Single machine scheduling problem with interval processing times to minimize mean weighted completion time

The single resource scheduling problem is commonly applicable in practice not only when there is a single resource but also in some multiple-resource production systems where only one of the resources is bottle neck. Thus, the single resource (machine) scheduling problem has been widely addressed in the scheduling literature. In this paper, the single machine scheduling problem with uncertain and interval processing times is addressed. The objective is to minimize mean weighted completion time. The problem has been addressed in the literature and efficient heuristics have been presented. In this paper, some new polynomial time heuristics, utilizing the bounds of processing times, are proposed. The proposed and existing heuristics are compared by extensive computational experiments. The conducted experiments include a generalized simulation environment and several additional representative distributions in addition to the restricted experiments used in the literature. The results indicate that the proposed heuristics perform significantly better than the existing heuristics. Specifically, the best performing proposed heuristic reduces the error of the best existing heuristic in the literature by more than 75% while the computational time of the best performing proposed heuristic is less than that of the best existing heuristic. Moreover, the absolute error of the best performing heuristic is only about 1% of the optimal solution. Having a very small absolute error along with a negligible computational time indicates the superiority of the proposed heuristics.     

An artificial immune system heuristic for two-stage multi-machine assembly scheduling problem to minimize total completion time

We address the two-stage multi-machine assembly scheduling problem. The first stage consists of m independently working machines where each machine produces its own component. The second stage consists of two independent and identical assembly machines. The objective is to come up with a schedule that minimizes total or mean completion time for all jobs. The problem has been addressed in the scheduling literature and several heuristics have been proposed. In this paper, we propose a new heuristic called artificial immune system (AIS). We conduct experimental analysis for comparing the newly proposed heuristic AIS with the best known heuristic in the literature. Experimental results show that our proposed heuristic AIS performs better than the best known existing heuristic. More specifically, our new heuristic AIS reduces the error of the best known heuristic by 60% while the computational times of both AIS and the best known heuristic are almost the same.     

Single machine scheduling with interfering job sets

We consider two single machine bicriteria scheduling problems in which jobs belong to either of two different disjoint sets, each set having its own performance measure. The problem has been referred to as interfering job sets in the scheduling literature and also been called multi-agent scheduling where each agent's objective function is to be minimized. In the first problem (P1) we look at minimizing total completion time and number of tardy jobs for the two sets of jobs and present a forward SPT-EDD heuristic that attempts to generate the set of non-dominated solutions. The complexity of this specific problem is NP-hard; however some pseudo-polynomial algorithms have been suggested by earlier researchers and they have been used to compare the results from the proposed heuristic. In the second problem (P2) we look at minimizing total weighted completion time and maximum lateness. This is an established NP-hard problem for which we propose a forward WSPT-EDD heuristic that attempts to generate the set of supported points and compare our solution quality with MIP formulations. For both of these problems, we assume that all jobs are available at time zero and the jobs are not allowed to be preempted.     

Solving the uncapacitated facility location problem using tabu search

A tabu search heuristic procedure is developed to solve the uncapacitated facility location problem. Tabu search is used to guide the solution process when evolving from one solution to another. A move is defined to be the opening or closing of a facility. The net cost change resulting from a candidate move is used to measure the attractiveness of the move. After a move is made, the net cost change of a candidate move is updated from its old value. Updating, rather than re-computing, the net cost changes substantially reduces computation time needed to solve a problem when the problem is not excessively large. Searching only a small subset of the feasible solutions that contains the optimal solution, the procedure is computationally very efficient. A computational experiment is conducted to test the performance of the procedure and computational results are reported. The procedure can easily find optimal or near optimal solutions for benchmark test problems from the literature. For randomly generated test problems, this tabu search procedure not only obtained solutions completely dominating those obtained with other heuristic methods recently published in the literature but also used substantially less computation time. Therefore, this tabu search procedure has advantage over other heuristic methods in both solution quality and computation speed.     

