Analysis of Heuristics for Number Partitioning

We illustrate the use of phase transition behavior in the study of heuristics. Using an "annealed" theory, we define a parameter that measures the "constrainedness" of an ensemble of number partitioning problems. We identify a phase transition at a critical value of constrainedness. We then show that constrainedness can be used to analyze and compare algorithms and heuristics for number partitioning in a precise and quantitative manner. For example, we demonstrate that on uniform random problems both the Karmarkar–Karp and greedy heuristics minimize the constrainedness, but that the decisions made by the Karmarkar–Karp heuristic are superior at reducing constrainedness. This supports the better performance observed experimentally for the Karmarkar–Karp heuristic. Our results refute a conjecture of Fu that phase transition behavior does not occur in number partitioning. Additionally, they demonstrate that phase transition behavior is useful for more than just simple benchmarking. It can, for instance, be used to analyze heuristics, and to compare the quality of heuristic solutions.     

Experiments on drawing 2-level hierarchical graphs

This paper studies different heuristics for drawing 2-level hierarchical graphs. Especially, we compare the barycenter and the median heuristics. We show that the barycenter heuristic clearly outperforms the median heuristic, although only the latter has a proved bound for the maximum error done when two vertices are ordered. Moreover, we improve a known heuristic, called the greedy switching, by introducing the barycenter heuristic as a preprocessing phase for it.     

Two simple and effective heuristics for minimizing the makespan in non-permutation flow shops

We propose a constructive and an iterated local search heuristic for minimizing the makespan in the non-permutation flow shop scheduling problem. Both heuristics are based on the observation that optimal non-permutation schedules often exhibit a permutation structure with a few local job inversions. In computational experiments we compare our heuristics to the best heuristics for finding non-permutation and permutation flow shop schedules, and evaluate the reduction in makespan and buffer size that can be achieved by non-permutation schedules.     

Solving the traveling salesman problem with annealing-basedheuristics: a computational study

Recently, several general optimization algorithms based on the demon algorithm from statistical physics have been developed and tested on a few traveling salesman problems with encouraging results. In this paper, we conduct an extensive computational study of 11 annealing-based heuristics for the traveling salesman problem. We code versions of simulated annealing, threshold accepting, record-to-record travel and eight heuristics based on the demon algorithm. We apply each heuristic to 29 traveling salesman problems taken from a well-known online library, compare the results with respect to accuracy and running time and provide insights and suggestions for future work     

New heuristics for planning operating rooms

We tackle the operating room planning problem of the Plastic Surgery and Major Burns Specialty of the University Hospital “Virgen del Rocio” in Seville (Spain). The decision problem is to assign an intervention date and an operating room to a set of surgeries on the waiting list, minimizing access time for patients with diverse clinical priority values. This problem has been previously addressed in the literature considering different objective functions. The clinical priority depends on the surgery priority and the number of days spent on the waiting list. We propose a set of 83 heuristics (81 constructive heuristics, a composite heuristic, and a meta-heuristic) based on a new solution encoding, and we compare these methods against existing heuristics from the literature for solving operating room planning problems. The heuristics are adapted to the problem under consideration (i.e. considering all constraints and the new objective function), being re-implemented using the information provided by the authors. In total, after a calibration procedure, we compare 17 heuristics. The computational experiments show that our proposed meta-heuristic is the best for the problem under consideration. Finally, the proposed heuristics are tested using data from the Plastic Surgery and Major Burns Specialty. The results show significant improvements on several key performance indicators (number of scheduled surgeries, quality of surgical plan, resources utilization, etc.) when comparing with the actual results obtained by the specialty in the current practice. The aforementioned hospital is currently implementing the heuristic methods.     

Scheduling identical jobs with unequal ready times on uniform parallel machines to minimize the maximum lateness

We consider the problem of scheduling n identical jobs with unequal ready times on m parallel uniform machines to minimize the maximum lateness. This paper develops a branch-and-bound procedure that optimally solves the problem and introduces six simple single-pass heuristic procedures that approximate the optimal solution. The branch-and-bound procedure uses the heuristics to establish an initial upper bound. On sample problems, the branch-and-bound procedure in most instances was able to find an optimal solution within 100,000 iterations with n≤80 and m≤3. For larger values of m, the heuristics provided approximate solutions close to the optimal values.     

Comparison and analysis of eight scheduling heuristics for the optimization of energy consumption and makespan in large-scale distributed systems

In this paper, we study the problem of scheduling tasks on a distributed system, with the aim to simultaneously minimize energy consumption and makespan subject to the deadline constraints and the tasks’ memory requirements. A total of eight heuristics are introduced to solve the task scheduling problem. The set of heuristics include six greedy algorithms and two naturally inspired genetic algorithms. The heuristics are extensively simulated and compared using an simulation test-bed that utilizes a wide range of task heterogeneity and a variety of problem sizes. When evaluating the heuristics, we analyze the energy consumption, makespan, and execution time of each heuristic. The main benefit of this study is to allow readers to select an appropriate heuristic for a given scenario.     

