A cutting plane algorithm for the capacitated facility location problem

We present a separation procedure for a class of valid inequalities (mixed lifted cover inequalities) for the mixed binary knapsack set with a single continuous variable. It consists of the following steps: (i) the continuous variable is fixed to a given value, (ii) a valid inequality for the corresponding binary knapsack set is computed, (iii) the inequality is lifted using an iterative procedure to become valid for the mixed integer knapsack set. Computational experience on a wide set of mixed integer programming instances from MIPLIB and Mittleman sets is carried out, showing that our cutting plane algorithm leads to significant improvement in lower bounds, with negligible additional computational effort.

Encoding transformation-based differential evolution algorithm for solving knapsack problem with single continuous variable

A novel matheuristic approach is presented and tested on a well-known optimisation problem, namely, capacitated facility location problem (CFLP). The algorithm combines local search and mathematical programming. While the local search algorithm is used to select a subset of promising facilities, mathematical programming strategies are used to solve the subproblem to optimality. Proposed local search is influenced by instance-specific information such as installation cost and the distance between customers and facilities. The algorithm is tested on large instances of the CFLP, where neither local search nor mathematical programming is able to find good quality solutions within acceptable computational times. Our approach is shown to be a very competitive alternative to solve large-scale instances for the CFLP.

Capacitated facility location problem with general setup cost

Facility Location embodies a class of problems concerned with locating a set of facilities to serve a geographically distributed population of customers at minimum cost. We address the classical Capacitated Facility Location Problem (CFLP) in which the assignment of facilities to customers must ensure enough facility capacity and all the customers must be served. This is a well-known NP-hard problem in combinatorial optimization that has been extensively studied in the literature. Due to the difficulty of the problem, significant research efforts have been devoted to developing advanced heuristic methods aimed at finding high-quality solutions in reasonable computational times. We propose a Relaxation Adaptive Memory Programming (RAMP) approach for the CFLP. Our method combines lagrangean subgradient search with an improvement method to explore primal-dual relationships to create advanced memory structures that integrate information from both primal and dual solution spaces. The algorithm was tested on the standard ORLIB dataset and on other very large-scale instances for the CFLP. Our approach efficiently found the optimal solution for all ORLIB instances and very competitive results for the large-scale ones. Comparisons with current best-performing algorithms for the CFLP show that our RAMP algorithm exhibits excellent results.

Background: By observing the high prevalence of failures in the surgical treatment of myocardial revascularization (MR), with the use of the Left Internal Thoracic Artery (LITA) as a graft, evidenced by the international literature, it was sought to demonstrate the prevalence of lesions that would not allow the use of LITA as a graft in myocardial revascularization surgery, with possible alteration in the surgical management performed by the cardiac surgeon, and reduction of the morbimortality of these patients. Objectives: To evaluate the prevalence of atherosclerotic lesions of the LITA, through selective preoperative angiography, in patients submitted to coronary angiography and indicated for myocardial revascularization. We also analyzed other lesions that made the use of LITA unfeasible as a main graft in cases of myocardial revascularization surgery (MRS). Methods: This was a cross-sectional, prevalence study that evaluated, through selective angiography, the LITA of 39 patients with a median age of 63 years, submitted to coronary angiography, with indication of Coronary Artery Bypass Graft (CABG). Categorical variables were compared by chi-square test and Fisher's exact test. The single continuous variable, age, was tested for normality by the Kolmogorov-Smirnov test, described in median (P25; P75) and the groups compared with the Mann-Whitney test. The level of statistical significance adopted was p < 0.05. The analyzes were performed in SPSS® software version 20. Results: It was identified the presence of 7.7% of disorders in the LITA that made it unfeasible to be used. In all of the patients there was no specific symptomatology evidencing the lesion. No variable was shown as a predictor for the occurrence of the outcomes. Conclusion: The prevalence of the lesions found in the study was significant, indicating that a preoperative evaluation of LITA could bring future benefits to the patients submitted to CABG.

Green supply chain network design to reduce carbon emissions

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

A practical approach for hybrid distributed MPC

Efficient train re-routing and rescheduling: Valid inequalities and reformulation of RECIFE-MILP

The natural performance of the location model is a potential tool for allocating an object into one of the two observed groups involving mixtures of continuous and binary variables. In constructing location model, continuous variable is used to estimate parameters while binary variable is utilized to create segmentation in each group. Such segmentation is called as multinomial cells. Basically, the multinomial cells will grow exponentially according to the number of the binary variable. These multinomial cells will become empty when there is no object can be assigned into some of them. Then the occurring of empty cells will lead to unreliable parameter estimation. Consequently, the construction of the discriminant rule based on location model is impossible. Therefore, this paper attempts to discuss how the location model based on maximum likelihood estimation can be constructed even dealing with many measured binary variables. In other word, how is location model able to deal with the issue of many empty ...

Integrating Genetic Risk Factors with Age, Presenting White Cell Count and MRD Response As Continuous Variables to Predict Relapse in Paediatric Acute Lymphoblastic Leukemia (ALL)

Ignoring information in binary choice with continuous variables: When is less “more”?

Branch-and-price-and-cut for large-scale multicommodity capacitated fixed-charge network design

Problems in structural optimization typically involve decisions modeled as binary variables that lead to difficult combinatorial optimization problems. The literature presents different techniques to relax the binary variables in order to avoid the high computational costs required by the solution of combinatorial problems. This note develops a novel relaxation strategy to map a problem with binary variables into an equivalent problem with continuous variables. A set of theoretical results prove the equivalence of the proposed approach and the original binary optimization problem. The strategy is applied to the unassigned distance geometry problem, relying on the design of a new formulation for the problem. Computational studies illustrate the benefits of the proposed relaxation.