An iterative rounding search-based algorithm for the disjunctively constrained knapsack problem

This article proposes an iterative rounding search-based algorithm for approximately solving the disjunctively constrained knapsack problem. The problem can be viewed as a variant of the well-known knapsack problem with some sets of incompatible items. The algorithm considers two key features: a rounding strategy applied to the fractional variables of a linear relaxation and a neighbouring strategy used for improving the quality of the solutions at hand. Both strategies are iterated into a process based on adding a series of (i) valid cardinality constraints and (ii) lower bounds used for bounding the objective function. The proposed algorithm is analysed computationally on a set of benchmark instances of the literature. The proposed algorithm outperforms the Cplex solver and the results obtained improve on most existing solutions.     

A hybrid heuristic for the multiple choice multidimensional knapsack problem

In this article, a new solution approach for the multiple choice multidimensional knapsack problem is described. The problem is a variant of the multidimensional knapsack problem where items are divided into classes, and exactly one item per class has to be chosen. Both problems are NP-hard. However, the multiple choice multidimensional knapsack problem appears to be more difficult to solve in part because of its choice constraints. Many real applications lead to very large scale multiple choice multidimensional knapsack problems that can hardly be addressed using exact algorithms. A new hybrid heuristic is proposed that embeds several new procedures for this problem. The approach is based on the resolution of linear programming relaxations of the problem and reduced problems that are obtained by fixing some variables of the problem. The solutions of these problems are used to update the global lower and upper bounds for the optimal solution value. A new strategy for defining the reduced problems is explored, together with a new family of cuts and a reformulation procedure that is used at each iteration to improve the performance of the heuristic. An extensive set of computational experiments is reported for benchmark instances from the literature and for a large set of hard instances generated randomly. The results show that the approach outperforms other state-of-the-art methods described so far, providing the best known solution for a significant number of benchmark instances.     

An iterative bidirectional heuristic placement algorithm for solving the two-dimensional knapsack packing problem

This article presents an efficient heuristic placement algorithm, namely, a bidirectional heuristic placement, for solving the two-dimensional rectangular knapsack packing problem. The heuristic demonstrates ways to maximize space utilization by fitting the appropriate rectangle from both sides of the wall of the current residual space layer by layer. The iterative local search along with a shift strategy is developed and applied to the heuristic to balance the exploitation and exploration tasks in the solution space without the tuning of any parameters. The experimental results on many scales of packing problems show that this approach can produce high-quality solutions for most of the benchmark datasets, especially for large-scale problems, within a reasonable duration of computational time.     

Investigating Ahuja–Orlin’s large neighbourhood search approach for examination timetabling

Since the 1960s, automated approaches to examination timetabling have been explored and a wide variety of approaches have been investigated and developed. In this paper we build upon a recently presented, sequential solution improvement technique which searches efficiently over a very large set of “adjacent” (neighbourhood) solutions. This solution search methodology, originally developed by Ahuja and Orlin, has been applied successfully in the past to a number of difficult combinatorial optimisation problems. It is based on an improvement graph representation of solution adjacency and identifies improvement moves by finding cycle exchange operations using a modified shortest path label-correcting algorithm. We have drawn upon Ahuja–Orlin’s basic methodology to develop an effective automated exam timetabling technique. We have evaluated our approach against the latest methodologies in the literature on standard benchmark problems. We demonstrate that our approach produces some of the best known results on these problems.     

A parallel genetic algorithm for dynamic cell formation in cellular manufacturing systems

Instead of using expensive multiprocessor supercomputers, parallel computing can be implemented on a cluster of inexpensive personal computers. Commercial accesses to high performance parallel computing are also available on the pay-per-use basis. However, literature on the use of parallel computing in production research is limited. In this paper, we present a dynamic cell formation problem in manufacturing systems solved by a parallel genetic algorithm approach. This method improves our previous work on the use of sequential genetic algorithm (GA). Six parallel GAs for the dynamic cell formation problem were developed and tested. The parallel GAs are all based on the island model using migration of individuals but are different in their connection topologies. The performance of the parallel GA approach was evaluated against a sequential GA as well as the off-shelf optimization software. The results are very encouraging. The considered dynamic manufacturing cell formation problem incorporates several design factors. They include dynamic cell configuration, alternative routings, sequence of operations, multiple units of identical machines, machine capacity, workload balancing, production cost and other practical constraints.     

