A grouped storage method for minimizing relocations in block stacking systems

When storage and retrieval times of inventories are uncertain and the storage space for the inventories is limited, it is an important problem to assign the inventories to storage spaces so that the total expected number of relocations is minimized. This paper addresses a dynamic location problem as well as a static location problem. Mathematical models are proposed for obtaining the optimal solution. To overcome the excessive computational time of optimizing methods, a genetic algorithm is suggested. Also, simple heuristic rules are suggested to solve the dynamic location problem. Performance of various solution methods are compared with each other. Received: June 2005 / Accepted: December 2005     

A heuristic method for two-stage hybrid flow shop with dedicated machines

This paper considers a two-stage hybrid flow shop scheduling problem with dedicated machines, in which the first stage contains a single common critical machine, and the second stage contains several dedicated machines. Each job must be first processed on the critical machine in stage one and depending on the job type, the job will be further processed on the dedicated machine of its type in stage two. The objective is to minimize the makespan. To solve the problem, a heuristic method based on branch and bound (B&B) algorithm is proposed. Several lower bounds are derived and four constructive heuristics are used to obtain initial upper bounds. Then, three dominance properties are employed to enhance the performance of the proposed heuristic method. Extensive computational experiments on two different problem categories each with various problem configurations are conducted. The results show that the proposed heuristic method can produce very close-to-optimal schedules for problems up to 100 jobs and five dedicated machines within 60 s. The comparisons with solutions of two other meta-heuristic methods also prove the better performance of the proposed heuristic method.     

Efficient primal-dual heuristic for a dynamic location problem

In this paper the dynamic location problem with opening, closure and reopening of facilities is formulated and an efficient primal-dual heuristic that computes both upper and lower limits to its optimal solution is described. The problem here studied considers the possibility of reconfiguring any location more than once over the planning horizon. This problem is NP-hard (the simple plant location problem is a special case of the problem studied). A primal-dual heuristic based on the work of Erlenkotter [A dual-based procedure for uncapacitated facility location. Operations Research 1978;26:992–1009] and Van Roy and Erlenkotter [A dual-based procedure for dynamic facility location. Management Science 1982;28:1091–105] was developed and tested over a set of randomly generated test problems. The results obtained are quite good, both in terms of the quality of lower and upper bounds calculated as in terms of the computational time spent by the heuristic. A branch-and-bound procedure that enables to optimize the problem is also described and tested over the same set of randomly generated problems.     

A new heuristic algorithm for rectangle packing

The rectangle packing problem often appears in encasement and cutting as well as very large-scale integration design. To solve this problem, many algorithms such as genetic algorithm, simulated annealing and other heuristic algorithms have been proposed. In this paper, a new heuristic algorithm is recommended based on two important concepts, namely, the corner-occupying action and caving degree. Twenty-one rectangle-packing instances are tested by the algorithm developed, 16 of which having achieved optimum solutions within reasonable runtime. Experimental results demonstrate that the algorithm developed is fairly efficient for solving the rectangle packing problem.     

A heuristic for job shop scheduling to minimize total weighted tardiness

This paper considers the job shop scheduling problem to minimize the total weighted tardiness with job-specific due dates and delay penalties, and a heuristic algorithm based on the tree search procedure is developed for solving the problem. A certain job shop scheduling to minimize the maximum tardiness subject to fixed sub-schedules is solved at each node of the search tree, and the successor nodes are generated, where the sub-schedules of the operations are fixed. Thus, a schedule is obtained at each node, and the sub-optimum solution is determined among the obtained schedules. Computational results on some 10 jobs and 10 machines problems and 15 jobs and 15 machines problems show that the proposed algorithm can find the sub-optimum solutions with a little computation time.     

A heuristic block-loading algorithm based on multi-layer search for the container loading problem

This paper presents an efficient heuristic block-loading algorithm based on multi-layer search for the three-dimensional container loading problem. First, a basic heuristic block-loading algorithm is introduced. This algorithm loads one block, determined by a block selecting algorithm, in one packing phase, according to a fixed strategy, until no blocks are available. Second, the concept of composite block is introduced, the difference between traditional block and composite block being that composite block can contain multiple types of boxes in one block under some restrictions. Third, based on the depth-first search algorithm, a multi-layer search algorithm is developed for determining the selected block in each packing phase, and making this result closer to the optimal solution. Computational results on a classic data set show that the proposed algorithm outperforms the best known algorithm in almost all the test data.     

