Improved LP-based algorithms for the closest string problem

In a recent paper by Liu et al. [Exact algorithm and heuristic for the closest string problem, Computers & Operations Research 2011;38:1513-20], a polynomial time heuristic procedure is proposed for the closest string problem (CSP). Such heuristic called LDDA_LSS is a combination of a previously published approximation algorithm and local search strategies. This paper points out that an instant algorithm deriving a feasible solution directly from the continuous relaxation solution of a standard ILP formulation of CSP already strongly outperforms LDDA_LSS both in terms of solution quality and computing time. Two core based procedures are then proposed that further improve the results of the instant algorithm. Based on these results, we conclude that such LP-based approaches for their efficiency and simplicity should be used as a benchmark for future heuristics on CSP.     

Effect of solution representations on Tabu search in scheduling applications

This research investigates the application of meta-heuristic algorithms to a scheduling problem called permutation manufacturing-cell flow shop (PMFS) from two perspectives. First, we examine the effect of using different solution representations (S_new and S_old) while applying Tabu-search algorithm. Experimental results reveal that Tabu_S_new outperforms Tabu_S_old. The rationale why Tabu_S_new is superior is further examined by characterizing the intermediate outcomes of the evolutionary processes in these two algorithms. We find that the superiority of S_new is due to its relatively higher degree of freedom in modeling Tabu neighborhood. Second, we propose a new algorithm GA_Tabu_S_new, which empirically outperforms the state-of-the-art meta-heuristic algorithms in solving the PMFS problem. This research highlights the importance of solution representation in the application of meta-heuristic algorithm, and establishes a significant milestone in solving the PMFS problem.     

Efficient task assignment for spatial crowdsourcing: A combinatorial fractional optimization approach with semi-bandit learning

Spatial crowdsourcing has emerged as a new paradigm for solving problems in the physical world with the help of human workers. A major challenge in spatial crowdsourcing is to assign reliable workers to nearby tasks. The goal of such task assignment process is to maximize the task completion in the face of uncertainty. This process is further complicated when tasks arrivals are dynamic and worker reliability is unknown. Recent research proposals have tried to address the challenge of dynamic task assignment. Yet the majority of the proposals do not consider the dynamism of tasks and workers. They also make the unrealistic assumptions of known deterministic or probabilistic workers’ reliabilities. In this paper, we propose a novel approach for dynamic task assignment in spatial crowdsourcing. The proposed approach combines bi-objective optimization with combinatorial multi-armed bandits. We formulate an online optimization problem to maximize task reliability and minimize travel costs in spatial crowdsourcing. We propose the distance-reliability ratio (DRR) algorithm based on a combinatorial fractional programming approach. The DRR algorithm reduces travel costs by 80% while maximizing reliability when compared to existing algorithms. We extend the DRR algorithm for the scenario when worker reliabilities are unknown. We propose a novel algorithm (DRR-UCB) that uses an interval estimation heuristic to approximate worker reliabilities. Experimental results demonstrate that the DRR-UCB achieves high reliability in the face of uncertainty. The proposed approach is particularly suited for real-life dynamic spatial crowdsourcing scenarios. This approach is generalizable to the similar problems in other areas in expert systems. First, it encompasses online assignment problems when the objective function is a ratio of two linear functions. Second, it considers situations when intelligent and repeated assignment decisions are needed under uncertainty.     

Decomposition based hybrid VNS–TS algorithm for distributed parallel factories scheduling with virtual corporation

