Breakout local search for the Steiner tree problem with revenue, budget and hop constraints

The Steiner tree problem (STP) is one of the most popular combinatorial optimization problems with various practical applications. In this paper, we propose a Breakout Local Search (BLS) algorithm for an important generalization of the STP: the Steiner tree problem with revenue, budget and hop constraints (STPRBH), which consists of determining a subtree of a given undirected graph which maximizes the collected revenues, subject to both budget and hop constraints. Starting from a probabilistically constructed initial solution, BLS uses a Neighborhood Search (NS) procedure based on several specifically designed move operators for local optimization, and employs an adaptive diversification strategy to escape from local optima. The diversification mechanism is implemented by adaptive perturbations, guided by dedicated information of discovered high-quality solutions. Computational results based on 240 benchmarks show that BLS produces competitive results with respect to several previous approaches. For the 56 most challenging instances with unknown optimal results, BLS succeeds in improving 49 and matching one best known results within reasonable time. For the 184 instances which have been solved to optimality, BLS can also match 167 optimal results

Dynamic programming driven memetic search for the Steiner tree problem with revenues, budget and hop constraints

We present a highly effective dynamic programming driven memetic algorithm for the Steiner tree problem with revenues, budget, and hop constraints (STPRBH), which aims at determining a subtree of an undirected graph, so as to maximize the collected revenue, subject to both budget and hop constraints. The main features of the proposed algorithm include a probabilistic constructive procedure to generate initial solutions, a neighborhood search procedure using dynamic programming to significantly speed up neighborhood exploration, a backbone-based crossover operator to generate offspring solutions, as well as a quality-and-distance updating strategy to manage the population. Computational results based on four groups of 384 well-known benchmarks demonstrate the value of the proposed algorithm, compared to the state of the art approaches. In particular, for the 56 most challenging instances with unknown optima, our algorithm succeeds in providing 45 improved best known solutions within a short computing time. We additionally provide results for a group of 30 challenging instances that are introduced in the paper. We provide a complexity analysis of the proposed algorithm and study the impact of some ingredients on the performance of the algorithm

Knowledge-guided local search for the prize-collecting Steiner tree problem in graphs

The prize-collecting Steiner tree problem in graphs (PCSPG), as well as its rooted variant (RPCST), are target problems of the 11th DIMACS (the Center for Discrete Mathematics and Theoretical Computer Science) Implementation Challenge held in collaboration with ICERM (the Institute for Computational and Experimental Research in Mathematics). To solve these two problems, this paper proposes a knowledge-guided local search algorithm (K-ILS), 1 which integrates dedicated search strategies and explores structure information of problem instances. K-ILS uses an effective swap-vertex operator for tree transformation associated with a discriminating auxiliary evaluation function as well as several knowledge-guided perturbation strategies. K-ILS additionally employs two new path-based move operators to generate neighboring solutions. The computational results achieved on the benchmark instances of the 11th DIMACS Implementation Challenge using the same computing platform and competition rules demonstrate that K-ILS performs very well compared to the leading algorithms of the challenge. We report additional experiments to analyze the impact of the key components to the performance of the proposed algorithm

Swap-vertex based neighborhood for Steiner tree problems

Steiner tree problems (STPs) are very important in both theory and practice. In this paper, we introduce a powerful swap-vertex move operator which can be used as a basic element of any neighborhood search heuristic to solve many STP variants. Given the incumbent solution tree T, the swap-vertex move operator exchanges a vertex in T with another vertex out of T, and then attempts to construct a minimum spanning tree, leading to a neighboring solution (if feasible). We develop a series of dynamic data structures, which allow us to efficiently evaluate the feasibility of swap-vertex moves. Additionally, in order to discriminate different swap-vertex moves corresponding to the same objective value, we also develop an auxiliary evaluation function. We present a computational assessment based on a number of challenging problem instances (corresponding to three representative STP variants) which clearly shows the effectiveness of the techniques introduced in this paper. Particularly, as a key element of our KTS algorithm which participated in the 11th DIMACS implementation challenge, the swap-vertex operator as well as the auxiliary evaluation function contributed significantly to the excellent performance of our algorithm

Reoperation rates following intramedullary nailing versus external fixation of Gustilo Type 3A open tibia shaft fractures

Background: Open tibia fractures are among the most difficult to manage due to the lack of soft tissue coverage and poor blood supply. This is especially true in developing settings primarily due to a lack of resources. Both locked Intramedullary Nailing (IM) and External Fixation (EF) are two possible modalities for surgical treatment of open tibia fractures. However, it is unknown at this time which one is most suitable in low resource regions especially with regards to the risk of serious complications requiring reoperation. This study was conducted to identify which method is safest and minimizes this risk in patients with open tibia fractures.Methodology: A prospective cohort study of Gustilo 3A open tibia shaft factures treated either by intramedullary nailing or external fixation was conducted from March 2013 to February 2014 at Muhimbili Orthopaedic Institute (Dar es Salaam, Tanzania). Follow-up was conducted at 2, 6 10, 14, and 18 weeks postoperatively. The primary outcome assessed was all-cause reoperation.Results: Fifty patients were enrolled and completed follow-up at all-time points; twenty-six were treated with IM nail and twenty-four were treated by EF. There were 9 (37.5%) EF patients who required reoperation compared to 1(3.8%) IM nail patient (p=0.004). Reasons for reoperation among EF patients were infection (2 patients), malalignment (3 patients), and delayed union (4 patients). The one IM nail patient presented with signs of infection and wound dehiscence at 14 weeks postoperatively. No patients presented with hardware failure or malrotation.Conclusion: Treatment of Gustilo Type 3A open tibia shaft fractures with interlocking intramedullary nailing results in lower reoperation rate in the early stages of treatment compared to uniplanar external fixation.Keywords: Orthopaedic surgery, Tanzania, Intramedullary nail, External fixation, Open tibia fractur

Characterization of an expressed Triticum monococcum Glu-A1y gene containing a premature termination codon in its C-terminal coding region

Premature termination codons (PTCs) are an important reason for the silence of highmolecular- weight glutenin subunits in Triticum species. Although the Glu-A1y gene is generally silent in common wheat, we here isolated an expressed Glu-A1y gene containing a PTC, named 1Ay8.3, from Triticum monococcum ssp. monococcum (AmAm, 2n = 2x = 14). Despite the presence of a PTC (TAG) at base pair positions 1879–1881 in the C-terminal coding region, this did not obviously affect 1Ay8.3 expression in seeds. This was demonstrated by the fact that when the PTC TAG of 1Ay8.3 was mutated to the CAG codon, the mutant in Escherichia coli bacterial cells expressed the same subunit as in the seeds. However, in E. coli, 1Ay8.3 containing the PTC expressed a truncated protein with faster electrophoretic mobility than that in seeds, suggesting that PTC translation termination suppression probably occurs in vivo (seeds) but not in vitro (E. coli). This may represent one of only a few reports on the PTC termination suppression phenomenon in genes