An Improved Petal Heuristic for the Vehicle Routeing Problem

Solutions produced by the first generation of heuristics for the vehicle routeing problem are often far from optimal. Recent adaptations of local search improvement heuristics, like tabu search, produce much better solutions but require increased computing time. However there are situations where good solutions must be obtained quickly. The algorithm proposed in this paper yields solutions almost as good as those produced by tabu search adaptations, but at only a small fraction of their computing time. This heuristic can be seen as an improved version of the original petal heuristic. On 14 benchmark test problems, the proposed heuristic yields solutions whose values lie on average within 2.38% of that of the best known solutions.     

Greedy heuristics for the diameter-constrained minimum spanning tree problem

The diameter-constrained minimum spanning tree problem is an NP-hard combinatorial optimization problem that seeks a minimum cost spanning tree with a limit D imposed upon the length of any path in the tree. We begin by presenting four constructive greedy heuristics and, secondly, we present some second-order heuristics, performing some improvements on feasible solutions, hopefully leading to better objective function values. We present a heuristic with an edge exchange mechanism, another that transforms a feasible spanning tree solution into a feasible diameter-constrained spanning tree solution, and finally another with a repetitive mechanism. Computational results show that repetitive heuristics can improve considerably over the results of the greedy constructive heuristics, but using a huge amount of computation time. To obtain computational results, we use instances of the problem corresponding to complete graphs with a number of nodes between 20 and 60 and with the value of D varying between 4 and 9.     

Exact and heuristic methods for placing ships in locks

The ship placement problem constitutes a daily challenge for planners in tide river harbours. In essence, it entails positioning a set of ships into as few lock chambers as possible while satisfying a number of general and specific placement constraints. These constraints make the ship placement problem different from traditional 2D bin packing. A mathematical formulation for the problem is presented. In addition, a decomposition model is developed which allows for computing optimal solutions in a reasonable time. A multi-order best fit heuristic for the ship placement problem is introduced, and its performance is compared with that of the left-right-left-back heuristic. Experiments on simulated and real-life instances show that the multi-order best fit heuristic beats the other heuristics by a landslide, while maintaining comparable calculation times. Finally, the new heuristic’s optimality gap is small, while it clearly outperforms the exact approach with respect to calculation time.     

A cooperative hyper-heuristic search framework

In this paper, we aim to investigate the role of cooperation between low level heuristics within a hyper-heuristic framework. Since different low level heuristics have different strengths and weaknesses, we believe that cooperation can allow the strengths of one low level heuristic to compensate for the weaknesses of another. We propose an agent-based cooperative hyper-heuristic framework composed of a population of heuristic agents and a cooperative hyper-heuristic agent. The heuristic agents perform a local search through the same solution space starting from the same or different initial solution, and using different low level heuristics. The heuristic agents cooperate synchronously or asynchronously through the cooperative hyper-heuristic agent by exchanging the solutions of the low level heuristics. The cooperative hyper-heuristic agent makes use of a pool of the solutions of the low level heuristics for the overall selection of the low level heuristics and the exchange of solutions. Computational experiments carried out on a set of permutation flow shop benchmark instances illustrated the superior performance of the cooperative hyper-heuristic framework over sequential hyper-heuristics. Also, the comparative study of synchronous and asynchronous cooperative hyper-heuristics showed that asynchronous cooperative hyper-heuristics outperformed the synchronous ones.     

Heuristics for the Maximum Outerplanar Subgraph Problem

Determining the maximum outerplanar subgraph of a given graph is known to be an NP-complete problem. In the literature there are no earlier experiment on approximating the maximum outerplanar subgraph problem. In this paper we compare solution quality and running times of different heuristics for finding maximum outerplanar subgraphs. We compare a greedy heuristic against a triangular cactus heuristic and its greedy variation. We also use the solutions from the greedy heuristics as initial solutions for a simulated annealing algorithm.The main experimental result is that simulated annealing with initial solution taken from the greedy triangular cactus heuristic yields the best known approximations for the maximum outerplanar subgraph problem.Work funded by the Tampere Graduate School in Information Science and Engineering (TISE) and supported by the Academy of Finland (Project 51528).     