Hybrid simulated annealing and reduced variable neighbourhood search for an aircraft scheduling and parking problem

Aircraft stands and runways at airports are critical airport resources for aircraft scheduling and parking. Making use of limited apron and runway resources to improve airport efficiency is becoming increasingly important. In this paper, we study a realistic Aircraft Scheduling and Parking Problem (ASPP) with the goal of simultaneously determining the takeoff and landing time of each aircraft with consideration for wake vortex effect constraints and parking positions in the limited parking apron at a target airport. The objective of the ASPP is to minimise the total service time for aircraft. We developed a mixed-integer linear programme formulation for the ASPP. A novel improved bottom-left/right strategy is applied to construct solutions and a Hybrid Simulated Annealing and Reduced Variable Neighborhood Search (HSARVNS) is proposed to identify near-optimal solutions. Numerical experiments on randomly generated ASPP instances and on a large set of benchmarks for a reduced version of the ASPP (i.e. the classical Two-Dimensional Strip-Packing Problem (2D-SPP)) demonstrate the effectiveness and efficiency of the proposed approach. For the ASPP, HSARVNS can find optimal solutions for small instances in a fraction of a second and can find high-quality solutions for instances with up to 250 aircraft within a reasonable timeframe. For the 2D-SPP, the HSARVNS can find optimal solutions for 32 of 38 tested benchmarks within 90 s on average.     

hp-version discontinuous Galerkin methods for hyperbolic conservation laws: A parallel adaptive strategy

This paper describes a parallel algorithm based on discontinuous hp-finite element approximations of linear, scalar, hyperbolic conservation laws. The paper focuses on the development of an effective parallel adaptive strategy for such problems. Numerical experiments suggest that these techniques are highly parallelizable and exponentially convergent, thereby yielding efficiency many times superior to conventional schemes for hyperbolic problems.     

Iterative mesh partitioning optimization for parallel nonlinear dynamic finite element analysis with direct substructuring

 This work presents a novel iterative approach for mesh partitioning optimization to promote the efficiency of parallel nonlinear dynamic finite element analysis with the direct substructure method, which involves static condensation of substructures' internal degrees of freedom. The proposed approach includes four major phases – initial partitioning, substructure workload prediction, element weights tuning, and partitioning results adjustment. The final three phases are performed iteratively until the workloads among the substructures are balanced reasonably. A substructure workload predictor that considers the sparsity and ordering of the substructure matrix is used in the proposed approach. Several numerical experiments conducted herein reveal that the proposed iterative mesh partitioning optimization often results in a superior workload balance among substructures and reduces the total elapsed time of the corresponding parallel nonlinear dynamic finite element analysis. Received 22 August 2001 / Accepted 20 January 2002     

An adaptive scheduling algorithm for a parallel machine problem with rework processes

The development of a scheduling methodology for a parallel machine problem with rework processes is presented in this paper. The problem is to make a schedule for parallel machines with rework probabilities, due-dates, and sequence dependent setup times. Two heuristics are developed based on a dispatching algorithm and problem-space-based search method. In order to evaluate the efficacy of the proposed algorithms, six performance indicators are considered: total tardiness, maximum lateness, mean flow-time, mean lateness, the number of tardy jobs, and the number of reworks. This paper shows how these algorithms can adaptively capture the characteristics of manufacturing facilities for enhancing the performance under changing production environments. Extensive experimental results show that the proposed algorithms give very efficient performance in terms of computational time and each objective value.     

