23 research outputs found
Cutting-Plane Separation Strategies for Semidefinite Programming Models to Solve Single-Row Facility Layout Problems
The single-row facility layout problem (SRFLP) is concerned with finding the optimal linear placement of n departments with different lengths in a straight line. It is typically achieved by minimizing the cost associated with the interactions between the departments. The semidefinite programming (SDP) relaxation model that incorporates cutting planes proposed recently by Anjos, Kennings, and Vannelli (AKV) was considered a breakthrough in the field. This thesis presents a new SDP model AKV' and compares the two relaxations. The AKV' is largely based on the previous model, but it reduces the number of linear constraints from O(n³) to O(n²). Therefore, it reduces the computing time at the expense of a slightly weaker lower bound. However, AKV' is observed to pay off as the instance size increases. By examining the gap for both the AKV and AKV' relaxations, we notice that both relaxations generate very small gaps at the root node, which demonstrates the effectiveness of the relaxations.
Six different strategies are presented to separate the cutting planes for the medium-sized SRFLP. In combination with the two SDP relaxations, we compare the six strategies using three instances of different characteristics. An overall best strategy is deduced from the computational results, but the best choice of relaxations and the best number of cuts added at each iteration changes depending on the characteristics of the instances. Two new cutting plane strategies are proposed for large instances. This allows the solution to optimality of new instances with 36 departments, which is higher than previously published results in literature. We also briefly point out how the computing time can vary greatly between different sets of data of the same size due to the characteristics of the department lengths
Recommended from our members
The role of chemotherapy and radiotherapy in localized extraskeletal osteosarcoma.
PURPOSE: The role of chemotherapy (CT) and radiotherapy (RT) for management of extraskeletal osteosarcoma (ESOS) remains controversial. We examined disease outcomes for ESOS patients and investigated the association between CT/RT with recurrence and survival. PATIENTS AND METHODS: Retrospective review at 25 international sarcoma centers identified patients ≥18 years old treated for ESOS from 1971 to 2016. Patient/tumour characteristics, treatment, local/systemic recurrence, and survival data were collected. Kaplan-Meier survival and Cox proportional-hazards regression and cumulative incidence competing risks analysis were performed. RESULTS: 370 patients with localized ESOS treated definitively with surgery presented with mainly deep tumours (n = 294, 80%). 122 patients underwent surgical resection alone, 96 (26%) also received CT, 70 (19%) RT and 82 (22%) both adjuvants. Five-year survival for patients with localized ESOS was 56% (95% CI 51%-62%). Almost half of patients (n = 173, 47%) developed recurrence: local 9% (35/370), distant 28% (102/370) or both 10% (36/370). Considering death as a competing event, there was no significant difference in cumulative incidence of local or systemic recurrence between patients who received CT, RT, both or neither (local p = 0.50, systemic p = 0.69). Multiple regression Cox analysis showed a significant association between RT and decreased local recurrence (HR 0.46 [95% CI 0.26-0.80], p = 0.01). CONCLUSION: Although the use of RT significantly decreased local recurrences, CT did not decrease the risk of systemic recurrence, and neither CT, nor RT nor both were associated with improved survival in patients with localized ESOS. Our results do not support the use of CT; however, adjuvant RT demonstrates benefit in patients with locally resectable ESOS
Recommended from our members
The role of chemotherapy and radiotherapy in localized extraskeletal osteosarcoma.
PurposeThe role of chemotherapy (CT) and radiotherapy (RT) for management of extraskeletal osteosarcoma (ESOS) remains controversial. We examined disease outcomes for ESOS patients and investigated the association between CT/RT with recurrence and survival.Patients and methodsRetrospective review at 25 international sarcoma centers identified patients ≥18 years old treated for ESOS from 1971 to 2016. Patient/tumour characteristics, treatment, local/systemic recurrence, and survival data were collected. Kaplan-Meier survival and Cox proportional-hazards regression and cumulative incidence competing risks analysis were performed.Results370 patients with localized ESOS treated definitively with surgery presented with mainly deep tumours (n = 294, 80%). 122 patients underwent surgical resection alone, 96 (26%) also received CT, 70 (19%) RT and 82 (22%) both adjuvants. Five-year survival for patients with localized ESOS was 56% (95% CI 51%-62%). Almost half of patients (n = 173, 47%) developed recurrence: local 9% (35/370), distant 28% (102/370) or both 10% (36/370). Considering death as a competing event, there was no significant difference in cumulative incidence of local or systemic recurrence between patients who received CT, RT, both or neither (local p = 0.50, systemic p = 0.69). Multiple regression Cox analysis showed a significant association between RT and decreased local recurrence (HR 0.46 [95% CI 0.26-0.80], p = 0.01).ConclusionAlthough the use of RT significantly decreased local recurrences, CT did not decrease the risk of systemic recurrence, and neither CT, nor RT nor both were associated with improved survival in patients with localized ESOS. Our results do not support the use of CT; however, adjuvant RT demonstrates benefit in patients with locally resectable ESOS