A multi-heuristic approach for solving the pre-marshalling problem

Minimizing the number of reshuffling operations at maritime container terminals incorporates the pre-marshalling problem (PMP) as an important problem. Based on an analysis of existing solution approaches we develop new heuristics utilizing specific properties of problem instances of the PMP. We show that the heuristic performance is highly dependent on these properties. We introduce a new method that exploits a greedy heuristic of four stages, where for each of these stages several different heuristics may be applied. Instead of using randomization to improve the performance of the heuristic, we repetitively generate a number of solutions by using a combination of different heuristics for each stage. In doing so, only a small number of solutions is generated for which we intend that they do not have undesirable properties, contrary to the case when simple randomization is used. Our experiments show that such a deterministic algorithm significantly outperforms the original nondeterministic method. The improvement is twofold, both in the quality of found solutions, and in the computational effort.     

The tree representation for the pickup and delivery traveling salesman problem with LIFO loading

The feasible solutions of the traveling salesman problem with pickup and delivery (TSPPD) are commonly represented by vertex lists. However, when the TSPPD is required to follow a policy that loading and unloading operations must be performed in a last-in-first-out (LIFO) manner, we show that its feasible solutions can be represented by trees. Consequently, we develop a novel variable neighborhood search (VNS) heuristic for the TSPPD with last-in-first-out loading (TSPPDL) involving several search operators based on the tree data structure. Extensive experiments suggest that our VNS heuristic is superior to the current best heuristics for the TSPPDL in terms of solution quality, while requiring no more computing time as the size of the problem increases.     

An ILS heuristic for the traveling tournament problem with predefined venues

The Traveling Tournament Problem with Predefined Venues (TTPPV) is a single round robin variant of the Traveling Tournament Problem, in which the venue of each game to be played is known beforehand. We propose an Iterated Local Search (ILS) heuristic for solving real-size instances of the TTPPV, based on two types of moves. Initial solutions are derived from an edge coloring algorithm applied to complete graphs. We showed that canonical edge colorings should not be used as initial solutions in some situations. Instead, the use of Vizing’s edge coloring method lead to considerably better results. We also establish that the solution space defined by some commonly used neighborhoods in the sport scheduling literature is not connected in the case of single round robin tournaments, which explains the hardness of finding high quality solutions to some problem instances. Computational results show that the new ILS heuristic performs much better than heuristics based on integer programming and that it improves the best known solutions for benchmark instances.     

A multi-level composite heuristic for the multi-depot vehicle fleet mix problem

The problem of simultaneously allocating customers to depots, finding the delivery routes and determining the vehicle fleet composition is addressed. A multi-level composite heuristic is proposed and two reduction tests are designed to enhance its efficiency. The proposed heuristic is tested on benchmark problems involving up to 360 customers, 2 to 9 depots and 5 different vehicle capacities. When tested on the special case, the multi-depot vehicle routing, our heuristic yields solutions almost as good as those found by the best known heuristics but using only 5 to 10% of their computing time. Encouraging results were also obtained for the case where the vehicles have different capacities.     

Optimizing heuristic search in forest planning

Heuristic search methods are being used more and more in forest planning since the current formulations of exact methods such as linear programming are not suitable to all today's planning problems. A practical problem with most heuristics is that their performance greatly depends on the parameters that guide their search process. The effect of parameters is hard to know without extensive tests, but these tests cannot be conducted in forest planning practice, because of lacking time and experience. This study presented a method that uses Hooke and Jeeves direct search to optimize the parameters of a heuristic, taking into account the allowed computing time. The method was used to optimize three local-improvement heuristics in a non-spatial and a spatial forest planning problem, and with a short and long computing time. The heuristics were simulated annealing, threshold accepting, and tabu search, all of which are used in forestry. The results were logical and showed that while the optimal values of some parameters were rather constant the others were sensitive to problem type, allowed computing time, or problem size. The objective function value of the forest planning problem was not sensitive to small changes in the parameters of the heuristics. However, because computing time was very sensitive to many parameters, there was not much freedom to set the parameters if both the quality of the solution and speed of the algorithm had to be maintained.     