Testing local search move operators on the vehicle routing problem with split deliveries and time windows

The vehicle routing problem (VRP) is an important transportation problem. The literature addresses several extensions of this problem, including variants having delivery time windows associated with customers and variants allowing split deliveries to customers. The problem extension including both of these variations has received less attention in the literature. This research effort sheds further light on this problem. Specifically, this paper analyzes the effects of combinations of local search (LS) move operators commonly used on the VRP and its variants. We find when paired with a MAX-MIN Ant System constructive heuristic, Or-opt or 2-opt⁎ appear to be the ideal LS operators to employ on the VRP with split deliveries and time windows with Or-opt finding higher quality solutions and 2-opt⁎ requiring less run time.     

A hybrid data mining heuristic to solve the point‐feature cartographic label placement problem

A clean map visualization requires the fewest possible overlaps and depends on how labels are attached to point features. In this paper, we address the cartographic label placement variant problem whose objective is to label a set of points maximizing the number of conflict‐free points. Thus, we propose a hybrid data mining heuristic to solve the point‐feature cartographic label placement problem based on a clustering search (CS) heuristic, a state‐of‐the‐art method for this problem. Although several works have investigated the combination of data mining and multistart metaheuristics, this is the first time data mining has been used to improve CS and simulated annealing based heuristics. Computational experiments showed that the proposed hybrid heuristic was able to reach better cost solutions than the original strategy, with the same time effort. The proposed heuristic also could find almost all known optimal solutions and improved most of the best results for the set of large instances reported so far in the literature.     

Unidirectional loop network layout by a LP heuristic and design of telecommunications networks

In this paper, we present a new linear programming-based heuristic procedure for optimal design of the unidirectional loop network layout problem. The heuristic procedure employs a linear programming formulation and solves the problem using the flow matrix of the unidirectional loop problem. To find an optimal solution, one can either generate all possible solutions or use a branch-and-bound procedure. But, both above methods require very high computational time and computer memory for larger problems. The heuristic developed in this paper is quite fast and obtains near optimal solutions. The heuristic procedure was tested on 16 different problems selected from the literature. The results showed that in most cases optimal—and in a few cases near optimal—solutions were obtained with very little computational time. Several examples are discussed. We also demonstrate that the above problem formulation and approach can be used to solve a special class of telecommunication networks where a set of computers (or processors) are attached by unidirectional point-to-point links around a loop.     

Setting a common due date in a constrained flowshop: A variable neighbourhood search approach

In this paper we study a due date setting problem in a flowshop layout. The problem consists of scheduling a set of jobs arriving to the system together with jobs already present (denoted as old jobs), in order to set a common due date for the new jobs. Since the old jobs have a common due date that must not be violated, our problem is a rescheduling problem with the objective of minimising the makespan of the new jobs (thus obtaining the tightest possible due date for the new jobs) and a constraint since the maximum tardiness of the old jobs must be equal to zero. This approach leads to an interesting scheduling problem in which two different objectives are considered, each one for a subset of the jobs that must be scheduled. To the best of our knowledge, this type of problems have been scarcely considered in the literature, and only for very specific purposes. Since our problem is clearly NP-hard, a new heuristic based on variable neighbourhood search (VNS) has been designed. The computational results show that our proposed heuristic outperforms two existing heuristic methods for similar problems in the literature.     

A hybrid discrete particle swarm optimization for vehicle routing problem with simultaneous pickup and delivery

Vehicle routing problem (VRP) is an important and well-known combinatorial optimization problem encountered in many transport logistics and distribution systems. The VRP has several variants depending on tasks performed and on some restrictions, such as time windows, multiple vehicles, backhauls, simultaneous delivery and pick-up, etc. In this paper, we consider vehicle routing problem with simultaneous pickup and delivery (VRPSPD). The VRPSPD deals with optimally integrating goods distribution and collection when there are no precedence restrictions on the order in which the operations must be performed. Since the VRPSPD is an NP-hard problem, we present a heuristic solution approach based on particle swarm optimization (PSO) in which a local search is performed by variable neighborhood descent algorithm (VND). Moreover, it implements an annealing-like strategy to preserve the swarm diversity. The effectiveness of the proposed PSO is investigated by an experiment conducted on benchmark problem instances available in the literature. The computational results indicate that the proposed algorithm competes with the heuristic approaches in the literature and improves several best known solutions.     

