Improved formulations and branch-and-cut algorithms for the angular constrained minimum spanning tree problem

Journal of Combinatorial Optimization - The Angular Constrained Minimum Spanning Tree Problem ( $$\alpha $$ -MSTP) is defined in terms of a complete undirected graph $$G=(V,E)$$ and an angle...     

Distance constrained vehicle routing problem to minimize the total cost: algorithms and complexity

Journal of Combinatorial Optimization - Given $$\lambda >0$$ , an undirected complete graph $$G=(V,E)$$ with nonnegative edge-weight function obeying the triangle inequality and a depot...     

Priority algorithms for the subset-sum problem

Greedy algorithms are simple, but their relative power is not well understood. The priority framework (Borodin et al. in Algorithmica 37:295–326, 2003) captures a key notion of “greediness” in the sense that it processes (in some locally optimal manner) one data item at a time, depending on and only on the current knowledge of the input. This algorithmic model provides a tool to assess the computational power and limitations of greedy algorithms, especially in terms of their approximability. In this paper, we study priority algorithm approximation ratios for the Subset-Sum Problem, focusing on the power of revocable decisions, for which the accepted data items can be later rejected to maintain the feasibility of the solution. We first provide a tight bound of α≈0.657 for irrevocable priority algorithms. We then show that the approximation ratio of fixed order revocable priority algorithms is between β≈0.780 and γ≈0.852, and the ratio of adaptive order revocable priority algorithms is between 0.8 and δ≈0.893. A preliminary version of this paper appeared in the Proceedings of COCOON 2007, LNCS 4598, pp. 504–514.     

Combinatorial algorithms for the maximum k-plex problem

The maximum clique problem provides a classic framework for detecting cohesive subgraphs. However, this approach can fail to detect much of the cohesive structure in a graph. To address this issue, Seidman and Foster introduced k-plexes as a degree-based clique relaxation. More recently, Balasundaram et al. formulated the maximum k-plex problem as an integer program and designed a branch-and-cut algorithm. This paper derives a new upper bound on the cardinality of k-plexes and adapts combinatorial clique algorithms to find maximum k-plexes.     

Approximation algorithms for the bus evacuation problem

We consider the bus evacuation problem. Given a positive integer B, a bipartite graph G with parts S and \(T \cup \{r\}\) in a metric space and functions \(l_i :S \rightarrow {\mathbb {Z}}_+\) and \({u_j :T \rightarrow \mathbb {Z}_+ \cup \{\infty \}}\), one wishes to find a set of B walks in G. Every walk in B should start at r and finish in T and r must be visited only once. Also, among all walks, each vertex i of S must be visited at least \(l_i\) times and each vertex j of T must be visited at most \(u_j\) times. The objective is to find a solution that minimizes the length of the longest walk. This problem arises in emergency planning situations where the walks correspond to the routes of B buses that must transport each group of people in S to a shelter in T, and the objective is to evacuate the entire population in the minimum amount of time. In this paper, we prove that approximating this problem by less than a constant is \(\text{ NP }\)-hard and present a 10.2-approximation algorithm. Further, for the uncapacitated BEP, in which \(u_j\) is infinity for each j, we give a 4.2-approximation algorithm.     

Target-guided algorithms for the container pre-marshalling problem

The container pre-marshalling problem (CPMP) aims to rearrange containers in a bay with the least movement effort; thus, in the final layout, containers are piled according to a predetermined order. Previous researchers, without exception, assumed that all the stacks in a bay are functionally identical. Such a classical problem setting is reexamined in this paper. Moreover, a new problem, the CPMP with a dummy stack (CPMPDS) is proposed. At terminals with transfer lanes, a bay includes a row of ordinary stacks and a dummy stack. The dummy stack is actually the bay space that is reserved for trucks. Therefore, containers can be shipped out from the bay. During the pre-marshalling process, the dummy stack temporarily stores containers as an ordinary stack. However, the dummy stack must be emptied at the end of pre-marshalling. In this paper, target-guided algorithms are proposed to handle both the classical CPMP and new CPMPDS. All the proposed algorithms guarantee termination. Experimental results in terms of the CPMP show that the proposed algorithms surpass the state-of-the-art algorithm.     

Optimal algorithms for uncovering synteny problem

The syntenic distance between two genomes is the minimum number of fusions, fissions, and translocations that can transform one genome to the other, ignoring the gene order within chromosomes. As the problem is NP-hard in general, some particular classes of synteny instances, such as linear synteny, exact synteny and nested synteny, are examined in the literature. In this paper, we propose a new special class of synteny instances, called uncovering synteny. We first present a polynomial time algorithm to solve the connected case of uncovering synteny optimally. By performing only intra-component moves, we then solve the unconnected case of uncovering synteny. We will further calculate the diameters of connected and unconnected uncovering synteny, respectively.     

