A MAX-MIN ant system for unconstrained multi-level lot-sizing problems

In this paper, we present an ant-based algorithm for solving unconstrained multi-level lot-sizing problems called ant system for multi-level lot-sizing algorithm (ASMLLS). We apply a hybrid approach where we use ant colony optimization in order to find a good lot-sizing sequence, i.e. a sequence of the different items in the product structure in which we apply a modified Wagner–Whitin algorithm for each item separately. Based on the setup costs each ant generates a sequence of items. Afterwards a simple single-stage lot-sizing rule is applied with modified setup costs. This modification of the setup costs depends on the position of the item in the lot-sizing sequence, on the items which have been lot-sized before, and on two further parameters, which are tried to be improved by a systematic search. For small-sized problems ASMLLS is among the best algorithms, but for most medium- and large-sized problems it outperforms all other approaches regarding solution quality as well as computational time.     

一种启发式算法求解批量计划和排序集成问题

文章针对基于JIT思想建立的一种批量计划和作业排序集成问题,建立整体模型,设计了一种启发式算法采用集成方法求求解。针对问题的特点和遗传算法的特性,各层优化时均采用遗传算法求解,借鉴递阶优化方法的思想,首先从优化作业排序层出发,将其优化结果作为约束来优化批量计划层,然后利用利用批量优化的结果再重新来协调优化作业排序层,进而进一步去求解更好的批量计划。基于这种协调传递的思想,使各层的优化形成一个闭环,直到满足循环终止条件,得到比较理想的结果。最后通过算例试验表明,这种启发式算法与采用整体求解方法相比,具有比较满意的寻优性能和收敛速度。     

Online maintenance of very large random samples on flash storage

Recent advances in flash storage have made it an attractive alternative for data storage in a wide spectrum of computing devices, such as embedded sensors, mobile phones, PDA’s, laptops, and even servers. However, flash storage has many unique characteristics that make existing data management/analytics algorithms designed for magnetic disks perform poorly with flash storage. For example, while random reads can be nearly as fast as sequential reads, random writes and in-place data updates are orders of magnitude slower than sequential writes. In this paper, we consider an important fundamental problem that would seem to be particularly challenging for flash storage: efficiently maintaining a very large random sample of a data stream (e.g., of sensor readings). First, we show that previous algorithms such as reservoir sampling and geometric file are not readily adapted to flash. Second, we propose B-File, an energy-efficient abstraction for flash storage to store self-expiring items, and show how a B-File can be used to efficiently maintain a large sample in flash. Our solution is simple, has a small (RAM) memory footprint, and is designed to cope with flash constraints in order to reduce latency and energy consumption. Third, we provide techniques to maintain biased samples with a B-File and to query the large sample stored in a B-File for a subsample of an arbitrary size. Finally, we present an evaluation with flash storage that shows our techniques are several orders of magnitude faster and more energy-efficient than (flash-friendly versions of) reservoir sampling and geometric file. A key finding of our study, of potential use to many flash algorithms beyond sampling, is that “semi-random” writes (as defined in the paper) on flash cards are over two orders of magnitude faster and more energy-efficient than random writes.     

The multi-product,economic lot-sizing problem in flow shops: the powers-of-two heuristic

This paper presents a new and efficient heuristic to solve the multi-product, multi-stage, economic lot-sizing problem. The proposed heuristic, called the powers-of-two method, first determines sequencing decisions then lot sizing and scheduling decisions are determined. This method assumes that cycle times are integer multiples of a basic period and restricts these multiples to the powers of two. Once time multiples are chosen, we determine for each basic period of the global cycle the set of products to be produced and the production sequence to be used. Then a non-linear program is solved to simultaneously determine lot sizes and a feasible production schedule. To evaluate its performance, the powers-of-two method was compared to both the common cycle method and a reinforced version of the job-splitting heuristic. Numerical results show that the powers-of-two method outperforms both of these methods.Scope and purposeThe multi-product, multi-stage, economic lot-sizing problem studied in this paper is the problem of making sequencing, lot-sizing and scheduling decisions for several products manufactured through several stages in a flow shop environment so as to minimize the sum of setup and inventory holding costs while a given demand is fulfilled without backlogging. This problem and similar problems are met in many different industries like the food canning industry, the appliance assembly facilities or in beverage bottling companies. The most commonly used approach to deal with this problem is the common cycle approach where a lot of each product is produced each cycle. A few other approaches are also proposed. In this paper we propose a new and more efficient solution approach that assigns different cycle times to different products.     