The main purpose of this paper is to develop a decomposition based hybrid variable neighborhood search/tabu search (DVT) algorithm for multi-factory production network scheduling problem where a number of different individual factories collaborate despite their different objectives. It is assumed some of the network's factories are interested in total processing cost minimization whereas the remaining factories are interested in the production profits maximization. It is also assumed that jobs can migrate from their original factory to other factories but a transportation time is incurred. Our proposed algorithm comprises of a tabu search and a variable neighborhood search with several local search algorithms. In this hybridization, to improve the search ability of the algorithm, we make use of guiding principles with ordering of neighborhood structures by mixed integer linear programming relaxation. In the proposed algorithm, the parallel search strategy is designed for a scalar bi-objective. Multiple objectives are combined with L₁-metric technique then each sub-search procedure evolves separately until a good approximation of the Pareto-front is obtained. The non-dominated sets obtained from our algorithm and original heuristic (algorithm without ordering concept) are compared using three different indices. Furthermore, the problem is modeled as a mixed integer linear programming and solved by improved ϵ-constraint approach (IEA) with CPLEX solver. The results of comparisons between IEA and DVT algorithm showed the proposed algorithm yielded most of the solutions in the net non-dominated front.     

The optimum assignments and a new heuristic approach for the traveling salesman problem

In this paper the equivalent problem approach to the n × n optimum assignment problem is exploited for providing a heuristic solution to the traveling salesman problem. It is shown that the simplified problem of finding an optimum tour using the n ? k arcs of the cycles of an n × n optimum assignment and k other arcs is NP-hard. Next by using the “nearest neighbor rule” for zero cost cycles, an O(n²) algorithm is presented for obtaining a suboptimal solution to the simplified problem. Using the notion of a path switching operation that always results in a new tour having a lower cost than the original tour, an algorithm for a systematic refinement of the suboptimal tour is given. The algorithm presented in this paper efficiently solves the problem for k = 2,3 for any n. Examples illustrating the algorithm are given, and the time complexities as well as error bounds have been studied. Further work needed in the area is indicated.     

Random walks for selected boolean implication and equivalence problems

This paper is concerned with the design and analysis of a random walk algorithm for the 2CNF implication problem (2CNFI). In 2CNFI, we are given two 2CNF formulas f₁{\phi_{1}} and f₂{\phi_{2}} and the goal is to determine whether every assignment that satisfies f₁{\phi_{1}} , also satisfies f₂{\phi_{2}} . The implication problem is clearly coNP-complete for instances of kCNF, k ≥ 3; however, it can be solved in polynomial time, when k ≤ 2. The goal of this paper is to provide a Monte Carlo algorithm for 2CNFI with a bounded probability of error. The technique developed for 2CNFI is then extended to derive a randomized, polynomial time algorithm for the problem of checking whether a given 2CNF formula Nae-implies another 2CNF formula.     

Determining the prices of remanufactured products,capacity of internal workstations and the contracting strategy within queuing framework

This paper studies a remanufacturing facility with several types of incoming nonconforming products and different independent remanufacturing workstations. The workstations have limited capacities so that an outsourcing strategy can be practiced. Each workstation is modeled with an M/M/1/k queuing system considering k as a decision variable. Additionally, a binary decision variable is taken into account to determine the contracting strategy along with some decision variables for the prices of remanufactured products. Thus, a bi-objective mixed-integer nonlinear programming is built to obtain optimal values of the decision variables. The first objective attempts to maximize the total profit and the second minimizes the average length of queuing at workstations. To solve the complex bi-objective mixed-integer nonlinear programming problem, the best out of six multi-objective decision-making (MODM) methods is selected in order to make the bi-objective optimization problem a single-objective one. Afterward, a genetic algorithm (GA) is developed to find a near-optimum solution of the single-objective problem. Besides, all of the important parameters of the algorithm are calibrated using regression analysis. To validate the results obtained, the solutions of some test problems are compared to the ones obtained by the GAMS software. The applicability of the proposed model and the solution procedure are shown with an illustrative example.     

Two-machine flowshop scheduling with bicriteria problem

This paper attempts to solve a two-machine flowshop bicriteria scheduling problem with release dates for the jobs, in which the objective function is to minimize a weighed sum of total flow time and makespan. To tackle this scheduling problem, an integer programming model with N²+3N variables and 5N constraints where N is the number of jobs, is formulated. Because of the lengthy computing time and high computing complexity of the integer programming model, a heuristic scheduling algorithm is presented. Experimental results show that the proposed heuristic algorithm can solve this problem rapidly and accurately. The average solution quality of the heuristic algorithm is above 99% and is much better than that of the SPT rule as a benchmark. A 15-job case requires only 0.018 s, on average, to obtain an ultimate or even optimal solution. The heuristic scheduling algorithm is a more practical approach to real world applications than the integer programming model.     