Genetic algorithms with path relinking for the minimum tardiness permutation flowshop problem

In this work three genetic algorithms are presented for the permutation flowshop scheduling problem with total tardiness minimisation criterion. The algorithms include advanced techniques like path relinking, local search and a procedure to control the diversity of the population. We also include a speed up procedure in order to reduce the computational effort needed for the local search technique, which results in large CPU time savings. A complete calibration of the different parameters and operators of the proposed algorithms by means of a design of experiments approach is also given. We carry out a comparative evaluation with the best methods that can be found in the literature for the total tardiness objective, and with adaptations of other state-of-the-art methods originally proposed for other objectives, mainly makespan. All the methods have been implemented with and without the speed up procedure in order to test its effect. The results show that the proposed algorithms are very effective, outperforming the remaining methods of the comparison by a considerable margin.     

Efficient algorithms for shared backup allocation in networks with partial information

We study efficient algorithms for establishing reliable connections with bandwidth guarantees in communication networks. In the normal mode of operation, each connection uses a primary path to deliver packets from the source to the destination. To ensure continuous operation in the event of an edge failure, each connection uses a set of backup bridges, each bridge protecting a portion of the primary path. To meet the bandwidth requirement of the connection, a certain amount of bandwidth must be allocated the edges of the primary path, as well as on the backup edges. In this paper, we focus on minimizing the amount of required backup allocation by sharing backup bandwidth among different connections. We consider efficient sharing schemes that require only partial information about the current state of the network. Specifically, the only information available for each edge is the total amount of primary allocation and the cost of allocating backup bandwidth on this edge. We consider the problem of finding a minimum cost backup allocation together with a set of bridges for a given primary path. We prove that this problem is NP-hard and present an approximation algorithm whose performance is within of the optimum, where n is the number of edges in the primary path. We also consider the problem of finding both a primary path and backup allocation of minimal total cost. A preliminary version of this paper appears in the Proceedings of 13th Annual European Symposium on Algorithms - ESA 2005, Mallorca, Spain. J. (Seffi) Naor: This research is supported in part by a foundational and strategical research grant from the Israeli Ministry of Science, and by a US-Israel BSF Grant 2002276.     

Exact and approximate algorithms for the loop layout problem

Control parameters, such as order frequency, safety stock and safety time, are important tools to improve the logistic performance in material planning. In practice, the adjustment of control parameters appears to be very difficult. One of the reasons is the lack of relevant tactical control information: a simple, periodical and per-commodity integrated feedback of performance and process information often is not available to the logistic operator. Therefore, the material planner is offered a fairly limited overview and insight of the processes to be controlled. This problem has been investigated in several plants in the Netherlands. A solution to this problem is first to measure the performance, the frequency of process disturbances and the effect of the parameters on performance for all commodities involved. And second, to integrate this information and provide feedback to the responsible material planner. In this article a design for decision support is presented to integrate and give feedback of relevant tactical control information. Prototype information systems are now being tested in practice and in the laboratory. The expectation is that this type of decision support will help the operator to make more systematic and effective diagnoses.     

Greedy algorithms for the profit-aware social team formation problem

Motivated by applications in online labor markets, we study the problem of forming multiple teams of experts in a social network to accomplish multiple tasks that require different combinations of skills. Our goal is to maximize the total profit of tasks that are completed by these teams subject to the capacity constraints of the experts. We study both the offline and online settings of the problem. For the offline problem, we present a simple and practical algorithm that improves upon previous results in many situations. For the online problem, we design competitive deterministic and randomized online algorithms. These are complemented by some hardness results in both settings.

     

Combinatorial approximation algorithms for the submodular multicut problem in trees with submodular penalties

Journal of Combinatorial Optimization - In this paper, we introduce the submodular multicut problem in trees with submodular penalties, which generalizes the prize-collecting multicut problem in...     

具有最大总加权满意度的单机调度问题的dynasearch算法

研究了总加权满意程度最大化的单机调度问题.对最优解的性质进行分析和证明,提出该类问题的统治规则.提出该问题新的基于dynasearch 邻域的迭代局域搜索算法(ILS).算法主要特点:1)dynasearch 是基于多摄动的思想,即一次可以做多个相互独立的交换(或插入);2)用动态规划获得最优dynasearch移动;3)ILS采用随机kick 策略对局部最优解进行摄动,然后继续迭代.实现了该问题的两种dynaearch算法;把两种dynasearch算法与统治规则相结合;在进行kick时引入误差限制.实验表明:嵌入统治规则的算法优于没有统治规则的算法;基于dynasearch交换的ILS 优于基于dynasearch插入的ILS;dynaearch算法要优于以交换为邻域的多初始点改进算法.     