A genetic algorithm for integrating lot-sizing and sequencing in scheduling a capacitated flow line

In this paper we present a genetic algorithm for solving an important but difficult scheduling problem: that of integrating the lot-sizing and sequencing decisions in scheduling a flow line involving sequence dependent setup times, capacity constraints, limited buffer capacity between machines, and due dates. The problem is based on a real world manufacturing facility that is also described. Novel crossover and mutation operators are presented for both the lot-sizing and sequencing parts of the scheduling problem and the performance of the genetic algorithm is compared to a heuristic approach of integration previously shown to have been effective.     

Implizite Determinierung von Plan-Belegungszeiten

Correct standard times are needed for logistic operating curves, manufacturing planning and control systems and Advanced Planning Systems (APS) for scheduling, lot-sizing and sequencing. This paper presents a model for calculation of standard times based on the knowledge of the total busy time of a work center and the produced number of items in a fixed time period. The developed method requires little effort in comparison to other methods such as Work-Factor or time observation. It can regularly determine standard times using current confirmation data.     

Integrating the lot-sizing and sequencing decisions for scheduling a capacitated flow line

In this paper we consider a general problem of scheduling a single flow line consisting of multiple machines and producing a given set of jobs. The manufacturing environment is characterized by sequence dependent set-up times, limited intermediate buffer space, and capacity constraints. In addition, jobs are assigned with due dates that have to be met. The objectives of the scheduling are: (1) to meet the due dates without violating the capacity constraints, (2) to minimize the makespan, and (3) to minimize the inventory holding costs. While most of the approaches in the literature treat the problem of scheduling in flow lines as two independent sub-problems of lot-sizing and sequencing, our approach integrates the lot-sizing and sequencing heuristics. The integrated approach uses the Silver-Meal heuristic (modified to include lot-splitting) for lot-sizing and an improvement procedure applied to Palmer's heuristic for sequencing, which takes into account the actual sequence dependent set-up times and the limited intermedite buffer capacity. We evaluate the performance of the integrated approach and demonstrate its efficacy for scheduling a real world SMT manufacturing environment.     

Heuristics for the strip packing problem with unloading constraints

This article addresses the Strip Packing Problem with Unloading Constraints (SPU). In this problem, we are given a strip of fixed width and unbounded height, and n items of C different classes. As in the well-known two-dimensional Strip Packing problem, we have to pack all items minimizing the used height, but now we have the additional constraint that items of higher classes cannot block the way out of lower classes items. This problem appears as a sub-problem in the Two-Dimensional Loading Capacitated Vehicle Routing Problem (2L-CVRP), where one has to optimize the delivery of goods, demanded by a set of clients, that are transported by a fleet of vehicles of limited capacity based at a central depot. We propose two approximation algorithms and a GRASP heuristic for the SPU problem and provide an extensive computational experiment with these algorithms using well know instances for the 2L-CVRP problem as well as new instances adapted from the Strip Packing problem.     

Kernel search: A general heuristic for the multi-dimensional knapsack problem

In this paper we apply the kernel search framework to the solution of the strongly NP-hard multi-dimensional knapsack problem (MKP). Kernel search is a heuristic framework based on the identification of a restricted set of promising items (kernel) and on the exact solution of ILP sub-problems. Initially, the continuous relaxation of the MKP, solved on the complete set of available items, is used to identify the initial kernel. Then, a sequence of ILP sub-problems are solved, where each sub-problem is restricted to the present kernel and to a subset of other items. Each ILP sub-problem may find better solutions with respect to the previous one and identify further items to insert into the kernel. The kernel search was initially proposed to solve a complex portfolio optimization problem. In this paper we show that the method has general key features that make it appropriate to solve other combinatorial problems using binary variables to model the decisions to select or not items. We adapt the kernel search to the solution of MKP and show that the method is very effective and efficient with respect to known problem-specific approaches. Moreover, the best known values of some MKP benchmark problems from the MIPLIB library have been improved.     