SIMD tabu search for the quadratic assignment problem with graphics hardware acceleration

This paper presents a single instruction multiple data tabu search (SIMD-TS) algorithm for the quadratic assignment problem (QAP) with graphics hardware acceleration. The QAP is a classical combinatorial optimisation problem that is difficult to solve optimally for even small problems with over 30 items. By using graphic hardware acceleration, the developed SIMD-TS algorithm executes 20 to 45 times faster than traditional CPU code. The computational improvement is made possible by the utilisation of the parallel computing capability of a graphics processing unit (GPU). The speed and effectiveness of this algorithm are demonstrated on QAP library problems. The main contribution of this paper is a fast and effective SIMD-TS algorithm capable of producing results for large QAPs on a desktop personal computer equivalent to the results achieved with a CPU cluster.     

Ant colony optimisation with parameterised search space for the job shop scheduling problem

The job-shop scheduling problem (JSSP) is known to be NP-hard. Due to its complexity, many metaheuristic algorithm approaches have arisen. Ant colony metaheuristic algorithm, lately proposed, has successful application to various combinatorial optimisation problems. In this study, an ant colony optimisation algorithm with parameterised search space is developed for JSSP with an objective of minimising makespan. The problem is modelled as a disjunctive graph where arcs connect only pairs of operations related rather than all operations are connected in pairs to mitigate the increase of the spatial complexity. The proposed algorithm is compared with a multiple colony ant algorithm using 20 benchmark problems. The results show that the proposed algorithm is very accurate by generating 12 optimal solutions out of 20 benchmark problems, and mean relative errors of the proposed and the multiple colony ant algorithms to the optimal solutions are 0.93% and 1.24%, respectively.     

Tabu search for the redundancy allocation problem of homogenous series–parallel multi-state systems

This paper develops an efficient tabu search (TS) heuristic to solve the redundancy allocation problem for multi-state series–parallel systems. The system has a range of performance levels from perfect functioning to complete failure. Identical redundant elements are included in order to achieve a desirable level of availability. The elements of the system are characterized by their cost, performance and availability. These elements are chosen from a list of products available in the market. System availability is defined as the ability to satisfy consumer demand, which is represented as a piecewise cumulative load curve. A universal generating function technique is applied to evaluate system availability. The proposed TS heuristic determines the minimal cost system configuration under availability constraints. An originality of our approach is that it proceeds by dividing the search space into a set of disjoint subsets, and then by applying TS to each subset. The design problem, solved in this study, has been previously analyzed using genetic algorithms (GAs). Numerical results for the test problems from previous research are reported, and larger test problems are randomly generated. Comparisons show that the proposed TS out-performs GA solutions, in terms of both the solution quality and the execution time.     

Multiple-choice knapsack-based heuristic algorithm for the two-stage two-dimensional cutting stock problem in the paper industry

This study examines a two-stage two-dimensional cutting stock problem encountered by a paper mill company. The problem includes various machine-related and operational constraints based on real-world situations. Paper products are manufactured using two major cutting processes. Each cutting machine has a specific minimum and maximum width for input and output rolls and is limited by the maximum number of rolls it can cut at the same time. A mathematical model is presented to formally address the problem and an efficient multiple-choice knapsack-based heuristic algorithm is proposed to solve the problem. To demonstrate the efficiency of the proposed heuristic algorithm, computational experiments are conducted on test data-set generated from real-world data provided by a large paper mill company in the Republic of Korea.     

Makespan minimisation for a parallel machine scheduling problem with preemption and job incompatibility

In this paper, an extension of the graph colouring problem is introduced to model a parallel machine scheduling problem with job incompatibility. To get closer to real-world applications, where the number of machines is limited and jobs have different processing times, each vertex of the graph requires multiple colours and the number of vertices with the same colour is bounded. In addition, several objectives related to scheduling are considered: makespan, number of pre-emptions and summation over the jobs’ throughput times. Different solution methods are proposed, namely, two greedy heuristics, two tabu search methods and an adaptive memory algorithm. The latter uses multiple recombination operators, each one being designed for optimising a subset of objectives. The most appropriate operator is selected dynamically at each iteration, depending on its past performance. Experiments show that the proposed algorithm is effective and robust, while providing high-quality solutions on benchmark instances for the graph multi-colouring problem, a simplification of the considered problem.     