Efficient approximation algorithms for computing <Emphasis Type="Italic">k</Emphasis> disjoint constrained shortest paths

Let \(G=(V,\, E)\) be a given directed graph in which every edge e is associated with two nonnegative costs: a weight w(e) and a length l(e). For a pair of specified distinct vertices \(s,\, t\in V\), the k-(edge) disjoint constrained shortest path (kCSP) problem is to compute k (edge) disjoint paths between s and t, such that the total length of the paths is minimized and the weight is bounded by a given weight budget \(W\in \mathbb {R}_{0}^{+}\). The problem is known to be \({\mathcal {NP}}\)-hard, even when \(k=1\) (Garey and Johnson in Computers and intractability, 1979). Approximation algorithms with bifactor ratio \(\left( 1\,+\,\frac{1}{r},\, r\left( 1\,+\,\frac{2(\log r\,+\,1)}{r}\right) (1\,+\,\epsilon )\right) \) and \((1\,+\,\frac{1}{r},\,1\,+\,r)\) have been developed for \(k=2\) in Orda and Sprintson (IEEE INFOCOM, pp. 727–738, 2004) and Chao and Hong (IEICE Trans Inf Syst 90(2):465–472, 2007), respectively. For general k, an approximation algorithm with ratio \((1,\, O(\ln n))\) has been developed for a weaker version of kCSP, the k bi-constraint path problem which is to compute k disjoint st-paths satisfying a given length constraint and a weight constraint simultaneously (Guo et al. in COCOON, pp. 325–336, 2013). This paper first gives an approximation algorithm with bifactor ratio \((2,\,2)\) for kCSP using the LP-rounding technique. The algorithm is then improved by adopting a more sophisticated method to round edges. It is shown that for any solution output by the improved algorithm, there exists a real number \(0\le \alpha \le 2\) such that the weight and the length of the solution are bounded by \(\alpha \) times and \(2-\alpha \) times of that of an optimum solution, respectively. The key observation of the ratio proof is to show that the fractional edges, in a basic solution against the proposed linear relaxation of kCSP, exactly compose a graph in which the degree of every vertex is exactly two. At last, by a novel enhancement of the technique in Guo et al. (COCOON, pp. 325–336, 2013), the approximation ratio is further improved to \((1,\,\ln n)\).     

A heuristic for the time constrained asymmetric linear sum assignment problem

The linear sum assignment problem is a fundamental combinatorial optimisation problem and can be broadly defined as: given an \(n \times m, m \ge n\) benefit matrix \(B = (b_{ij})\), matching each row to a different column so that the sum of entries at the row-column intersections is maximised. This paper describes the application of a new fast heuristic algorithm, Asymmetric Greedy Search, to the asymmetric version (\(n \ne m\)) of the linear sum assignment problem. Extensive computational experiments, using a range of model graphs demonstrate the effectiveness of the algorithm. The heuristic was also incorporated within an algorithm for the non-sequential protein structure matching problem where non-sequential alignment between two proteins, normally of different numbers of amino acids, needs to be maximised.     

Decomposition algorithms for the integrated process planning and scheduling problem

There are several algorithms to solve the integrated process planning and scheduling (IPPS) problem (i.e., flexible job shop scheduling with process plan flexibility) in the literature. All the existing algorithms for IPPS are heuristic-based search methods and no research has investigated the use of exact solution methods for this problem. We develop several decomposition approaches based on the logic-based Benders decomposition (LBBD) algorithm. Our LBBD algorithm allows us to partition the decision variables in the IPPS problem into two models, master-problem and sub-problem. The master-problem determines process plan and operation-machine assignment, while the sub-problem optimizes sequencing and scheduling decisions. To achieve faster convergence, we develop two relaxations for the optimal makespan objective function and incorporate them into the master-problem. We analyze the performance and further enhance the algorithm with two ideas, a Benders optimality cut based on the critical path and a faster heuristic way to solve the sub-problem. 16 standard benchmark instances available in the literature are solved to evaluate and compare the performances of our algorithms with those of the state-of-the-art methods in the literature. The proposed algorithm either results in the optimal solution or improves the best-known solutions in all the existing instances, demonstrating its superiority to the existing state-of-the-art methods in literature.     

Polynomial-time approximation algorithms for the coloring problem in some cases

We consider the coloring problem for hereditary graph classes, i.e. classes of simple unlabeled graphs closed under deletion of vertices. For the family of the hereditary classes of graphs defined by forbidden induced subgraphs with at most four vertices, there are three classes with an open complexity of the problem. For the problem and the open three cases, we present approximation polynomial-time algorithms with performance guarantees.     

Approximation algorithms for the maximally balanced connected graph tripartition problem

Journal of Combinatorial Optimization - Given a vertex-weighted connected graph $$G = (V, E, w(\cdot ))$$ , the maximally balanced connected graph k-partition (k-BGP) seeks to partition the vertex...