An efficient heuristic based on machine workload for the flowshop scheduling problem with setup and removal

We are concerned in this paper with solving ann jobs,M machines flowshop scheduling problem where the objective function is the minimization of the makespan. We take into account setup, processing and removal times separately. After drawing up a synthesis of existing work which addresses this type of problems, we propose a new heuristic algorithm which is based on the machine workload to find an efficient permutation schedule. Computational experiences show that our algorithm yields excellent results, particularly when bottleneck machines are present.     

Applying mod-k-cuts for solving linear ordering problems

The linear ordering problem consists of finding an ordering of the nodes of the weighted complete digraph on n nodes such that the sum of the weights of the arcs compatible with the ordering is maximized. In this paper, we report about the usefulness of mod-k cuts in a branch-and-cut algorithm for solving linear ordering problems to optimality.      

A note on scheduling flowshops with flexible stage ordering

We develop an asymptotically optimal heuristic for the m-stage flowshop problem with flexible stage ordering. Our algorithm supplies a job permutation which has the same worst case absolute bound for all possible m! orderings of the m stages. The development of our algorithm is motivated by the observation that it is sometimes beneficial to reverse the processing order in multi-stage manufacturing processes. Our algorithm facilitates the development of a job sequence a priori before the processing order is determined.     

Heuristic algorithms for the minmax regret flow-shop problem with interval processing times

An uncertain version of the permutation flow-shop with unlimited buffers and the makespan as a criterion is considered. The investigated parametric uncertainty is represented by given interval-valued processing times. The maximum regret is used for the evaluation of uncertainty. Consequently, the minmax regret discrete optimization problem is solved. Due to its high complexity, two relaxations are applied to simplify the optimization procedure. First of all, a greedy procedure is used for calculating the criterion’s value, as such calculation is NP-hard problem itself. Moreover, the lower bound is used instead of solving the internal deterministic flow-shop. The constructive heuristic algorithm is applied for the relaxed optimization problem. The algorithm is compared with previously elaborated other heuristic algorithms basing on the evolutionary and the middle interval approaches. The conducted computational experiments showed the advantage of the constructive heuristic algorithm with regards to both the criterion and the time of computations. The Wilcoxon paired-rank statistical test confirmed this conclusion.

     

An Optimization Problem with a Separable Non-Convex Objective Function and a Linear Constraint

For a class of global optimization (maximization) problems, with a separable non-concave objective function and a linear constraint a computationally efficient heuristic has been developed.The concave relaxation of a global optimization problem is introduced. An algorithm for solving this problem to optimality is presented. The optimal solution of the relaxation problem is shown to provide an upper bound for the optimal value of the objective function of the original global optimization problem. An easily checked sufficient optimality condition is formulated under which the optimal solution of concave relaxation problem is optimal for the corresponding non-concave problem. An heuristic algorithm for solving the considered global optimization problem is developed.The considered global optimization problem models a wide class of optimal distribution of a unidimensional resource over subsystems to provide maximum total output in a multicomponent systems.In the presented computational experiments the developed heuristic algorithm generated solutions, which either met optimality conditions or had objective function values with a negligible deviation from optimality (less than 1/10 of a percent over entire range of problems tested).     

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.     

A finite algorithm for the least two-norm solution of a linear program 1

By perturbing properly a linear program to a separable quadratic program it is possible to solve the latter in its dual variable space by iterative techniques such as sparsity-preserving SOR (successive overtaxation techniques). In this way large sparse linear programs can be handled.

In this paper we give a new computational criterion to check whether the solution of the perturbed quadratic program provides the least 2-norm solution of the original linear program. This criterion improves on the criterion proposed in an earlier paper.

We also describe an algorithm for solving linear programs which is based on the SOR methods. The main property of this algorithm is that, under mild assumptions, it finds the least 2-norm solution of a linear program in a finite number of iteration.s     

Adaptive dynamic cost updating procedure for solving fixed charge network flow problems

We approximate the objective function of the fixed charge network flow problem (FCNF) by a piecewise linear one, and construct a concave piecewise linear network flow problem (CPLNF). A proper choice of parameters in the CPLNF problem guarantees the equivalence between those two problems. We propose a heuristic algorithm for solving the FCNF problem, which requires solving a sequence of CPLNF problems. The algorithm employs the dynamic cost updating procedure (DCUP) to find a solution to the CPLNF problems. Preliminary numerical experiments show the effectiveness of the proposed algorithm. In particular, it provides a better solution than the dynamic slope scaling procedure in less CPU time. Research was partially supported by NSF and Air Force grants.     

