An Almost Optimal Heuristic for Preemptive C max Scheduling of Dependent Tasks on Parallel Identical Machines

We consider the problem of scheduling preemptable, dependent tasks on parallel, identical machines to minimize the makespan. The computational complexity of this problem remains open if the number of machines is fixed and larger than 2. The aim of this paper is to compare two heuristic algorithms on a basis of a computational experiment. The solutions generated by the heuristics are compared with optimal solutions obtained by a branch-and-bound algorithm. Computational results show that the heuristic based on node ordering finds optimal schedules for 99.9% of instances with the maximum relative deviation from optimum of 4.8%.     

Heuristics for a coupled-operation scheduling problem

In this paper, we study a strongly NP-hard single machine scheduling problem in which each job consists of two operations that are separated by a time delay which lies within a specified range. The objective is to minimize the makespan. Determining the feasibility and, if applicable, makespan of any proposed permutation of the operations is non-trivial, requiring a longest path algorithm with O(n²) complexity for each permutation. Several heuristic algorithms are proposed: a deterministic and randomized construction algorithm, three descent algorithms and two reactive tabu search algorithms. The local search algorithms use a first improvement neighbourhood and mainly visit only feasible solutions within the search space. Results of extensive computational tests are reported, showing that the heavy computational burden of testing potential solutions renders the local search algorithms uncompetitive in comparison to the construction algorithms. The iterated descent algorithm performs least well.     

A hybrid iterated local search heuristic for the maximum weight independent set problem

This paper presents a hybrid iterated local search (ILS) algorithm for the maximum weight independent set (MWIS) problem, a generalization of the classical maximum independent set problem. Two efficient neighborhood structures are proposed and they are explored using the variable neighborhood descent procedure. Moreover, we devise a perturbation mechanism that dynamically adjusts the balance between intensification and diversification during the search. The proposed algorithm was tested on two well-known benchmarks (DIMACS-W and BHOSLIB-W) and the results obtained were compared with those found by state-of-the-art heuristics and exact methods. Our heuristic outperforms the best-known heuristic for the MWIS as well as the best heuristics for the maximum weight clique problem. The results also show that the hybrid ILS was capable of finding all known optimal solutions in milliseconds.     

A Genetic Algorithm for the Multidimensional Knapsack Problem

In this paper we present a heuristic based upon genetic algorithms for the multidimensional knapsack problem. A heuristic operator which utilises problem-specific knowledge is incorporated into the standard genetic algorithm approach. Computational results show that the genetic algorithm heuristic is capable of obtaining high-quality solutions for problems of various characteristics, whilst requiring only a modest amount of computational effort. Computational results also show that the genetic algorithm heuristic gives superior quality solutions to a number of other heuristics.     

The linear ordering problem: Instances,search space analysis and algorithms

The linear ordering problem is an NP-hard problem that arises in a variety of applications. Due to its interest in practice, it has received considerable attention and a variety of algorithmic approaches to its solution have been proposed. In this paper we give a detailed search space analysis of available benchmark instance classes that have been used in various researches. The large fitness-distance correlations observed for many of these instances suggest that adaptive restart algorithms like iterated local search or memetic algorithms, which iteratively generate new starting solutions for a local search based on previous search experience, are promising candidates for obtaining high performing algorithms. We therefore experimentally compared two such algorithms and the final experimental results suggest that, in particular, the memetic algorithm is a new state-of-the-art approach to the linear ordering problem.     

A multi-period machine assignment problem

In this paper, a multi-period assignment problem is studied that arises as part of a weekly planning problem at mail processing and distribution centers. These facilities contain a wide variety of automation equipment that is used to cancel, sort, and sequence the mail. The input to the problem is an equipment schedule that indicates the number of machines required for each job or operation during the day. This result is then post-processed by solving a multi-period assignment problem to determine the sequence of operations for each machine. Two criteria are used for this purpose. The first is to minimize the number of startups, and the second is to minimize the number of machines used per operation.The problem is modeled as a 0–1 integer program that can be solved in polynomial time when only the first criterion is considered. To find solutions in general, a two-stage heuristic is developed that always obtains the minimum number of startups, but not necessarily the minimum number of machines per operation. In a comparative study, high quality solutions were routinely provided by the heuristic in negligible time when compared to a commercial branch-and-bound code (Xpress). For most hard instances, the branch-and-bound code was not able to even find continuous solutions within acceptable time limits.     