A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study

The assembly line worker assignment and balancing problem type-II (ALWABP-2) occurs when workers and tasks (where task times depend on workers’ skills) are to be simultaneously assigned to a fixed number of workstations with the goal of minimising the cycle time. In this study, a two-phase variable neighbourhood search (VNS) algorithm is proposed to solve the ALWABP-2 due to the NP-hard nature of this problem. In the first phase of the algorithm, a VNS approach is applied to assign tasks to workstations with the aim of minimising the cycle time while in the second phase, a variable neighbourhood descent method is applied to assign workers to workstations. The performance of the proposed algorithm is tested on well-known benchmark instances. In addition, the proposed algorithm has been used to solve a real case study from a consumer electronics company that manufactures LCD TVs. The results show that the algorithm is superior to the methods reported in the literature in terms of its higher efficiency and robustness. Furthermore, the algorithm is easy to implement and significantly improves the performance of the final assembly line for the investigated LCD TV real case study.     

Hybrid glowworm swarm optimization for task scheduling in the cloud environment

In recent years many heuristic algorithms have been proposed to solve task scheduling problems in the cloud environment owing to their optimization capability. This article proposes a hybrid glowworm swarm optimization (HGSO) based on glowworm swarm optimization (GSO), which uses a technique of evolutionary computation, a strategy of quantum behaviour based on the principle of neighbourhood, offspring production and random walk, to achieve more efficient scheduling with reasonable scheduling costs. The proposed HGSO reduces the redundant computation and the dependence on the initialization of GSO, accelerates the convergence and more easily escapes from local optima. The conducted experiments and statistical analysis showed that in most cases the proposed HGSO algorithm outperformed previous heuristic algorithms to deal with independent tasks.     

An improved method for the hot strip mill production scheduling problem

In most research on the hot strip mill production scheduling problem (HSMPSP) arising in the steel industry, it is accepted that a schedule with lower penalty caused by jumps of width, hardness, and gauge will result in lower roller wear, so it is regarded as a better schedule. However, based on the analysis of production processes, it is realised that rolling each coil also cause roller wear. In order to assessing the roller wear associated with production scheduling more precisely, it is necessary to consider it as another factor besides those jumps, especially when complicated constraints are involved. In this paper, an improved method is proposed to quantify the expected wear of the rollers done by those jumps and rolling processes. Then the HSMPSP whose objective is to maximise the total length of all scheduled coils is formulated as a team orienteering problem with time windows and additional production constraints. A heuristic method combining an improved Ant Colony Extended algorithm with local search procedures dedicated to HSMPSP is developed. Finally, computational results on instances generated based on production data from an integrated steel mill in China indicate that the proposed algorithm is a promising solution specific to HSMPSP.     

Genetic algorithm with adaptive and dynamic penalty functions for the selection of cleaner production measures: a constrained optimization problem

This paper presents a new approach of genetic algorithm (GA) to solve the constrained optimization problem. In a constrained optimization problem, feasible and infeasible regions occupy the search space. The infeasible regions consist of the solutions that violate the constraint. Oftentimes classical genetic operators generate infeasible or invalid chromosomes. This situation takes a turn for the worse when infeasible chromosomes alone occupy the whole population. To address this problem, dynamic and adaptive penalty functions are proposed for the GA search process. This is a novel strategy because it will attempt to transform the constrained problem into an unconstrained problem by penalizing the GA fitness function dynamically and adaptively. New equations describing these functions are presented and tested. The effects of the proposed functions developed have been investigated and tested using different GA parameters such as mutation and crossover. Comparisons of the performance of the proposed adaptive and dynamic penalty functions with traditional static penalty functions are presented. The result from the experiments show that the proposed functions developed are more accurate, efficient, robust and easy to implement. The algorithms developed in this research can be applied to evaluate environmental impacts from process operations.     

Fast parallel algorithms for the Maximum Empty Rectangle problem

We present efficient parallel algorithms for the maximum empty rectangle problem in this paper. On crew pram, we solve the area version of this problem inO(log ² n) time usingO(nlogn) processors. The perimeter version of this problem is solved inO(logn) time usingO(nlog ² n) processors. On erew pram, we solve both the problems inO(logn) time usingO(n ²/logn) processors. We also present anO(logn) time algorithm on a mesh-of-trees architecture.