A Hybrid Grey Wolf Optimizer for Process Planning Optimization with Precedence Constraints

Process planning optimization is a well-known NP-hard combinatorial problem extensively studied in the scientific community. Its main components include operation sequencing, selection of manufacturing resources and determination of appropriate setup plans. These problems require metaheuristic-based approaches in order to be effectively and efficiently solved. Therefore, to optimize the complex process planning problem, a novel hybrid grey wolf optimizer (HGWO) is proposed. The traditional grey wolf optimizer (GWO) is improved by employing genetic strategies such as selection, crossover and mutation which enhance global search abilities and convergence of the traditional GWO. Precedence relationships among machining operations are taken into account and precedence constraints are modeled using operation precedence graphs and adjacency matrices. Constraint handling heuristic procedure is adopted to move infeasible solutions to a feasible domain. Minimization of the total weighted machining cost of a process plan is adopted as the objective and three experimental studies that consider three different prismatic parts are conducted. Comparative analysis of the obtained cost values, as well as the convergence analysis, are performed and the HGWO approach demonstrated effectiveness and flexibility in finding optimal and near-optimal process plans. On the other side, comparative analysis of computational times and execution times of certain MATLAB functions showed that the HGWO have good time efficiency but limited since it requires more time compared to considered hybrid and traditional algorithms. Potential directions to improving efficiency and performances of the proposed approach are given in conclusions.

A Job-Shop Scheduling Problem with Bidirectional Circular Precedence Constraints

This paper introduces a job-shop scheduling problem (JSP) with bidirectional circular precedence constraints, called BCJSP. In the problem, each job can be started from any operation and continued by its remaining operations in a circular precedence-relation chain via either a clockwise or counterclockwise direction. To solve BCJSP, this paper proposes a multilevel metaheuristic consisting of top-, middle-, and bottom-level algorithms. The top- and middle-level algorithms are population-based metaheuristics, while the bottom-level algorithm is a local search algorithm. The top-level algorithm basically controls a start operation and an operation-precedence-relation direction of each job, so that BCJSP becomes a JSP instance that is a subproblem of BCJSP. Moreover, the top-level algorithm can also be used to control input parameters of the middle-level algorithm, as an optional extra function. The middle-level algorithm controls input parameters of the bottom-level algorithm, and the bottom-level algorithm then solves the BCJSP’s subproblem. The middle-level algorithm evolves the bottom-level algorithm’s parameter values by using feedback from the bottom-level algorithm. Likewise, the top-level algorithm evolves the start operations, the operation-precedence-relation directions, and the middle-level algorithm’s parameter values by using feedback from the middle-level algorithm. Performance of two variants of the multilevel metaheuristic (i.e., with and without the mentioned extra function) was evaluated on BCJSP instances modified from well-known JSP instances. The variant with the extra function performs significantly better in number than the other. The existing JSP-solving algorithms can also solve BCJSP; however, their results on BCJSP are clearly worse than those of the two variants of the multilevel metaheuristic.

Polynomial algorithms for some scheduling problems with one nonrenewable resource

This paper deals with the Extended Resource Constrained Project Scheduling Problem (ERCPSP) which is defined by events, nonrenewable resources and precedence constraints between pairs of events. The availability of a resource is depleted and replenished at the occurrence times of a set of events. The decision problem of ERCPSP consists of determining whether an instance has a feasible schedule or not. When there is only one nonrenewable resource, this problem is equivalent to find a feasible schedule that minimizes the number of resource units initially required. It generalizes the maximum cumulative cost problem and the two-machine maximum completion time flow-shop problem. In this paper, we consider this problem with some specific precedence constraints: parallel chains, series-parallel and interval order precedence constraints. For the first two cases, polynomial algorithms based on a linear decomposition of chains are proposed. For the third case, a polynomial algorithm is introduced to solve it. The priority between events is defined using the properties of interval orders.

Scheduling Multiprocessor Tasks with Equal Processing Times as a Mixed Graph Coloring Problem

This article extends the scheduling problem with dedicated processors, unit-time tasks, and minimizing maximal lateness for integer due dates to the scheduling problem, where along with precedence constraints given on the set of the multiprocessor tasks, a subset of tasks must be processed simultaneously. Contrary to a classical shop-scheduling problem, several processors must fulfill a multiprocessor task. Furthermore, two types of the precedence constraints may be given on the task set . We prove that the extended scheduling problem with integer release times of the jobs to minimize schedule length may be solved as an optimal mixed graph coloring problem that consists of the assignment of a minimal number of colors (positive integers) to the vertices of the mixed graph such that, if two vertices and are joined by the edge , their colors have to be different. Further, if two vertices and are joined by the arc , the color of vertex has to be no greater than the color of vertex . We prove two theorems, which imply that most analytical results proved so far for optimal colorings of the mixed graphs , have analogous results, which are valid for the extended scheduling problems to minimize the schedule length or maximal lateness, and vice versa.