A recursive branch-and-bound algorithm for the rectangular guillotine strip packing problem

A heuristic recursive algorithm for the two-dimensional rectangular strip packing problem is presented. It is based on a recursive structure combined with branch-and-bound techniques. Several lengths are tried to determine the minimal plate length to hold all the items. Initially the plate is taken as a block. For the current block considered, the algorithm selects an item, puts it at the bottom-left corner of the block, and divides the unoccupied region into two smaller blocks with an orthogonal cut. The dividing cut is vertical if the block width is equal to the plate width; otherwise it is horizontal. Both lower and upper bounds are used to prune unpromising branches. The computational results on a class of benchmark problems indicate that the algorithm performs better than several recently published algorithms.     

A branch and bound method for the line balancing problem in U-shaped assembly lines with equipment requirements

In this study we consider a U-shaped assembly line balancing problem where each task uses a specified set of equipments and each type of equipment has a specified cost. Our problem is to assign the tasks together with their equipments to the workstations so as to minimize the total equipment cost. We formulate the problem as a mixed integer linear programming model that is capable of solving small sized instances. We propose a branch and bound algorithm that uses efficient precedence relations and lower bounds. We find that the algorithm is able to solve moderate sized problem instances in reasonable times.     

A new heuristic approach for non-convex optimization problems

In this work a new optimization method, called the heuristic Kalman algorithm (HKA), is presented. This new algorithm is proposed as an alternative approach for solving continuous, non-convex optimization problems. The principle of HKA is to explicitly consider the optimization problem as a measurement process designed to give an estimate of the optimum. A specific procedure, based on the Kalman estimator, was developed to improve the quality of the estimate obtained through the measurement process. The main advantage of HKA, compared to other metaheuristics, lies in the small number of parameters that need to be set by the user. Further, it is shown that HKA converges almost surely to a near-optimal solution. The efficiency of HKA was evaluated in detail using several non-convex test problems, both in the unconstrained and constrained cases. The results were then compared to those obtained via other metaheuristics. The numerical experiments show that HKA is a promising approach for solving non-convex optimization problems, particularly in terms of computation time and success ratio.     

A new heuristic algorithm for cuboids packing with no orientation constraints

The three-dimensional cuboids packing is NP-hard and finds many applications in the transportation industry. The problem is to pack a subset of cuboid boxes into a big cuboid container such that the total volume of the packed boxes is maximized. The boxes have no orientation constraints, i.e. they can be rotated by 90^°${90}^{°}$ in any direction. A new heuristic algorithm is presented that defines a conception of caving degree to judge how close a packing box is to those boxes already packed into the container, and always chooses a packing with the largest caving degree to do. The performance is evaluated on all the 47 related benchmarks from the OR-Library. Experiments on a personal computer show a high average volume utilization of 94.6% with an average computation time of 23 min for the strengthened A1 algorithm, which improves current best records by 3.6%. In addition, the top-10 A2 algorithm achieved an average volume utilization of 91.9% with an average computation time of 55 s, which also got higher utilization than current best records reported in the literature.     

一个求解加权MAX-SAT问题的改进算法

提出了一种加权MAX-SAT问题求解的改进算法,给出了启发式的命题变量选择方法和新的下界计算方法,改善了加权MAX-SAT问题剪枝效率。当子句规模变大时,其优点更为明显。新的算法具有实现简单、求解速度快、处理变量规模大的特点。     

Solution algorithms for the makespan minimization problem with the general learning model

Most of the papers devoted to scheduling problems with the learning effect concern the Wright’s learning curve. On the other hand, the study about learning has pointed out that the learning curve in practice is very often an S-shaped function, which has not been considered in scheduling. Thus, in this paper, a single processor makespan minimization problem with an S-shaped learning model is investigated. We prove that this problem is strongly NP-hard even if the experience provided by each job is equal to its normal processing time. Therefore, to solve this problem, we prove some eliminating properties that are used to construct a branch and bound algorithm and some fast heuristic methods. Since the proposed algorithms are dedicated for the general case, i.e., where job processing times are arbitrary non-increasing experience dependent functions, their efficiency is verified numerically for the S-shaped model.     

A genetic algorithm with the heuristic procedure to solve the multi-line layout problem

The paper presents a genetic algorithm-based meta-heuristic to solve the facility layout problem (FLP) in a manufacturing system, where the material flow pattern of the multi-line layout is considered with the multi-products. The matrix encoding technique has been used for the chromosomes under the objective of minimizing the total material handling cost. The proposed algorithm produces a table with the descending order of the data corresponding to the input values of the flow and cost data. The generated table is used to create a schematic representation of the facilities, which in turn is utilized to heuristically generate the initial population of the chromosomes and to handle the heuristic crossover and mutation operators. The efficiency of the proposed algorithm has been proved through solving the two examples with the total cost less than the other genetic algorithms, CRAFT algorithm, and entropy-based algorithm.     