Minimizing the number of tardy jobs under piecewise-linear deterioration

In this paper, we consider a single machine scheduling problem with piecewise-linear deterioration where its objective is to minimize the number of tardy jobs, in which the processing time of each job depends on its starting time where all the jobs have a specific deterioration rate. The problem is known to be NP-hard; therefore a Branch and Bound algorithm and a heuristic algorithm with O(n²) are proposed. The proposed heuristic algorithm has been utilized for solving large scale problems and upper bound of the B&B algorithm. Computational experiments on 1840 problems demonstrate that the Branch and Bound procedure can solve problems with 28 jobs and 85.4% of all the sample problems optimally showing the high capability of the proposed procedure. Also it is shown that the average value of the ratio of optimal answer to the heuristic algorithm result with the objective ∑(1-_Ui)$\sum (1-U_i)$ is at last 1.08 which is more efficient in contrast to other proposed algorithms in related studies in the literature. According to high efficacy of the heuristic algorithm, large scale samples are also being solved and the results are presented. A specific form of this problem is also being considered and it is proven that the B&B procedure can handle problems with more jobs even up to 44 jobs.     

A discrete particle swarm optimization algorithm for scheduling parallel machines

As a novel evolutionary technique, particle swarm optimization (PSO) has received increasing attention and wide applications in a variety of fields. To our knowledge this paper investigates the first application of PSO algorithm to tackle the parallel machines scheduling problem. Proposing equations analogous to those of the classical PSO equations, we present a discrete PSO algorithm (DPSO) to minimize makespan (C_max) criterion. We also investigate the effectiveness of DPSO algorithm through hybridizing it with an efficient local search heuristic. To verify the performance of DPSO algorithm and its hybridized version (HDPSO), comparisons are made through using a recently proposed simulated annealing algorithm for the problem, addressed in the literature, as a comparator algorithm. Computational results signify that the proposed DPSO algorithm is very competitive and can be rapidly guided when hybridizing with a local search heuristic.     

Constant ratio fixed-parameter approximation of the edge multicut problem

The input of the Edge Multicut problem consists of an undirected graph G and pairs of terminals {s₁,t₁},…,{sm,tm}; the task is to remove a minimum set of edges such that si and ti are disconnected for every 1?i?m. The parameterized complexity of the problem, parameterized by the maximum number k of edges that are allowed to be removed, is currently open. The main result of the paper is a parameterized 2-approximation algorithm: in time f(k)⋅nO(1), we can either find a solution of size 2k or correctly conclude that there is no solution of size k.The proposed algorithm is based on a transformation of the Edge Multicut problem into a variant of the parameterized Max-2SAT problem, where the parameter is related to the number of clauses that are not satisfied. It follows from previous results that the latter problem can be 2-approximated in a fixed-parameter time; on the other hand, we show here that it is W[1]-hard. Thus the additional contribution of the present paper is introducing the first natural W[1]-hard problem that is constant-ratio fixed-parameter approximable.     

The hybrid heuristic genetic algorithm for job shop scheduling

Scheduling for the job shop is very important in both fields of production management and combinatorial optimization. However, it is quite difficult to achieve an optimal solution to this problem with traditional optimization methods owing to the high computational complexity (NP-hard). Genetic algorithms (GA) have been proved to be effective for a variety of situations, including scheduling and sequencing. Unfortunately, its efficiency is not satisfactory. In order to make GA more efficient and practical, the knowledge relevant to the problem to be solved is helpful. In this paper, a kind of hybrid heuristic GA is proposed for problem n/m/G/C_max, where the scheduling rules, such as shortest processing time (SPT) and MWKR, are integrated into the process of genetic evolution. In addition, the neighborhood search technique (NST) is adopted as an auxiliary procedure to improve the solution performance. The new algorithm is proved to be effective and efficient by comparing it with some popular methods, i.e. the heuristic of neighborhood search, simulated annealing (SA), and traditional GA.     