Iterated greedy for the maximum diversity problem

The problem of choosing a subset of elements with maximum diversity from a given set is known as the maximum diversity problem. Many algorithms and methods have been proposed for this hard combinatorial problem, including several highly sophisticated procedures. By contrast, in this paper we present a simple iterated greedy metaheuristic that generates a sequence of solutions by iterating over a greedy construction heuristic using destruction and construction phases. Extensive computational experiments reveal that the proposed algorithm is highly effective as compared to the best-so-far metaheuristics for the problem under consideration.     

Routing and wavelength assignment in optical networks using bin packing based algorithms

This paper addresses the problem of routing and wavelength assignment (RWA) of static lightpath requests in wavelength routed optical networks. The objective is to minimize the number of wavelengths used. This problem has been shown to be NP-complete and several heuristic algorithms have been developed to solve it. We suggest very efficient, yet simple, heuristic algorithms for the RWA problem developed by applying classical bin packing algorithms. The heuristics were tested on a series of large random networks and compared with an efficient existing algorithm for the same problem. Results indicate that the proposed algorithms yield solutions significantly superior in quality, not only with respect to the number of wavelength used, but also with respect to the physical length of the established lightpaths. Comparison with lower bounds shows that the proposed heuristics obtain optimal or near optimal solutions in many cases.     

Solving the routing and wavelength assignment problem with a multilevel distributed memetic algorithm

The Routing and Wavelength Assignment problem is a graph optimization problem which deals with optical networks, where communication requests in a network have to be fulfilled. In this paper, we present a multilevel distributed memetic algorithm (ML-DMA) for the static RWA which finds provable optimal solutions for most benchmark instances with known lower bounds and is capable of handling large instances. Components of our ML-DMA include iterated local search, recombination, multilevel scaling, and a gossip-based distribution algorithm. Results demonstrated that our ML-DMA is among the most sophisticated heuristic RWA algorithms published so far.     

Heuristic constructive algorithms for open shop scheduling to minimize mean flow time

In this paper, we consider the problem of scheduling n jobs on m machines in an open shop environment so that the sum of completion times or mean flow time becomes minimal. For this strongly NP-hard problem, we develop and discuss different constructive heuristic algorithms. Extensive computational results are presented for problems with up to 50 jobs and 50 machines, respectively. The quality of the solutions is evaluated by a lower bound for the corresponding preemptive open shop problem and by an alternative estimate of mean flow time. We observe that the recommendation of an appropriate constructive algorithm strongly depends on the ratio n/m.     

Image registration with iterated local search

This contribution is devoted to the application of iterated local search to image registration, a very complex, real-world problem in the field of image processing. To do so, we first re-define this parameter estimation problem as a combinatorial optimization problem, then analyze the use of image-specific information to guide the search in the form of an heuristic function, and finally propose its solution by iterated local search. Our algorithm is tested by comparing its performance to that of two different baseline algorithms: iterative closest point, a well-known, image registration technique, a hybrid algorithm including the latter technique within a simulated annealing approach, a multi-start local search procedure, that allows us to check the influence of the search scheme considered in the problem solving, and a real coded genetic algorithm. Four different problem instances are tackled in the experimental study, resulting from two images and two transformations applied on them. Three parameter settings are analyzed in our approach in order to check three heuristic information scenarios where the heuristic is not used at all, is partially used or almost completely guides the search process, as well as two different number of iterations in the algorithms outer-inner loops. This work was partially supported by the Spanish Ministerio de Ciencia y Tecnología under project TIC2003-00877 (including FEDER fundings) and under Network HEUR TIC2002-10866-E.     