A max-conflicts based heuristic search for the stable marriage problem with ties and incomplete lists

In this paper, we propose a heuristic search algorithm based on maximum conflicts to find a weakly stable matching of maximum size for the stable marriage problem with ties and incomplete lists. The key idea of our approach is to define a heuristic function based on the information extracted from undominated blocking pairs from the men’s point of view. By choosing a man corresponding to the maximum value of the heuristic function, we aim to not only remove all the blocking pairs formed by the man but also reject as many blocking pairs as possible for an unstable matching from the women’s point of view to obtain a solution of the problem as quickly as possible. Experiments show that our algorithm is efficient in terms of both execution time and solution quality for solving the problem.

     

Linear programming for the 0–1 quadratic knapsack problem

In this paper we consider the quadratic knapsack problem which consists in maximizing a positive quadratic pseudo-Boolean function subject to a linear capacity constraint. We propose a new method for computing an upper bound. This method is based on the solution of a continuous linear program constructed by adding to a classical linearization of the problem some constraints rebundant in 0–1 variables but nonredundant in continuous variables. The obtained upper bound is better than the bounds given by other known methods. We also propose an algorithm for computing a good feasible solution. This algorithm is an elaboration of the heuristic methods proposed by Chaillou, Hansen and Mahieu and by Gallo, Hammer and Simeone. The relative error between this feasible solution and the optimum solution is generally less than 1%. We show how these upper and lower bounds can be efficiently used to determine the values of some variables at the optimum. Finally we propose a branch-and-bound algorithm for solving the quadratic knapsack problem and report extensive computational tests.     

An approximation algorithm for the m-machine permutation flow shop scheduling problem with controllable processing times

The paper deals with the m-machine permutation flow shop scheduling problem in which job processing times, along with a processing order, are decision variables. It is assumed that the cost of processing a job on each machine is a linear function of its processing time and the overall schedule cost to be minimized is the total processing cost plus maximum completion time cost. A algorithm for the problem with m = 2 is provided; the best approximation algorithm until now has a worst-case performance ratio equal to . An extension to the m-machine (m ≥2) permutation flow shop problem yields an approximation algorithm with a worst-case bound equal to

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, where is the worst-case performance ratio of a procedure used, in the proposed algorithm, for solving the (pure) sequencing problem. Moreover, examples which achieve this bound for = 1 are also presented.     

On Heuristics for Solving Winner Determination Problem in Combinatorial Auctions

The winner determination problem (WDP) in combinatorial auctions is the problem of, given a finite set of combinatorial bids B, finding a feasible subset B of B with a maximum revenue. WDP is known to be equivalent to the maximum weight set packing problem, and hard to approximate by polynomial time algorithms. This paper proposes three heuristic bid ordering schemes for solving WDP; the first two schemes take into account the number of goods shared by conflicting bids, and the third one is based on a recursive application of such local heuristic functions. We conducted several experiments to evaluate the goodness of the proposed schemes. The result of experiments implies that the first two schemes are particularly effective to improve the performance of the resulting heuristic search procedures. More concretely, they are scalable compared with the conventional linear programming (LP) relaxation based schemes, and could quickly provide an optimum solution under optimization schemes such as the branch-and-bound method. In addition, they exhibit a good anytime performance competitive to the LP-based schemes, although it is sensitive to configurable parameters controlling the strength of contributions of bid conflicts to the resultant bid ordering schemes.     

A local search method for permutation flow shop scheduling

It is well known that a local search method, a widely used approach for solving the permutation flow shop scheduling problem, can easily be trapped at a local optimum. In this paper, we propose two escape-from-trap procedures to move away from local optima. Computational experiments carried out on a standard set of instances show that this heuristic algorithm generally outperforms an effective approximation algorithm.     

范数下无容量限制设施选址逆问题的求解方法

一个优化问题的逆问题是这样一类问题,在给定该优化问题的一个可行解时,通过最小化目标函数中参数的改变量(在某个范数下)使得该可行解成为改变参数后的该优化问题的最优解。对于本是NP-难问题的无容量限制设施选址问题,证明了其逆问题仍是NP-难的。研究了使用经典的行生成算法对无容量限制设施选址的逆问题进行计算,并给出了求得逆问题上下界的启发式方法。两种方法分别基于对子问题的线性松弛求解给出上界和利用邻域搜索以及设置迭代循环次数的方式给出下界。数值结果表明线性松弛法得到的上界与最优值差距较小,但求解效率提升不大;而启发式方法得到的下界与最优值差距极小,极大地提高了求解该逆问题的效率。     