A heuristic partitioning algorithm for a packaging problem

A heuristic algorithm for solving a problem of a minimum-cost packaging ofN items of the magnitudea _j intoM boxes of the capacityb _i with a costc _ij being assigned to the itemj packing into the boxi is presented. The principal idea of the algorithm consists in the preliminary partitioning of the problem into smaller subproblems and getting an approximate solution by solving these subproblems. A motivation of the heuristic and an application of the algorithm are given.     

Optimizing a bi-objective multi-product EPQ model with defective items,rework and limited orders: NSGA-II and MOPSO algorithms

In this paper, a bi-objective multi-products economic production quantity (EPQ) model is developed, in which the number of orders is limited and imperfect items that are re-workable are produced. The objectives of the problem are minimization of the total inventory costs as well as minimizing the required warehouse space. The model is shown to be of a bi-objective nonlinear programming type, and in order to solve it two meta-heuristic algorithms namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-objective particle swarm optimization (MOPSO) algorithm, are proposed. To verify the solution obtained and to evaluate the performance of proposed algorithms, two-sample t-tests are employed to compare the means of the first objective value, the means of the second objective values, and the mean required CPU time of solving the problem using two algorithms. The results show while both algorithms are efficient to solve the model and the solution qualities of the two algorithms do not differ significantly, the computational CPU time of MOPSO is considerably lower than that of NSGA-II.     

Minimum Congestion Redundant Assignments to Tolerate Random Faults

We consider the problem of computing minimum congestion, fault-tolerant, redundant assignments of messages to faulty, parallel delivery channels. In particular, we are given a set Kof faulty channels, each having an integer capacity c _i and failing independently with probability f _i . We are also given a set Mof messages to be delivered over K , and a fault-tolerance constraint (1-?) , and we seek a redundant assignment ?that minimizes congestion \lilsf Cong(?) , i.e. the maximum channel load, subject to the constraint that, with probability no less than (1-?) , all the messages have a copy on at least one active channel. We present a polynomial-time 4-approximation algorithm for identical capacity channels and arbitrary message sizes, and a 2 \lceil\ln(|K|/\e)/\ln(1/f _max ) \rceil -approximation algorithm for related capacity channels and unit size messages. Both algorithms are based on computing a collection {K ₁ , \ldots, K _ν }of disjoint channel subsets such that, with probability no less than (1-?) , at least one channel is active in each subset. The objective is to maximize the sum of the minimum subset capacities. Since the exact version of this problem is NP -complete, we provide a 2-approximation algorithm for identical capacities, and a polynomial-time (8+ \rm o (1)) -approximation algorithm for arbitrary capacities.     

A fuzzy multi-criteria decision making approach for solving a bi-objective personnel assignment problem

Effective personnel assignment is one of the most crucial tasks performed by the decision makers of a company. This paper proposes a systematic approach with a feedback mechanism in which the interdependences among positions and the differences among the selected employees are considered simultaneously. Unfortunately, the two combined considerations have rarely been discussed in the literature. The purpose of this approach is to obtain the best matching of candidates and positions in order to organize a collaboratively cross-functional team. In a fuzzy environment and, then, in the proposed approach, a bi-objective binary integer programming (BOBIP) model is formulated. Based on the weighted composite scores determined in the third step of the proposed procedure, the BOBIP model is transformed into a fuzzy bi-objective goal programming (FBOGP) model. An elaborately designed heuristic algorithm is developed to determine the appropriate values of several important parameters in the FBOGP model, which is solved using LINDO 8.0. An application example is illustrated, and two additional examples are tested. The results indicate that the proposed approach achieves the acceptable satisfaction level and requires less computation time than the brute force enumerative method.     

