteria scheduling problems, and multiobjective facility location problems. In the tests, two different preference functions are used to represent actual decision maker preferences, linear and Chebyshev. The results indicate that it is possible to obtain solutions that are very good or even nearly optimal with a reasonable number of interactions. The results also indicate that the algorithm is robust to minor inconsistencies in decision maker responses. There is also surprising robustness toward different patterns of interaction with the decision maker. The results are of interest to the evolutionary multiobjective (EMO) community actively developing hybrid interactive EMO approaches.

A new approach for multi-criteria scheduling

In this paper we propose a new approach, recommended for solving certain class of multi-criteria scheduling problems, with the use of cloud exploration of the solution space supported by fine-grained parallel computing. The approach allow us to approximate Pareto front more accurately than other known algorithms in competitive time. To show and check advantageous properties of the proposed approach, the new solution algorithm, called VESA, was implemented for the case of bi-criteria flow shop scheduling problem and tested against a number of high-quality benchmarks known in the literature. Vector processing technologies are used to enhance the efficiency of solution search and acceptance rates for the extended simulated annealing metaheuristic. Results are compared using, among others, the independent Hyper-Volume Indicator (IH) measure. Computer test of VESA confirms excellent approximation of the Pareto front.

Genetic algorithm application for multi-criteria scheduling problem

The paper describes mathematical model and method of task solution for defining an enterprise work performance schedule. Two-stage feedstock processing is supposed to exist at the enterprise. At the first stage the sawing process into semimanufactured products is done. The second stage (finished products manufacturing stage) includes durable processing of obtained semimanufactured products at one of the interchangeable work centers. The sawing process into semimanufactured products is carried out according to a plan, developed in advance and in compliance with technological charts. Scheduling consists of separate cutting calculation and planning of all feedstock cutting with the aim of the most effective specification task performance based on available reserves. Following the cutting plan, an enterprise work performance schedule is created. This schedule consists of the cutting sequence with volume, start and end time, and plan for loading of after-treatment. The solution to this problem becomes more involved due to the necessity of taking into account all features, limitations and parameters of process equipment, as well as of raw material and production orders. Special method based on genetic algorithm has been proposed for handling the problem. The algorithm has been tested on several different real production plans. Its efficiency estimation is given. The software system implemented on the proposed algorithm has been tested on real operating data of several sawmills. Reduction of machine idle time and incomplete production decrease has been confirmed by the enterprise specialists.

Multi-criteria scheduling: an agent-based approach for expert knowledge integration

In this work, we present an agent-based approach to multi-criteria combinatorial optimization. It allows to flexibly combine elementary heuristics that may be optimal for corresponding single-criterion problems. We optimize an instance of the scheduling problem 1|d j |∑C j ,L max and show that the modular building block architecture of our optimization model and the distribution of acting entities enables the easy integration of problem specific expert knowledge. We present a universal mutation operator for combinatorial problem encodings that allows to construct certain solution strategies, such as advantageous sorting or known optimal sequencing procedures. In this way, it becomes possible to derive more complex heuristics from atomic local heuristics that are known to solve fractions of the complete problem. We show that we can approximate both single-criterion problems such as P m |d j |∑U j as well as more challenging multi-criteria scheduling problems, like P m ||C max,∑C j and P m |d j |C max,∑C j ,∑U j . The latter problems are evaluated with extensive simulations comparing the standard multi-criteria evolutionary algorithm NSGA-2 and the new agent-based model.