Constraint Propagation and Problem Decomposition: A Preprocessing Procedure for the Job Shop Problem

In recent years, constraint propagation techniques have been shown to be highly effective for solving difficult scheduling problems. In this paper, we present an algorithm which combines constraint propagation with a problem decomposition approach in order to simplify the solution of the job shop scheduling problem. This is mainly guided by the observation that constraint propagation is more effective for small problem instances. Roughly speaking, the algorithm consists of deducing operation sequences that are likely to occur in an optimal solution of the job shop scheduling problem (JSP).The algorithm for which the name edge-guessing procedure has been chosen – since with respect to the job shop scheduling problem (JSP) the deduction of machine sequences is mainly equivalent to orienting edges in a disjunctive graph – can be applied in a preprocessing step, reducing the solution space, thus speeding up the overall solution process. In spite of the heuristic nature of edge-guessing, it still leads to near-optimal solutions. If combined with a heuristic algorithm, we will demonstrate that given the same amount of computation time, the additional application of edge-guessing leads to better solutions. This has been tested on a set of well-known JSP benchmark problem instances.     

A decomposition approach for a very large scale optimal diversity management problem

This paper focuses on the solution of the optimal diversity management problem formulated as a p-Median problem. The problem is solved for very large scale real instances arising in the car industry and defined on a graph with several tens of thousands of nodes and with several millions of arcs. The particularity is that the graph can consist of several non connected components. This property is used to decompose the problem into a series of p-Median subproblems of a smaller dimension. We use a greedy heuristic and a Lagrangian heuristic for each subproblem. The solution of the whole problem is obtained by solving a suitable assignment problem using a Branch-and-Bound algorithm.Received: June 2004 / Revised version: December 2004MSC classification: 49M29, 90C06, 90C27, 90C60All correspondence to: Antonio SforzaIgor Vasilev: Support for this author was provided by NATO grant CBP.NR.RIG.911258.     

An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers

This article presents an exact algorithm for the precedence-constrained traveling salesman problem, which is also known as the sequential ordering problem. This NP-hard problem has applications in various domains, including operational research and compilers. In this article, the problem is presented and solved in the context of minimizing switching energy in compilers. Most previous work on minimizing switching energy in the compiler domain has been limited to simple heuristics that are not guaranteed to give an optimal solution. In this work, we present an exact algorithm for solving the switching energy minimization problem using a branch-and-bound approach. The proposed algorithm is simple and intuitive, yet powerful. It is the first exact algorithm for the switching energy problem that is shown to solve real instances of the problem within a few seconds per instance. Compared to previous work in the operational research domain, the proposed algorithm is believed to be the most powerful exact algorithm that does not require a linear programming formulation. The proposed algorithm is experimentally evaluated using instances taken from a production compiler. The results show that with a time limit of 10 ms per node, the proposed algorithm optimally solves 99.8 % of the instances. It optimally solves instances with up to 598 nodes within a few seconds. The resulting switching cost is 16 % less than that produced without energy awareness and 5 % less than that produced by a commonly used heuristic.     

Exploring the constrained maximum edge-weight connected graph problem

Given an edge weighted graph, the maximum edge-weight connected graph （MECG） is a connected subgraph with a given number of edges and the maximal weight sum. Here we study a special case, i.e. the Constrained Maximum Edge-Weight Connected Graph problem （CMECG）, which is an MECG whose candidate subgraphs must include a given set of k edges, then also called the k-CMECG. We formulate the k-CMECG into an integer linear programming model based on the network flow problem. The k-CMECG is proved to be NP-hard. For the special case 1-CMECG, we propose an exact algorithm and a heuristic algorithm respectively. We also propose a heuristic algorithm for the k-CMECG problem. Some simulations have been done to analyze the quality of these algorithms. Moreover, we show that the algorithm for 1-CMECG problem can lead to the solution of the general MECG problem.     

Approximate solutions to the turbine balancing problem

The turbine balancing problem (TBP) is an NP-Hard combinatorial optimization problem arising in the manufacturing and maintenance of turbine engines. Exact solution methods for solving the TBP are not appropriate since the problem has to be solved in real time and the input data is itself inaccurate. In this paper the TBP is formulated as a quadratic assignment problem (QAP) and we propose a heuristic algorithm for solving the resulting problem. Computational results on a set of instances provided by Pratt & Whitney (P&W) and from the literature, indicate that the proposed algorithm outperforms the current methods used for solving the TBP, and has the best overall performance with respect to other heuristic algorithms in the literature.