Average-weight-controlled bin-oriented heuristics for the one-dimensional bin-packing problem

Bin-oriented heuristics for one-dimensional bin-packing problem construct solutions by packing one bin at a time. Several such heuristics consider two or more subsets for each bin and pack the one with the largest total weight. These heuristics sometimes generate poor solutions, due to a tendency to use many small items early in the process. To address this problem, we propose a method of controlling the average weight of items packed by bin-oriented heuristics. Constructive heuristics and an improvement heuristic based on this approach are introduced. Additionally, reduction methods for bin-oriented heuristics are presented. The results of an extensive computational study show that: (1) controlling average weight significantly improves solutions and reduces computation time of bin-oriented heuristics; (2) reduction methods improve solutions and processing times of some bin-oriented heuristics; and (3) the new improvement heuristic outperforms all other known complex heuristics, in terms of both average solution quality and computation time.     

Resource levelling for projects with schedule-dependent time windows

The paper presents polynomial heuristic procedures for different types of resource levelling problems for projects with minimum and maximum time lags between project activities. Both problems without and with explicit resource constraints are treated. Thus far, only pseudopolynomial heuristics for special resource levelling problems without maximum time lags and resource constraints have been proposed. An experimental performance analysis shows that the new heuristics approximately solve problem instances with up to 500 activities and five resources within reasonable computing time.     

Maximizing the Net Present Value of a Project Under Resource Constraints Using a Lagrangian Relaxation Based Heuristic with Tight Upper Bounds

Resource-constrained project scheduling under a net present value objective attracts growing interest. Because this is an NP-hard problem, it is unlikely that optimum solutions can be computed for large instances within reasonable computation time. Thus, heuristics have become a popular research field. Up to now, however, upper bounds are not well researched. Therefore, most researchers evaluate their heuristics on the basis of a best known lower bound, but it is unclear how good the performance really is. With this contribution we close this gap and derive tight upper bounds on the basis of a Lagrangian relaxation of the resource constraints. We also use this approach as a basis for a heuristic and show that our heuristic as well as the cash flow weight heuristic proposed by Baroum and Patterson yield solutions very close to the optimum result. Furthermore, we discuss the proper choice of a test-bed and emphasize that discount rates must be carefully chosen to give realistic instances.     

Time lag size in multiple operations flow shop scheduling heuristics

This paper considers a multistage flow shop where jobs require multiple operations at each stage and a finish-to-start time lag between any two consecutive operations of a job: the next operation of a job cannot start until the time lag after the former operation of that job has elapsed. The effect of the size of this time lag is considered when studying the effectiveness of solution approaches for this problem. Since the problem of minimizing the makespan is shown to be NP-hard even for the two-stage case, we present a lower bound based heuristic approach that is used to construct several heuristic procedures. These heuristics use lower bounds on the minimum makespan to solve the problem. The effectiveness of these heuristics is empirically evaluated for various time lag sizes by solving a large number of randomly generated problems. We show that the relative performance of the heuristics depends on the size of the time lag. If the ratio of mean time lag and mean processing time is 20% or more, heuristics that construct an active schedule perform less well than heuristics that construct a non-delay schedule. The opposite holds true if this ratio is smaller. The performance of the widely used Shortest Processing Time heuristic (SPT) deteriorates quickly if the size of the time lags increases. We propose instead to use the Earliest Finish Time heuristic (EFT) in case time lags are present. EFT performs much better in this case and is identical to SPT if all time lags are zero. The use of the lower bound based heuristics results in an improvement of the makespan performance of up to 50% as compared with the performance of some simple dispatching heuristics that take the presence of multiple operations and time lags into account. This effect increases with the size of the time lags.     

A Two Stage Search Heuristic for Scheduling Payments in Projects

When the Net Present Value (NPV) of a project is used as a measure of its financial performance, effective management of cash flows over the duration of the project is critical for improved profitability. Progress payments are a major component of project cash flows. In many project environments, the contractor can negotiate payment terms. Payments are typically tied to completion of project activities and therefore have significant impact on the schedule of activities and the timing of the payments. In this paper, we consider the problem of simultaneously determining the amount, timing and location of progress payments in projects to maximize NPV. Due to the combinatorial nature of the problem, heuristics are a practical approach to solving the problem. We propose a two-stage heuristic where simulated annealing is used in the first stage to determine a set of payments. In the second stage, activities are rescheduled to improve project NPV. We compare the performance of this general purpose heuristic with other problem-dependent heuristics from the literature. Our results indicate that the simulated annealing heuristic significantly outperforms the parameter-based heuristics. Although rescheduling in the second stage improves NPV, increases are relatively small in magnitude. While the specific parameters settings suggested by the simulated annealing heuristic in this study may have limited generalizability at this time due to the narrow range of problems tested, our analysis suggests that a pure simulated annealing approach is a very attractive alternative for obtaining good heuristic solutions to the complex problem of scheduling payments in projects.     