A simple and effective metaheuristic for the Minimum Latency Problem

The Minimum Latency Problem (MLP) is a variant of the Traveling Salesman Problem which aims to minimize the sum of arrival times at vertices. The problem arises in a number of practical applications such as logistics for relief supply, scheduling and data retrieval in computer networks. This paper introduces a simple metaheuristic for the MLP, based on a greedy randomized approach for solution construction and iterated variable neighborhood descent with random neighborhood ordering for solution improvement. Extensive computational experiments on nine sets of benchmark instances involving up to 1000 customers demonstrate the good performance of the method, which yields solutions of higher quality in less computational time when compared to the current best approaches from the literature. Optimal solutions, known for problems with up to 50 customers, are also systematically obtained in a fraction of seconds.     

A new heuristic algorithm solving the linear ordering problem

The linear ordering problem is an NP-hard combinatorial problem with a large number of applications. Contrary to another very popular problem from the same category, the traveling salesman problem, relatively little space in the literature has been devoted to the linear ordering problem so far. This is particularly true for the question of developing good heuristic algorithms solving this problem.In the paper we propose a new heuristic algorithm solving the linear ordering problem. In this algorithm we made use of the sorting through insertion pattern as well as of the operation of permutation reversal. The surprisingly positive effect of the reversal operation, justified in part theoretically and confirmed in computational examples, seems to be the result of a unique property of the problem, called in the paper the symmetry of the linear ordering problem. This property consists in the fact that if a given permutation is an optimal solution of the problem with the criterion function being maximized, then the reversed permutation is a solution of the problem with the same criterion function being minimized.     

An Application of a Multi-Objective Tabu Search Algorithm to a Bicriteria Flowshop Problem

This paper proposes a new tabu search algorithm for multi-objective combinatorial problems with the goal of obtaining a good approximation of the Pareto-optimal or efficient solutions. The algorithm works with several paths of solutions in parallel, each with its own tabu list, and the Pareto dominance concept is used to select solutions from the neighborhoods. In this way we obtain at each step a set of local nondominated points. The dispersion of points is achieved by a clustering procedure that groups together close points of this set and then selects the centroids of the clusters as search directions. A nice feature of this multi-objective algorithm is that it introduces only one additional parameter, namely, the number of paths. The algorithm is applied to the permutation flowshop scheduling problem in order to minimize the criteria of makespan and maximum tardiness. For instances involving two machines, the performance of the algorithm is tested against a Branch-and-Bound algorithm proposed in the literature, and for more than two machines it is compared with that of a tabu search algorithm and a genetic local search algorithm, both from the literature. Computational results show that the heuristic yields a better approximation than these algorithms.     

A fast algorithm for two-dimensional pallet loading problems of large size

This paper concerns the two-dimensional pallet loading problem (PLP), which requires the determination of the orthogonal layout that loads the maximum number of identical small rectangles (i.e., boxes or products) onto a large rectangle (i.e., pallet or container) without overlapping. Although many algorithms have been developed for this problem, the large amount of time required to find efficient layouts for a large PLP presents great practical difficulties. In this paper, we develop a heuristic that finds efficient layouts with low complexity. We also propose a new algorithm, using the heuristic as a sub-algorithm, which rapidly finds complicated solutions having a 5-block structure. Finally, computational results show that the new algorithm can be successfully applied to large PLPs with sizes exceeding 6800 boxes.     

Iterated local search for workforce scheduling and routing problems

The integration of scheduling workers to perform tasks with the traditional vehicle routing problem gives rise to the workforce scheduling and routing problems (WSRP). In the WSRP, a number of service technicians with different skills, and tasks at different locations with pre-defined time windows and skill requirements are given. It is required to find an assignment and ordering of technicians to tasks, where each task is performed within its time window by a technician with the required skill, for which the total cost of the routing is minimized. This paper describes an iterated local search (ILS) algorithm for the WSRP. The performance of the proposed algorithm is evaluated on benchmark instances against an off-the-shelf optimizer and an existing adaptive large neighbourhood search algorithm. The proposed ILS algorithm is also applied to solve the skill vehicle routing problem, which can be viewed as a special case of the WSRP. The computational results indicate that the proposed algorithm can produce high-quality solutions in short computation times.     

