On the Effectiveness of Sequential Linear Programming for the Pooling Problem

The aim of this paper is to compare the performance of a local solution technique -- namely Sequential Linear Programming (SLP) employing random starting points -- with state-of-the-art global solvers such as Baron and more sophisticated local solvers such as Sequential Quadratic Programming and Interior Point for the pooling problem. These problems can have many local optima, and we present a small example that illustrates how this can occur. We demonstrate that SLP -- usually deemed obsolete since the arrival of fast reliable QP solvers, Interior Point Methods and sophisticated global solvers -- is still the method of choice for an important class of pooling problem when the criterion is the quality of the solution found within a given acceptable time budget. In addition we introduce a new formulation, the qq-formulation, for the case of fixed demands, that exclusively uses proportional variables. We compare the performance of SLP and the global solver Baron on the qq-formulation and other common formulations. While Baron with the qq-formulation generates weaker bounds than with the other formulations tested, for both SLP and Baron the qq-formulation finds the best solutions within a given time budget. The qq-formulation can be strengthened by pq-like cuts in which case the same bounds as for the pq-formulation are obtained. However the associated time penalty due to the additional constraints results in poorer solution quality within the time budget

A New Unblocking Technique to Warmstart Interior Point Methods Based on Sensitivity Analysis

One of the main drawbacks associated with Interior Point Methods (IPM) is the perceived lack of an efficient warmstarting scheme which would enable the use of information from a previous solution of a similar problem. Recently there has been renewed interest in the subject. A common problem with warmstarting for IPM is that an advanced starting point which is close to the boundary of the feasible region, as is typical, might lead to blocking of the search direction. Several techniques have been proposed to address this issue. Most of these aim to lead the iterate back into the interior of the feasible region- we classify them as either “modification steps” or “unblocking steps ” depending on whether the modification is taking place before solving the modified problem to prevent future problems, or during the solution if and when problems become apparent. A new “unblocking” strategy is suggested which attempts to directly address the issue of blocking by performing sensitivity analysis on the Newton step with the aim of increasing the size of the step that can be taken. This analysis is used in a new technique to warmstar

Approximate dynamic programming with B�zier Curves/Surfaces for Top-percentile Traffic Routing

Multi-homing is used by Internet Service Providers (ISPs) to connect to the Internet via different network providers. This study develops a routing strategy under multi-homing in the case where network providers charge ISPs according to top-percentile pricing (i.e. based on the ?th highest volume of traffic shipped). We call this problem the Top-percentile Traffic Routing Problem (TpTRP). Solution approaches based on Stochastic Dynamic Programming require discretization in state space, which introduces a large number of state variables. This is known as the curse of dimensionality in state space. To overcome this, in previous work we have suggested to use approximate dynamic programming (ADP) to construct value function approximations, which allow us to work in continuous state space. The resulting ADP model provides well performing routing policies for medium sized instances of the TpTRP. In this work we extend the ADP model, by using B�zier Curves/Surfaces to obtain continuous-time approximations of the time-dependent ADP parameters. This modification reduces the number of regression parameters to estimate, and thus accelerates the efficiency of parameter training in the solution of the ADP model, which makes realistically sized TpTRP instances tractable. We argue that our routing strategy is near optimal by giving bounds

Top-percentile traffic routing problem by dynamic programming

Multi-homing is a technology used by Internet Service Provider (ISP) to connect to the Internet via different network providers. To make full use of the underlying networks with minimum cost, an optimal routing strategy is required by ISPs. This study investigates the optimal routing strategy in case where network providers charge ISPs according to top-percentile pricing. We call this problem the Top-percentile Traffic Routing Problem (TpTRP). The TpTRP is a multistage stochastic optimisation problem in which routing decision should be made before knowing the amount of traffic that is to be routed in the following time period. The stochastic nature of the problem forms the critical difficulty of this study. In this paper several approaches are investigated in modelling and solving the problem. We begin by modelling the TpTRP as a multi-stage stochastic programming problem, which is hard to solve due to the integer variables introduced by top-percentile pricing. Several simplifications of the original TpTRP are then explored in the second part of this work. Some of these allow analytical solutions which lead to bounds on the achievable optimal solution. We also establish bounds by investigation several "naive" routing policies. In the end, we explore the solution of the TpTRP as a stochastic dynamic programming problem by a discretization of the state space. This SDP model gives us achievable routing policies on medium size instances of TpTRP, which of course improve the naive routing policies. With a classification of the SDP decision table, a crude routing policy for realistic size instances can be developed from the smaller size SDP model. © 2011 Springer Science+Business Media, LLC