Design of rectangular packings: Block structure-based reconstruction algorithm

Consideration was given to the problems of orthogonal packing of rectangulars in a given domain. There exist many single-pass heuristic methods of their solution which serve as decoders in the algorithms of local search of the optimum. Some are used as constructive heuristics. In both cases, it is recommendable to use hybrid methods including tricks that improve the quality of packing. One of such tricks, the reconstruction algorithm, was described. The authors succeeded in realizing it with linear complexity of computations. The results of numerical experiment were presented.     

Solving the ship inventory routing and scheduling problem with undedicated compartments

This paper presents a ship inventory routing and scheduling problem with undedicated compartments (sIRPSP-UC). The objective of the problem is to find a minimum cost solution while satisfying a number of technical and physical constraints within a given planning horizon. In this problem, we identify four sub-problems that need to be decided simultaneously: route selections, ship selection, loading, and unloading activity procedures. To solve this problem, first, we developed a mixed integer linear programming model. We then developed a one-step greedy heuristic, and then based on this heuristic, we propose a set of heuristics. Each heuristic has a combination of rules for each sub-problem. A number of problem instances are used to compare the solutions of the two approaches. We applied selected good combinations of rules to solve each problem using the heuristic approach. The results show that 8 out 12 of the considered problem instances have no gap with MILP solution solved using LINGO. We also find that the average gap is 1.96%. In contrast when we consistently use the same combination for all iterations, there are no dominant combinations of heuristics that can find good solutions for all the problem instances.     

Goal distance estimation for automated planning using neural networks and support vector machines

Many of today’s most successful planners perform a forward heuristic search. The accuracy of the heuristic estimates and the cost of their computation determine the performance of the planner. Thanks to the efforts of researchers in the area of heuristic search planning, modern algorithms are able to generate high-quality estimates. In this paper we propose to learn heuristic functions using artificial neural networks and support vector machines. This approach can be used to learn standalone heuristic functions but also to improve standard planning heuristics. One of the most famous and successful variants for heuristic search planning is used by the Fast-Forward (FF) planner. We analyze the performance of standalone learned heuristics based on nature-inspired machine learning techniques and employ a comparison to the standard FF heuristic and other heuristic learning approaches. In the conducted experiments artificial neural networks and support vector machines were able to produce standalone heuristics of superior accuracy. Also, the resulting heuristics are computationally much more performant than related ones.     

Finding optimal solutions to the graph partitioning problem with heuristic search

As search spaces become larger and as problems scale up, an efficient way to speed up the search is to use a more accurate heuristic function. A better heuristic function might be obtained by the following general idea. Many problems can be divided into a set of subproblems and subgoals that should be achieved. Interactions and conflicts between unsolved subgoals of the problem might provide useful knowledge which could be used to construct an informed heuristic function. In this paper we demonstrate this idea on the graph partitioning problem (GPP). We first show how to format GPP as a search problem and then introduce a sequence of admissible heuristic functions estimating the size of the optimal partition by looking into different interactions between vertices of the graph. We then optimally solve GPP with these heuristics. Experimental results show that our advanced heuristics achieve a speedup of up to a number of orders of magnitude. Finally, we experimentally compare our approach to other states of the art graph partitioning optimal solvers on a number of classes of graphs. The results obtained show that our algorithm outperforms them in many cases.     

Heuristics for tactical time slot management: a periodic vehicle routing problem view

In this study, we consider a tactical problem where a time slot schedule for delivery service over a given planning horizon must be selected in each zone of a geographical area. A heuristic search evaluates each schedule selection by constructing a corresponding tactical routing plan of minimum cost based on demand and service time estimates. At the end, the schedule selection leading to the best tactical routing plan is selected. The latter can then be used as a blueprint when addressing the operational problem (i.e., when real customer orders are received and operational routes are constructed). We propose two heuristics to address the tactical problem. The first heuristic is a three‐phase approach: a periodic vehicle routing problem (PVRP) is first solved, followed by a repair phase and a final improvement phase where a vehicle routing problem (VRP) with time windows is solved for each period of the planning horizon. The second heuristic tackles the problem as a whole by directly solving a PVRP with time windows. Computational results compare the two heuristics under various settings, based on instances derived from benchmark instances for the VRP with time windows.     

A Systematic and Generalizable Approach to the Heuristic Evaluation of User Interfaces

Heuristic evaluation is one of the most actively used techniques for analyzing usability, as it is quick and inexpensive. This technique is based on following a given set of heuristics, which are typically defined as broad rules of thumb. In this paper, we propose a systematic and generalizable approach to this type of evaluation based on using comprehensive taxonomies as a source for the heuristics. This approach contrasts with other typical approaches, such as following (or adapting) Jakob Nielsen’s heuristics or creating ad hoc heuristics (formally or informally). The usefulness of our approach is investigated in two ways. Firstly, we carry out an actual heuristic evaluation of a mobile app in this manner, which we describe in detail. Secondly, we compare our approach and Nielsen’s. Additionally, we identify some limitations in Nielsen’s heuristics and some inconsistencies between them and established usability models, including Nielsen’s own.     