A parallel algorithm for the dynamic lot-sizing problem

The dynamic lot-sizing model (DLS) is one of the most frequently used models in production and inventory system because lot decisions can greatly affect the performance of the system. The practicality of DLS algorithms is hindered by the huge amount of computer resources required for solving these models, even for a modest problem. This study developed a parallel algorithm to solve the lot-sizing problem efficiently. Given that n is the size of the problem, the complexity of the proposed parallel algorithm is O(n²p) with p processors. Numerical experiments are provided to verify the complexity of the proposed algorithm. The empirical results demonstrate that the speedup of this parallel algorithm approaches linearity, which means that the proposed algorithm can take full advantage of the distributed computing power as the size of the problem increases.     

Implementation of a three-stage approach for the dynamic resource-constrained shortest-path sub-problem in branch-and-price

The resource-constrained shortest-path problem (RCSP) is often used as a sub-problem in branch-and-price because it can model the complex logic by which many actual systems operate. This paper addresses two special issues that arise in such an application. First, RCSP in this context is dynamic in the sense that arc costs are updated at each column-generation iteration, but constraints are not changed. Often, only a few arc costs are updated at an iteration. Second, RCSP must be solved subject to arcs that are forbidden or prescribed as corresponding binary variables are fixed to 0 or 1 by the branching rule. A reoptimizing algorithm for dealing with a few arc-cost changes and a method for dealing with fixed arcs are proposed and incorporated into a three-stage approach, specializing it for repeatedly solving the dynamic RCSP as a sub-problem in branch-and-price. Computational tests evaluate the effectiveness of the proposed algorithms.     

基于遗传算法的不确定系统的鲁棒控制参数选择

遗传算法是一种基于生物自然选择与遗传机理的随机搜索算法。本文利用遗传算法对不确定系统中的鲁棒控制参数进行选择。结果表明,此算法不仅可以得到满足要求的解,而且该算法的简单易行性也是其它算法所无法比拟的。     

基于多权重相似度的随机漫步推荐算法

在传统个性化推荐算法的基础上,提出了一种基于多权重相似度的随机漫步推荐算法。为了解决传统协同过滤算法中忽略了社交网络、热门项目以及共同评分项目之间影响等问题,通过引入万有引力公式计算社交网络中的用户相似度,并对传统协同过滤算法中的相似度进行改进,采用权重因子结合这两者相似度,最后开拓性地结合随机漫步算法进行商品推荐。实验结果表明,提出的算法具有比其他推荐算法更好的推荐性能。     

Identifying frequent items in distributed data sets

Many practical problems in computer science require the knowledge of the most frequently occurring items in a data set. Current state-of-the-art algorithms for frequent items discovery are either fully centralized or rely on node hierarchies which are inflexible and prone to failures in massively distributed systems. In this paper we describe a family of gossip-based algorithms that efficiently approximate the most frequent items in large-scale distributed datasets. We show, both analytically and using real-world datasets, that our algorithms are fast, highly scalable, and resilient to node failures.     

A two-leveled symbiotic evolutionary algorithm for clustering problems

Because of its unsupervised nature, clustering is one of the most challenging problems, considered as a NP-hard grouping problem. Recently, several evolutionary algorithms (EAs) for clustering problems have been presented because of their efficiency for solving the NP-hard problems with high degree of complexity. Most previous EA-based algorithms, however, have dealt with the clustering problems given the number of clusters (K) in advance. Although some researchers have suggested the EA-based algorithms for unknown K clustering, they still have some drawbacks to search efficiently due to their huge search space. This paper proposes the two-leveled symbiotic evolutionary clustering algorithm (TSECA), which is a variant of coevolutionary algorithm for unknown K clustering problems. The clustering problems considered in this paper can be divided into two sub-problems: finding the number of clusters and grouping the data into these clusters. The two-leveled framework of TSECA and genetic elements suitable for each sub-problem are proposed. In addition, a neighborhood-based evolutionary strategy is employed to maintain the population diversity. The performance of the proposed algorithm is compared with some popular evolutionary algorithms using the real-life and simulated synthetic data sets. Experimental results show that TSECA produces more compact clusters as well as the accurate number of clusters.     