Generating subproblems in branch and bound algorithms for parallel machines scheduling problem

A branch and bound algorithm (B&B) has been widely used in various discrete and combinatorial optimization fields. To obtain optimal solutions as soon as possible for scheduling problems, three tools, which are branching, bounding and dominance rules, have been developed in the B&B algorithm. One of these tools, a branching is a method for generating subproblems and directly determines size of solution to be searched in the B&B algorithm. Therefore, it is very important to devise effective branching scheme for the problem.In this note, a survey of branching schemes is performed for parallel machines scheduling (PMS) problems with n independent jobs and m machines and new branching schemes that can be used for identical and unrelated PMS problems, respectively, are suggested. The suggested branching methods show that numbers of generated subproblems are much smaller than that of other methods developed earlier and therefore, it is expected that they help to reduce a lot of CPU time required to obtain optimal solutions in the B&B algorithm.     

Simplex filter: A novel heuristic filter for nonlinear systems state estimation

This paper introduces a new filter for nonlinear systems state estimation. The new filter formulates the state estimation problem as a stochastic dynamic optimization problem and utilizes a new stochastic method based on simplex technique to find and track the best estimation. The vertices of the simplex search the state space dynamically in a similar scheme to the optimization algorithm, known as Nelder-Mead simplex. The parameters of the proposed filter are tuned, using an information visualization technique to identify the optimal region of the parameters space. The visualization is performed using the concept of parallel coordinates. The proposed filter is applied to estimate the state of some nonlinear dynamic systems with noisy measurement and its performance is compared with other filters.     

A new iterated fast local search heuristic for solving QAP formulation in facility layout design

In facility layout design, the problem of locating facilities with material flow between them was formulated as a quadratic assignment problem (QAP), so that the total cost to move the required material between the facilities is minimized, where the cost is defined by a quadratic function. In this paper, we propose a modification to iterated fast local search algorithm (IFLS) with a new recombination crossover operator and the modified IFLS is addressed as NIFLS. The ideas we incorporate in the NIFLS are iterated self-improvement with evolutionary based perturbation tool, which includes (i) recombination crossover as perturbation tool and (ii) self-improvement in mutation operation followed by a local search. Three schemes of NIFLS are proposed and the obtained solution qualities by the three schemes are compared. We test our algorithm on all the benchmark instances of QAPLIB, a well-known library of QAP instances. The performance of proposed recombination crossover with sliding mutation (RCSM) scheme of NIFLS is well superior to the other two schemes of NIFLS.     

On the variable-depth-search heuristic for the linear-cost generalized assignment problem

The classical assignment problem seeks to determine a mapping between a set of assignees and a set of assignments. The linear cost assignment problem (LCGAP), as a generalized model, incorporates the relative workloads between assignees and assignments. Although LCGAP is computationally intractable, it has been extensively studied because of its practical implications in many real world situations. Variable-depth-search heuristic (VDSH) method is one of the solution methods that have been developed to produce quality near-optimal solutions to LCGAP. The main structure of VDSH consists of two basic operations: reassign and swap. In this paper, we make further observations on this effective heuristic method through a series of computational experiments. The numerical results statistically evince that different combina-tions of these two operations will result in solutions of different quality levels. These findings are expected to have similar implications to search heuristics for other optimization problems.     

Exact algorithm and heuristic for the Closest String Problem

The Closest String Problem (CSP) is an NP-hard problem, which arises in computational molecular biology and coding theory. This class of problems is to find a string that minimizes the maximum Hamming distance to a given set of strings. In this paper, we present an exact algorithm called Distance First Algorithm (DFA) for three strings of CSP with alphabet size two. For the general CSP, we design a polynomial heuristic which is a combination of our proposed approximation algorithm LDDA ([10] Liu Xiaolan, Fu Keqiang, Shao Renxiang. Largest distance decreasing algorithm for the Closest String Problem. Journal of Information & Computational Science 2004; 1(2): 287–92) and local search strategies. Numerical results show that the proposed heuristic may obtain a nearly optimal value in a reasonable time for small and large-scale instances of the CSP.     

A heuristic for the label printing problem

Label printing finds many applications in industry. However, this task is still labor intensive in many printing factories. Since each template can only accommodate a fixed number of labels, an important task is to work out the compositions of templates by allocating suitable labels to each template in order to fulfill the order requirements effectively. The template design could be rather arbitrary, which usually ends up with a lot of excessive printed labels. Enhancing the template design will significantly improve the efficiency of the printing process, and, at the same time, reduce the waste of resources. This motivates the study of more automatic design methods. In this paper, the problem is first formulated as a nonlinear integer programming problem. The main variables in the formulation are the compositions and the printing frequencies of templates. For practical purpose, each type of label is confined to one template only which allows automated packing and handling. The structure of the problems is carefully analyzed and a new algorithm is proposed. Numerical results show that the proposed method is a simple but effective way of generating good template designs.