A tabu search heuristic for the hybrid flowshop scheduling with finite intermediate buffers

This paper investigates the hybrid flowshop scheduling with finite intermediate buffers, whose objective is to minimize the sum of weighted completion time of all jobs. Since this problem is very complex and has been proven strongly NP-hard, a tabu search heuristic is proposed. In this heuristic there are two main features. One is that a scatter search mechanism is incorporated to improve the diversity of the search procedure. And the other is that a permutation of N jobs representing their processing order in the first stage instead of a complex complete schedule is used to denote a solution. Computational experiments on randomly generated instances with different structures show that the proposed tabu search heuristic can provide good solutions compared to both the lower bounds and the algorithm proposed for this problem in a lately published literature.     

A multi-criteria customer allocation problem in supply chain environment: An artificial immune system with fuzzy logic controller based approach

In the present day business environment, customer satisfaction is a pre-requisite for providing good service to the customer. The present day market is a customer driven market and only those who can fulfill customer demands at minimal rate and in shortest time can share a greater market share. Owing to the aforementioned factors, the problem of customers’ allocation to the vendors is considered to be very important problem and has attracted the attention of a lot of researchers. In this paper, a multiple vendor transportation problem having a variety of products and multiple customers has been taken into consideration. The problem considers two criteria: transportation time and transportation cost, thus making it a multi-criteria problem. To solve this problem, a heuristic based on a new approach, called artificial immune system (AIS) has been proposed. To strengthen AIS, a fuzzy logic controller (FLC) has been incorporated in the AIS heuristic. FLC changes the hyper mutation rate adaptively at iteration. A benchmark problem from the prominent literature review has been taken for showing the efficacy of the proposed algorithm. The supremacy of the problem has been shown by the randomly generated data set with increased complicacy of the problems.     

Improved Tabu search heuristics for the dynamic space allocation problem

The dynamic space allocation problem (DSAP) presented in this paper considers the task of assigning items (resources) to locations during a multi-period planning horizon such that the cost of rearranging the items is minimized. Three tabu search heuristics are presented for this problem. The first heuristic is a simple basic tabu search heuristic. The second heuristic adds diversification and intensification strategies to the first, and the third heuristic is a probabilistic tabu search heuristic. To test the performances of the heuristics, a set of test problems from the literature is used in the analysis. The results show that the tabu search heuristics are efficient techniques for solving the DSAP. More importantly, the proposed tabu search heuristic with diversification/intensification strategies found new best solutions using less computation time for one-half of all the test problems.     

Scheduling precedence constrained task graphs with non-negligibleintertask communication onto multiprocessors

The multiprocessor scheduling problem is the problem of scheduling the tasks of a precedence constrained task graph (representing a parallel program) onto the processors of a multiprocessor in a way that minimizes the completion time. Since this problem is known to be NP-hard in the strong sense in all but a few very restricted eases, heuristic algorithms are being developed which obtain near optimal schedules in a reasonable amount of computation time. We present an efficient heuristic algorithm for scheduling precedence constrained task graphs with nonnegligible intertask communication onto multiprocessors taking contention in the communication channels into consideration. Our algorithm for obtaining satisfactory suboptimal schedules is based on the classical list scheduling strategy. It simultaneously exploits the schedule-holes generated in the processors and in the communication channels during the scheduling process in order to produce better schedules. We demonstrate the effectiveness of our algorithm by comparing with two competing heuristic algorithms available in the literature     

A dynamic programming approach to GA-based heuristic for multi-period CF problems

In this paper we have introduced a multi-period cell formation (CF) model which is more computationally challenging than the most comprehensive CF models in the literature. A dynamic programming (DP) based approach coupled with GA-based heuristic is proposed to solve the multi-period problem. Since, the introduced dynamic programming is general and can be applied to any GA-based heuristic with full rejuvenation cycles to solve the multi-period part of the model, we focused only on the DP approach in this paper but have explained the interface with the GA-based heuristic. Illustrative example has been provided that clarifies the application of DP-heuristic. The performance of the DP-heuristic has been evaluated against LINGO and multi period GA-based heuristic.     