Wingrid-面向参数扫描应用的网格计算系统

参数扫描应用在计算网格环境下扮演十分重要的角色。在Wingrid项目中,我们提出并实现了一种面向参数扫描的自适应调度机制。客户端,主节点和从节点的调度基础设施,以及基于领导节点的通信系统能够改善调度的效率。同时,我们比较了自适应workqueue算法和标准启发式调度算法。实验结果显示大网络延迟下,启发式调度算法效率高于workqueue算法,在各种启发式算法中,min-min启发式算法的任务完成时间最小。     

A comparison of optimization heuristics for the data mapping problem

In the paper we compare the performance of six heuristics with suboptimal solutions for the data distribution of two dimensional meshes that are used for the numerical solution of partial differential equations (PDEs) on multicomputers. The data mapping heuristics are evaluated with respect to seven criteria covering load balancing, interprocessor communication, flexibility and ease of use for a class of single-phase iterative PDE solvers. Our evaluation suggests that the simple and fast block distribution heuristic can be as effective as the other five complex and computational expensive algorithms. © 1997 by John Wiley & Sons, Ltd.     

Allocation algorithms for personal TV advertisements

In this paper we consider the problem of allocating personal TV advertisements to viewers. The problem’s input consists of ad requests and viewers. Each ad is associated with a length, a payment, a requested number of viewers, a requested number of allocations per viewer and a target population profile. Each viewer is associated with a profile and an estimated viewing capacity which is uncertain. The goal is to maximize the revenue obtained from the allocation of ads to viewers for multiple periods while satisfying the ad constraints. First, we present the integer programming (IP) models of the problem and several heuristics for the deterministic version of the problem where the viewers’ viewing capacities are known in advance. We compare the performances of the proposed algorithms to those of the state-of-the-art IP solver. Later, we discuss the multi-period uncertain problem and, based on the best heuristic for the deterministic version, present heuristics for low and high uncertainty. Through computational experiments, we evaluate our heuristics. For the deterministic version, our best heuristic attains 98 % of the possible revenue and for the multi-period uncertain version our heuristics performances are very high, even in cases of high uncertainty, compared to the revenue obtained by the deterministic version.     

Scheduling algorithms for heterogeneous batch processors with incompatible job-families

We consider the problem of scheduling heterogeneous batch processors (i.e., batch processors with different capacity) with incompatible job-families and non-identical job sizes to maximize the utilization of the batch processors. We analyzed the computational complexity of this problem and showed that it is NP-hard and proposed eight variants of a fast greedy heuristic. A series of computational experiments were carried out to compare the performance of the heuristics and showed that the heuristics are capable of consistently obtaining near (estimated) optimal solutions with very low-computational burden for large-scale problems. We also carried out a study to find the effect of family processing time changes on the performance of the heuristics. This sensitivity analysis indicated that the processing time set of job-families influences the performance of the heuristic algorithms.     

Design of efficient hybrid neural networks for flexible flow shop scheduling

Abstract: Although neural networks have been successfully used in performing pattern recognition, their application for solving optimization problems has been limited. In this paper we design a neural network to solve a well‐known combinatorial problem, namely the flexible flow shop problem. A key feature of our neural network design is the integration of problem structure and heuristic information in the network structure and solution. We compare the performance of our neural network with well‐known current heuristics with respect to solution quality. The results indicate that our approach outperforms the heuristics.     

Heuristics for minimizing maximum lateness on a single machine with family-dependent set-up times

We address the problem of scheduling a single machine subject to family-dependent set-up times in order to minimize maximum lateness. We present a number of local improvement heuristics based on the work of previous researchers, a rolling horizon heuristic, and an incomplete dynamic programming heuristic. Extensive computational experiments on randomly generated test problems compare the performance of these heuristics. The rolling horizon procedures perform particularly well but require their parameters to be set based on problem characteristics to obtain their best performance.     

一种基于虚拟截止时间制导的改进的Min-Min元任务调度算法

在网格环境下,资源状况和用户行为相当复杂,是一个异构计算环境,元任务（meta—task）调度比传统并行调度更为复杂。如何映射一组任务到一组机器上被证明是NP问题,其目的一般是最小化任务完成时间（makespan）。为解决这一问题,已经提出一些启发式任务调度算法,例如具有代表性的MinMin元任务调度算法。本文在Min-Min元任务调度算法的基础上,通过虚拟截止时间制导的方法来改进Min-Min算法。实验结果表明,本文提出的算法具有更短的任务完成时间。