Robust optimization methods for chance constrained, simulation-based, and bilevel problems

The objective of robust optimization is to find solutions that are immune to the uncertainty of the parameters in a mathematical optimization problem. It requires that the constraints of a given problem should be satisfied for all realizations of the uncertain parameters in a so-called uncertainty set. The robust version of a mathematical optimization problem is generally referred to as the robust counterpart problem. Robust optimization is popular because of the computational tractability of the robust counterpart for many classes of uncertainty sets, and its applicability in wide range of topics in practice. In this thesis, we propose robust optimization methodologies for different classes of optimization problems. In Chapter 2, we give a practical guide on robust optimization. In Chapter 3, we propose a new way to construct uncertainty sets for robust optimization using the available historical data information. Chapter 4 proposes a robust optimization approach for simulation-based optimization problems. Finally, Chapter 5 proposes approximations of a specific class of robust and stochastic bilevel optimization problems by using modern robust optimization techniques

Safe Approximations of Chance Constraints Using Historical Data

This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability that the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical-data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach.robust optimization;chance constraint;phi-divergence;goodness-of-fit statistics

Adjustable Robust Parameter Design with Unknown Distributions

Abstract This article presents a novel combination of robust optimization developed in mathematical programming, and robust parameter design developed in statistical quality control. Robust parameter design uses metamodels estimated from experiments with both controllable and environmental inputs (factors). These experiments may be performed with either real or simulated systems; we focus on simulation experiments. For the environmental inputs, classic robust parameter design assumes known means and covariances, and sometimes even a known distribution. We, however, develop a robust optimization approach that uses only experimental data, so it does not need these classic assumptions. Moreover, we develop `adjustable' robust parameter design which adjusts the values of some or all of the controllable factors after observing the values of some or all of the environmental inputs. We also propose a new decision rule that is suitable for adjustable integer decision variables. We illustrate our novel method through several numerical examples, which demonstrate its effectiveness.

Effects of hospital facilities on patient outcomes after cancer surgery: an international, prospective, observational study

Background Early death after cancer surgery is higher in low-income and middle-income countries (LMICs) compared with in high-income countries, yet the impact of facility characteristics on early postoperative outcomes is unknown. The aim of this study was to examine the association between hospital infrastructure, resource availability, and processes on early outcomes after cancer surgery worldwide.Methods A multimethods analysis was performed as part of the GlobalSurg 3 study-a multicentre, international, prospective cohort study of patients who had surgery for breast, colorectal, or gastric cancer. The primary outcomes were 30-day mortality and 30-day major complication rates. Potentially beneficial hospital facilities were identified by variable selection to select those associated with 30-day mortality. Adjusted outcomes were determined using generalised estimating equations to account for patient characteristics and country-income group, with population stratification by hospital.Findings Between April 1, 2018, and April 23, 2019, facility-level data were collected for 9685 patients across 238 hospitals in 66 countries (91 hospitals in 20 high-income countries; 57 hospitals in 19 upper-middle-income countries; and 90 hospitals in 27 low-income to lower-middle-income countries). The availability of five hospital facilities was inversely associated with mortality: ultrasound, CT scanner, critical care unit, opioid analgesia, and oncologist. After adjustment for case-mix and country income group, hospitals with three or fewer of these facilities (62 hospitals, 1294 patients) had higher mortality compared with those with four or five (adjusted odds ratio [OR] 3.85 [95% CI 2.58-5.75]; p<0.0001), with excess mortality predominantly explained by a limited capacity to rescue following the development of major complications (63.0% vs 82.7%; OR 0.35 [0.23-0.53]; p<0.0001). Across LMICs, improvements in hospital facilities would prevent one to three deaths for every 100 patients undergoing surgery for cancer.Interpretation Hospitals with higher levels of infrastructure and resources have better outcomes after cancer surgery, independent of country income. Without urgent strengthening of hospital infrastructure and resources, the reductions in cancer-associated mortality associated with improved access will not be realised

Safe Approximations of Chance Constraints Using Historical Data

This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability that the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical-data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach

Safe approximations of ambiguous chance constraints using historical data

This paper proposes a new way to construct uncertainty sets for robust optimization. Our approach uses the available historical data for the uncertain parameters and is based on goodness-of-fit statistics. It guarantees that the probability the uncertain constraint holds is at least the prescribed value. Compared to existing safe approximation methods for chance constraints, our approach directly uses the historical data information and leads to tighter uncertainty sets and therefore to better objective values. This improvement is significant, especially when the number of uncertain parameters is low. Other advantages of our approach are that it can handle joint chance constraints easily, it can deal with uncertain parameters that are dependent, and it can be extended to nonlinear inequalities. Several numerical examples illustrate the validity of our approach

Hints for practical robust optimization

Robust optimization (RO) is a young and active research field that has been mainly developed in the last 15 years. RO techniques are very useful for practice and not difficult to understand for practitioners. It is therefore remarkable that real-life applications of RO are still lagging behind; there is much more potential for real-life applications than has been exploited hitherto. The aim of this paper is to help practitioners to successfully apply RO in practice. We pinpoint several important items that may be helpful for successfully applying RO. We use many small examples to illustrate our discussions

Hints for practical robust optimization

Robust optimization (RO) is a young and active research field that has been mainly developed in the last 15 years. RO techniques are very useful for practice and not difficult to understand for practitioners. It is therefore remarkable that real-life applications of RO are still lagging behind; there is much more potential for real-life applications than has been exploited hitherto. The aim of this paper is to help practitioners to successfully apply RO in practice. We pinpoint several important items that may be helpful for successfully applying RO. We use many small examples to illustrate our discussions

Adjustable Robust Parameter Design with Unknown Distributions

Abstract This article presents a novel combination of robust optimization developed in mathematical programming, and robust parameter design developed in statistical quality control. Robust parameter design uses metamodels estimated from experiments with both controllable and environmental inputs (factors). These experiments may be performed with either real or simulated systems; we focus on simulation experiments. For the environmental inputs, classic robust parameter design assumes known means and covariances, and sometimes even a known distribution. We, however, develop a robust optimization approach that uses only experimental data, so it does not need these classic assumptions. Moreover, we develop `adjustable' robust parameter design which adjusts the values of some or all of the controllable factors after observing the values of some or all of the environmental inputs. We also propose a new decision rule that is suitable for adjustable integer decision variables. We illustrate our novel method through several numerical examples, which demonstrate its effectiveness

Determination of subclinical atherosclerosis in plaque type psoriasis patients without traditional risk factors for atherosclerosis

PubMed ID: 23363939Objectives: Systemic inflammation plays an important role in the pathogenesis of atherosclerosis in psoriasis patients. Therefore, persistent skin inflammation in psoriasis patients may contribute to the development of premature atherosclerosis, as it occurs in rheumatoid arthritis and systemic lupus erythematosus. We aimed to evaluate the relationship between subclinical atherosclerosis and psoriasis by using pulse wave velocity (PWV) and the measurement of carotid intima media thickness (CIMT) in psoriatic patients. Study design: Fifty-seven plaque-type psoriasis patients (31 males, 26 females; mean age 41±10.8 years) and 60 healthy individuals (32 males, 28 females; mean age 40±9.4 years) were included. Atherosclerotic risk factors were excluded in both of the groups. Demographic, bio-chemical data, psoriasis area and severity index (PASI) score of the psoriasis group, and disease duration were recorded. Carotid-femoral artery PWV and CIMT values were compared. Results: PWV, and the maximum and average CIMT values of psoriasis patients were higher than those of the healthy group (PWV: 7.04±1.1 m/sn vs. 6.03±0.61 m/sn, p<0.001; maximum CIMT: 0.86±0.09 mm vs. 0.77±0.06 mm, p<0.001; mean CIMT: 0.73±0.09 mm vs. 0.66±0.06 mm p<0.001, respectively). Although there was no difference in the lipid levels of the groups, total/HDL cholesterol (4.40±1.26 vs. 3.88±1.18, p=0.02, respectively), and LDL/HDL cholesterol ratios (2.78±0.98 vs. 2.32±0.92, p=0.01, respectively) of the psoriasis group were higher than those of the healthy group. A positive correlation was observed between PASI and the PWV (r=0.417, p=0.001). Conclusion: Despite the nonexistence of atherosclerotic risk factors, the risk of development of atherosclerosis is higher in psoriasis patients compared to healthy individuals. In addition to damage of the artery wall caused by systemic inflammation, lipid metabolism disorders may contribute to the development of atherosclerosis in these patients. © 2012 Turkish Society of Cardiology