An iterated local search algorithm for the vehicle routing problem with backhauls

The Vehicle Routing Problem with Backhauls (VRPB) is an extension of the VRP that deals with two types of customers: the consumers (linehaul) that request goods from the depot and the suppliers (backhaul) that send goods to the depot. In this paper, we propose a simple yet effective iterated local search algorithm for the VRPB. Its main component is an oscillating local search heuristic that has two main features. First, it explores a broad neighborhood structure at each iteration. This is efficiently done using a data structure that stores information about the set of neighboring solutions. Second, the heuristic performs constant transitions between feasible and infeasible portions of the solution space. These transitions are regulated by a dynamic adjustment of the penalty applied to infeasible solutions. An extensive statistical analysis was carried out in order to identify the most important components of the algorithm and to properly tune the values of their parameters. The results of the computational experiments carried out show that this algorithm is very competitive in comparison to the best metaheuristic algorithms for the VRPB. Additionally, new best solutions have been found for two instances in one of the benchmark sets. These results show that the performance of existing metaheuristic algorithms can be considerably improved by carrying out a thorough statistical analysis of their components. In particular, it shows that by expanding the exploration area and improving the efficiency of the local search heuristic, it is possible to develop simpler and faster metaheuristic algorithms without compromising the quality of the solutions obtained.     

Minimizing total tardiness on a two-machine re-entrant flowshop

We present a branch and bound algorithm for a two-machine re-entrant flowshop scheduling problem with the objective of minimizing total tardiness. In the re-entrant flowshop considered here, all jobs must be processed twice on each machine, that is, each job should be processed on machine 1, machine 2 and then machine 1 and machine 2. By regarding a job as a pair of sub-jobs, each of which represents a pass through the two machines, we develop dominance properties, a lower bound and heuristic algorithms for the problem, and use these to develop a branch and bound algorithm. For evaluation of the performance of the algorithms, computational experiments are performed on randomly generated test problems and results are reported. Results of the experiments show that the suggested branch and bound algorithm can solve problems with up to 20 sub-jobs in a reasonable amount of CPU time, and the average percentage gap of the heuristic solutions is about 13%.     

A deterministic iterated local search algorithm for the vehicle routing problem with backhauls

The vehicle routing problem with backhauls is a variant of the classical capacitated vehicle routing problem. The difference is that it contains two distinct sets of customers: those who receive goods from the depot, who are called linehauls, and those who send goods to the depot, who are referred to as backhauls. In this paper, we describe a new deterministic iterated local search algorithm, which is tested using a large number of benchmark problems chosen from the literature. These computational tests have proven that this algorithm competes with the best known algorithms in terms of the quality of the solutions and at the same time, it is simpler and faster.     

A multi-period ordering and clearance pricing model considering the competition between new and out-of-season products

The joint management of pricing and inventory for perishable products has become an important problem for retailers. This paper investigates a multi-period ordering and clearance pricing model under consideration of the competition between new and out-of-season products. In each period, the ordering quantity of the new product and the clearance price of the out-of-season product are determined as decision variables before the demand is realized, and the unsold new product becomes the out-of-season one of the next period. We establish a finite-horizon Markov decision process model to formulate this problem and analyze its properties. A traditional dynamic program (DP) approach with two-dimensional search is provided. In addition, a myopic policy is derived in which only the profit of the current period is considered. Finally, we apply genetic algorithm (GA) to this problem and design a GA-based heuristic approach, showing by comparison among different algorithms that the GA-based heuristic approach is more performance sound than the myopic policy and much less time consuming than the DP approach.