Lot-sizing on a single imperfect machine: ILP models and FPTAS extensions

A single-machine multi-product lot-sizing and sequencing problem is studied. In this problem, items of n different products are manufactured in lots. Demands for products as well as per item processing times are known. There are losses of productivity because of non perfect production. There is also a sequence dependent set-up time between lots of different products. Machine yields and product lead times are assumed to be known deterministic functions. The objective is to minimize the cost of the demand dissatisfaction provided that the total processing time does not exceed a given time limit. We propose two integer linear programming (ILP) models for the NP-hard “fraction defective” case of this problem and compare effectiveness of their ILOG CPLEX realizations with a dynamic programming algorithm in a computer experiment. We also show how an earlier developed fully polynomial time approximation scheme (FPTAS) and one of the ILP models can be extended for a more complex case.     

Finding interesting associations without support pruning

Association-rule mining has heretofore relied on the condition of high support to do its work efficiently. In particular, the well-known a priori algorithm is only effective when the only rules of interest are relationships that occur very frequently. However, there are a number of applications, such as data mining, identification of similar Web documents, clustering, and collaborative filtering, where the rules of interest have comparatively few instances in the data. In these cases, we must look for highly correlated items, or possibly even causal relationships between infrequent items. We develop a family of algorithms for solving this problem, employing a combination of random sampling and hashing techniques. We provide analysis of the algorithms developed and conduct experiments on real and synthetic data to obtain a comparative performance analysis     

Improved initialisation for centroidal Voronoi tessellation and optimal Delaunay triangulation

Centroidal Voronoi tessellations and optimal Delaunay triangulations can be approximated efficiently by non-linear optimisation algorithms. This paper demonstrates that the point distribution used to initialise the optimisation algorithms is important. Compared to conventional random initialisation, certain low-discrepancy point distributions help convergence towards more spatially regular results and require fewer iterations for planar and volumetric tessellations.     

两种改进的模拟退火算法求解大值域约束满足问题

随机约束满足问题的相变现象及求解算法是NP-完全问题的研究热点。RB模型（Revised B）是一个非平凡的随机约束满足问题,它具有精确的可满足性相变现象和极易产生难解实例这两个重要特征。针对RB模型这一类具有大值域的随机约束满足问题,提出了两种基于模拟退火的改进算法即RSA（Revised Simulated Annealing Algorithm）和GSA（Genetic-simulated Annealing Algorithm）。将这两种算法用于求解RB模型的随机实例,数值实验结果表明：在进入相变区域时,RSA和GSA算法依然可以有效地找到随机实例的解,并且在求解效率上明显优于随机游走算法。在接近相变阈值点时,由这两种算法得到的最优解仅使得极少数的约束无法满足。     

Genetic algorithms with memory- and elitism-based immigrants in dynamic environments

Abstract In recent years the genetic algorithm community has shown a growing interest in studying dynamic optimization problems. Several approaches have been devised. The random immigrants and memory schemes are two major ones. The random immigrants scheme addresses dynamic environments by maintaining the population diversity while the memory scheme aims to adapt genetic algorithms quickly to new environments by reusing historical information. This paper investigates a hybrid memory and random immigrants scheme, called memory-based immigrants, and a hybrid elitism and random immigrants scheme, called elitism-based immigrants, for genetic algorithms in dynamic environments. In these schemes, the best individual from memory or the elite from the previous generation is retrieved as the base to create immigrants into the population by mutation. This way, not only can diversity be maintained but it is done more efficiently to adapt genetic algorithms to the current environment. Based on a series of systematically constructed dynamic problems, experiments are carried out to compare genetic algorithms with the memory-based and elitism-based immigrants schemes against genetic algorithms with traditional memory and random immigrants schemes and a hybrid memory and multi-population scheme. The sensitivity analysis regarding some key parameters is also carried out. Experimental results show that the memory-based and elitism-based immigrants schemes efficiently improve the performance of genetic algorithms in dynamic environments.