具有机器适用限制的分布式置换流水车间问题的模型与算法

考虑具有机器适用限制的多个不同置换流水车间的调度问题. 机器适用限制指的是每个工件只能分配到其可加工工厂集合. 所有置换流水车间拥有的机器数相同但是具有不同的加工能力. 首先, 针对该问题建立了基于位置的混合整数线性规划模型; 进而, 对一般情况和三种特殊情况给出了具有较小近似比的多项式时间算法. 其次, 基于NEH方法提出了启发式算法NEHg, 并给出了以NEHg为上界的分支定界算法. 最后, 通过例子说明了NEHg启发式算法和分支定界算法的计算过程, 并进行大量的实验将NEHg与NEH算法结果进行比较, 从而验证了NEHg算法的有效性.     

Production scheduling with supply and delivery considerations to minimize the makespan

In this paper we study a scheduling model that simultaneously considers production scheduling, material supply, and product delivery. One vehicle with limited loading capacity transports unprocessed jobs from the supplier’s warehouse to the factory in a fixed travelling time. Another capacitated vehicle travels between the factory and the customer to deliver finished jobs to the customer. The objective is to minimize the arrival time of the last delivered job to the customer. We show that the problem is NP-hard in the strong sense, and propose an O(n) time heuristic with a tight performance bound of 2. We identify some polynomially solvable cases of the problem, and develop heuristics with better performance bounds for some special cases of the problem. Computational results show that all the heuristics are effective in producing optimal or near-optimal solutions quickly.     

Multiple orders per job batch scheduling with incompatible jobs

The multiple orders per job (MOJ) scheduling problem is presented for the batch-processing environment such as that exemplified by diffusion ovens. A mixed-integer programming formulation is presented for the incompatible job family case wherein only jobs that belong to the same family may be grouped together in a production batch. This optimization formulation is tested through an extensive experimental design with the objective of minimizing total weighted tardiness (maximizing on-time delivery performance). Optimal solutions are achievable for this initial set of 6-to-12 order problems, but it is noted that the optimization model takes an unreasonable amount of computation time, which suggests the need for heuristic development to support the analysis of larger, more practical MOJ batch scheduling problems. A number of simple heuristic approaches are investigated in an attempt to find near-optimal solutions in a reasonable amount of computation time. It is seen that a combination of the heuristics produces near-optimal solutions for small order problems. Further testing proves that these heuristic combinations are the best for large order problems as well.     

Cooperative Strategies for Solving the Bicriteria Sparse Multiple Knapsack Problem

For hard optimization problems, it is difficult to design heuristic algorithms which exhibit uniformly superior performance for all problem instances. As a result it becomes necessary to tailor the algorithms based on the problem instance. In this paper, we introduce the use of a cooperative problem solving team of heuristics that evolves algorithms for a given problem instance. The efficacy of this method is examined by solving six difficult instances of a bicriteria sparse multiple knapsack problem. Results indicate that such tailored algorithms uniformly improve solutions as compared to using predesigned heuristic algorithms.     

An artificial bee colony algorithm for the capacitated vehicle routing problem

This paper introduces an artificial bee colony heuristic for solving the capacitated vehicle routing problem. The artificial bee colony heuristic is a swarm-based heuristic, which mimics the foraging behavior of a honey bee swarm. An enhanced version of the artificial bee colony heuristic is also proposed to improve the solution quality of the original version. The performance of the enhanced heuristic is evaluated on two sets of standard benchmark instances, and compared with the original artificial bee colony heuristic. The computational results show that the enhanced heuristic outperforms the original one, and can produce good solutions when compared with the existing heuristics. These results seem to indicate that the enhanced heuristic is an alternative to solve the capacitated vehicle routing problem.