Association of baseline absolute neutrophil counts and survival in patients with metastatic colorectal cancer treated with second-line antiangiogenic therapies : exploratory analyses of the RAISE trial and validation in an electronic medical record data set

In the RAISE trial, ramucirumab+leucovorin/fluorouracil/irinotecan (FOLFIRI) improved the median overall survival (mOS) of patients with previously treated metastatic colorectal cancer versus patients treated with placebo+FOLFIRI but had a higher incidence of neutropaenia, leading to more chemotherapy dose modifications and discontinuations. Thus, we conducted an exploratory post-hoc analysis of RAISE and a retrospective, observational analysis of electronic medical record (EMR) data to determine and verify the association of neutropaenia, baseline absolute neutrophil count (ANC) and survival. The RAISE analysis used the study safety population (n=1057). IMS Health Oncology Database (IMS EMR) was the source for the real-world data set (n=617). RAISE patients with treatment-emergent neutropaenia had improved mOS compared with those without (ramucirumab arm: 16.1 vs 10.7 months, HR=0.57, p<0.0001; placebo arm: 12.7 vs 10.7 months, HR=0.76, p=0.0065). RAISE patients with low ANC versus high baseline ANC also had longer mOS (ramucirumab arm: 15.2 vs 8.9 months, HR=0.49, p<0.0001; placebo arm: 13.2 vs 7.3 months, HR=0.50, p<0.0001). The results were similar for IMS EMR low versus high baseline ANC (bevacizumab+FOLFIRI patients: 14.9 vs 7.7 months, HR=0.59, p<0.0001; FOLFIRI alone: 14.6 vs 5.4 months, HR=0.37, p<0.0001). Patients in the RAISE trial with low baseline ANC were more likely to develop neutropaenia (OR: ramucirumab arm=2.62, p<0.0001; placebo arm=2.16, p=0.0003). Neutropaenia during treatment, and subsequent dose modifications or discontinuations, do not compromise treatment efficacy. Baseline ANC is a strong prognostic factor for survival and is associated with treatment-emergent neutropaenia in the analysed population. , Results

Irinotecan plus folinic acid/continuous 5-fluorouracil as simplified bimonthly FOLFIRI regimen for first-line therapy of metastatic colorectal cancer

BACKGROUND: Combination therapy of irinotecan, folinic acid (FA) and 5-fluorouracil (5-FU) has been proven to be highly effective for the treatment of metastatic colorectal cancer. However, in light of safety and efficacy concerns, the best combination regimen for first-line therapy still needs to be defined. The current study reports on the bimonthly FOLFIRI protocol consisting of irinotecan with continuous FA/5-FU in five German outpatient clinics, with emphasis on the safety and efficiency, quality of life, management of delayed diarrhea, and secondary resection of regressive liver metastases. METHODS: A total of 35 patients were treated for metastatic colorectal cancer. All patients received first-line treatment according to the FOLFIRI regimen, consisting of irinotecan (180 mg/m(2)), L-FA (200 mg/m(2)) and 5-FU bolus (400 mg/m(2)) on day 1, followed by a 46-h continuous infusion 5-FU (2400 mg/m(2)). One cycle contained three fortnightly administrations. Staging was performed after 2 cycles. Dosage was reduced at any time if toxicity NCI CTC grade III/IV was observed. Chemotherapy was administered only to diarrhea-free patients. RESULTS: The FOLFIRI regimen was generally well tolerated. It was postponed for one-week in 51 of 415 applications (12.3%). Dose reduction was necessary in ten patients. Grade III/IV toxicity was rare, with diarrhea (14%), nausea/vomiting (12%), leucopenia (3%), neutropenia (9%) and mucositis (3%). The overall response rate was 31% (4 CR and 7 PR), with disease control in 74%. After primary chemotherapy, resection of liver metastases was achieved in three patients. In one patient, the CR was confirmed pathologically. Median progression-free and overall survival were seven and 17 months, respectively. CONCLUSIONS: The FOLFIRI regimen proved to be safe and efficient. Outpatient treatment was well tolerated. Since downstaging was possible, combinations of irinotecan and continuous FA/5-FU should further be investigated in neoadjuvant protocols