Applying the improved Chen and Han’s algorithm to different versions of shortest path problems on a polyhedral surface

The computation of shortest paths on a polyhedral surface is a common operation in many computer graphics applications. There are two best known exact algorithms for the “single source, any destination” shortest path problem. One is proposed by Mitchell et al. (1987) [1]. The other is by Chen and Han (1990) [11]. Recently, Xin and Wang (2009) [9] improved the CH algorithm by exploiting a filtering theorem and achieved a practical method that outperforms both the CH algorithm and the MMP algorithm whether in time or in space.In this paper, we apply the improved CH algorithm to different versions of shortest path problems. The contributions of this paper include: (1) For a surface point p∈△v₁v₂v₃, we present an unfolding technique for estimating the distance value at p using the distances at v₁,v₂ and v₃. (2) We show that the improved CH algorithm can be naturally extended to the “multiple sources, any destination” version. Also, introducing a well-chosen heuristic factor into the improved CH algorithm will induce an exact solution to the “single source, single destination” version. (3) At the conclusion of multi-source shortest path algorithms, we can use the distance values at vertices to approximately compute the geodesic-distance-based offsets, the Voronoi diagram and the Delaunay triangulation in O(n) time. (4) By importing a precision parameter λ, we obtain a precision controlled approximant which varies from the improved CH algorithm to Dijkstra’s algorithm as λ increases from 0 to 1. Thus, an interesting relationship between them can be naturally established.     

A variable neighborhood search approach for planning and scheduling of jobs on unrelated parallel machines

In this paper, we study a planning and scheduling problem for unrelated parallel machines. There are n jobs that have to be assigned and sequenced on m unrelated parallel machines. Each job has a weight that represents the priority of the corresponding customer order, a given due date, and a release date. An Automated Guided Vehicle is used to transport at maximum Load _max jobs into a storage space in front of the machines in a given period of time. We consider t _max consecutive periods. We are interested in minimizing the total weighted tardiness of the jobs across the periods. This measure is important when we are interested in a good on-time delivery performance. We present an appropriate mixed integer program. To solve this NP-hard problem, we develop a heuristic methodology based on decomposition and variable neighborhood search (VNS). The proposed approaches are assessed using randomly generated problem instances. We compare them with a simple heuristic based on decomposition and list scheduling using the Apparent Tardiness Cost dispatching rule. The results demonstrate that the heuristic approach based on VNS performs comparably to the mixed integer program while having reasonable solution times and outperforms the simple heuristic and a genetic algorithm (GA) from previous research.     

基于禁忌搜索算法求解随机约束满足问题

为了求解具有增长取值域的随机约束满足问题（CSP）,提出了一种基于禁忌搜索并与模拟退火相结合的算法。首先,利用禁忌搜索得到一组启发式的初始赋值,即由一个随机初始化的可行解通过邻域构造一组候选解,再利用禁忌表使候选解向最小化目标函数值的方向移动;如果得到的最优赋值不是问题的解,就把它作为启发式的初始赋值,再执行模拟退火对这组赋值进行修正直到得到全局最优解。数值实验结果表明,所提算法在接近问题的理论相变阈值时仍然能有效地找到问题的解,与其他局部搜索算法相比,表现出了显著的优越性,可用于随机CSP的算法设计。     

Class imbalance learning via a fuzzy total margin based support vector machine

The classification of imbalanced data is a major challenge for machine learning. In this paper, we presented a fuzzy total margin based support vector machine (FTM-SVM) method to handle the class imbalance learning (CIL) problem in the presence of outliers and noise. The proposed method incorporates total margin algorithm, different cost functions and the proper approach of fuzzification of the penalty into FTM-SVM and formulates them in nonlinear case. We considered an excellent type of fuzzy membership functions to assign fuzzy membership values and got six FTM-SVM settings. We evaluated the proposed FTM-SVM method on two artificial data sets and 16 real-world imbalanced data sets. Experimental results show that the proposed FTM-SVM method has higher G_Mean and F_Measure values than some existing CIL methods. Based on the overall results, we can conclude that the proposed FTM-SVM method is effective for CIL problem, especially in the presence of outliers and noise in data sets.