Multiobjective pseudo‐variable neighborhood descent for a bicriteria parallel machine scheduling problem with setup time

A multiobjective variable neighborhood descent (VND) based heuristic is developed to solve a bicriteria parallel machine scheduling problem. The problem considers two objectives, one related to the makespan and the other to the flow time, where the setup time depends on the sequence, and the machines are identical. The heuristic has a set of neighborhood structures based on swap, remove, and insertion moves. We propose changing the local search inside the VND to a sequential search through the neighborhoods to obtain nondominated points for the Pareto‐front quickly. In the numerical tests, we consider a single‐objective version of the heuristic, comparing the results on 510 benchmark instances to show that it is quite effective. Moreover, new instances are generated in accordance with the literature for the bicriteria problem, showing the ability of the proposed heuristic to return an efficient set of nondominate solutions compared with the well‐known nondominated sorting genetic algorithm II.     

New approximate algorithms for the customer order scheduling problem with total completion time objective

In this paper, we study a customer order scheduling problem where a number of orders, composed of several product types, have to be scheduled on a set of parallel machines, each one capable to process a single product type. The objective is to minimise the sum of the completion times of the orders, which is related to the lead time perceived by the customer, and also to the minimisation of the work-in-process. This problem has been previously studied in the literature, and it is known to be NP-hard even for two product types. As a consequence, the interest lies on devising approximate procedures to obtain fast, good performing schedules. Among the different heuristics proposed for the problem, the ECT (Earliest Completion Time) heuristic by Leung et al. [6] has turned to be the most efficient constructive heuristic, yielding excellent results in a wide variety of settings. These authors also propose a tabu search procedure that constitutes the state-of-the-art metaheuristic for the problem. We propose a new constructive heuristic based on a look-ahead mechanism. The computational experience conducted shows that it clearly outperforms ECT, while having both heuristics the same computational complexity. Furthermore, we propose a greedy search algorithm using a specific neighbourhood that outperforms the existing tabu search procedure for different stopping criteria, both in terms of quality of solutions and of required CPU effort.     

Bidirectional best-fit heuristic considering compound placement for two dimensional orthogonal rectangular strip packing

The two dimensional orthogonal rectangular strip packing problem is a common NP-hard optimisation problem whereby a set of rectangular shapes must be placed on a fixed width stock sheet with infinite length in such a way that wastage is minimised and material utilisation is maximised. The bidirectional best-fit heuristic is a deterministic approach which has previously been shown to outperform existing heuristic methods as well as many metaheuristics from the literature. Here, we propose a modification to the original bidirectional best-fit heuristic whereby combinations of pairs of rectangles are considered generating improved results over standard benchmark sets.     

A large neighbourhood search heuristic for ship routing and scheduling with split loads

The purpose of this paper is to present and solve a new, important planning problem faced by many shipping companies dealing with the transport of bulk products. These shipping companies are committed to carrying some contract cargoes and will try to derive additional revenue from optional spot cargoes. In most of the literature on ship routing and scheduling problems a cargo cannot be transported by more than one ship. By introducing split loads this restriction is removed and each cargo can be transported by several ships. In this paper we propose a large neighbourhood search heuristic for the ship routing and scheduling problem with split loads. Computational results show that the heuristic provides good solutions to real-life instances within reasonable time. It is also shown that introducing split loads can yield significant improvements.     

Scheduling multiprocessor tasks with genetic algorithms

In the multiprocessor scheduling problem, a given program is to be scheduled in a given multiprocessor system such that the program's execution time is minimized. This problem being very hard to solve exactly, many heuristic methods for finding a suboptimal schedule exist. We propose a new combined approach, where a genetic algorithm is improved with the introduction of some knowledge about the scheduling problem represented by the use of a list heuristic in the crossover and mutation genetic operations. This knowledge-augmented genetic approach is empirically compared with a “pure” genetic algorithm and with a “pure” list heuristic, both from the literature. Results of the experiments carried out with synthetic instances of the scheduling problem show that our knowledge-augmented algorithm produces much better results in terms of quality of solutions, although being slower in terms of execution time     

A GRASP/VND heuristic for the phylogeny problem using a new neighborhood structure

A phylogeny is a tree that relates taxonomic units, based on their similarity over a set of characters. The phylogeny problem consists in finding a phylogeny with the minimum number of evolutionary steps. We propose a new neighborhood structure for the phylogeny problem. A greedy randomized adaptive search procedure heuristic based on this neighborhood structure and using variable neighborhood descent for local search is described. Computational results on randomly generated and benchmark instances are reported, showing that the new heuristic is quite robust and outperforms the other algorithms in the literature in terms of solution quality and time‐to‐target value.