An improved algorithm for solving biobjective integer programs

We present the problem of planning mobile tours of inspectors on German motorways to enforce the payment of the toll for heavy good trucks. This is a special type of vehicle routing problem with the objective to conduct as good inspections as possible on the complete network. In addition, we developed a personalized crew rostering model, to schedule the crews of the tours. The planning of daily tours and the rostering are combined in a novel integrated approach and formulated as a complex and large scale Integer Program. The main focus of this paper extends our previous publications on how different requirements for the rostering can be modeled in detail. The second focus is on a bi-criteria analysis of the planning problem to find the balance between the control quality and the roster acceptance. Finally, computational results on real-world instances show the practicability of our method and how different input parameters influence the problem complexity.

show abstract

“…Ralphs et al (2006). But for the sake of completeness we repeat in a proposition a short proof of this result applied to the TEP.…”

Section: Analysing the Objective Functionmentioning

confidence: 78%

“…We analyze the interplay of the objectives with the well-known concept of Pareto optimality; see e.g. Ralphs et al (2006). First, we shortly recall its definition.…”

Section: Analysing the Objective Functionmentioning

confidence: 99%

Optimal duty rostering for toll enforcement inspectors

et al. 2016

View full text Add to dashboard Cite

show abstract

“…So, the total number of iterations is 2|Z N | − 1, cf. Chalmet et al [2] and Ralphs et al [18]. In Fig.…”

Section: Bicriteria Casementioning

confidence: 87%

“…Now, different from Algorithm 1, z s is compared componentwise to v(B) for every B ∈ B s . A split with respect to component i is 18 …”

Section: An Algorithm For Tricriteria Problems Based On the V-splitmentioning

confidence: 99%

A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems

Dächert

Klamroth

2014

J Glob Optim

View full text Add to dashboard Cite

Multi-objective optimization problems are often solved by a sequence of parametric single-objective problems, so-called scalarizations. If the set of nondominated points is finite, the entire nondominated set can be generated in this way. In the bicriteria case it is well known that this can be realized by an adaptive approach which requires the solution of at most 2|Z N | − 1 subproblems, where Z N denotes the nondominated set of the underlying problem and a subproblem corresponds to a scalarized problem. For problems with more than two criteria, no methods were known up to now for which the number of subproblems depends linearly on the number of nondominated points. We present a new procedure for finding the entire nondominated set of tricriteria optimization problems for which the number of subproblems to be solved is bounded by 3|Z N | − 2, hence, depends linearly on the number of nondominated points. The approach includes an iterative update of the search region that, given a (sub-)set of nondominated points, describes the area in which additional nondominated points may be located. If the ε-constraint method is chosen as scalarization, the upper bound can be improved to 2|Z N | − 1.

show abstract

“…The way to overcome this drawback is to add an augmentation l 1 norm, with the augmentation coefficient   , to the weighted l ∞ norm between the utopia point and the feasible set of a given problem is proposed by Steuer and Choo (1983). In other words, the way to ensure the generated outcome closet to the ideal point along one edge of the optimal level line is to utilize both l 1 norm and l ∞ norm (Ralphs et al, 2006). This is called the augmented weighted Tchebycheff model.…”

Section: Introductionmentioning

confidence: 99%

Augmented Weighted Tchebycheff Modeling and Robust Design Optimization on a Drug Development Process

Ho¹,

Shin²

2013

Journal of Korean Institute of Industrial Engineers

View full text Add to dashboard Cite

The quality of the products/processes has been improved remarkably since robust design (RD) methodology is applied into the practice manufacturing processes. A model building method based on the dual responses methods for multiple and time oriented responses on a drug development process is employed in this paper instead of the previous methods that handle the static nature of data and single response. Subsequently, the optimal solutions of a multiple and time series RD problem are obtained by using the proposed augmented weighted Tchebycheff method that has a significant flexibility on assigning weights. Finally, a pharmaceutical case study associated with a generic drug development process is conducted in order to illustrate the efficient optimal solutions from the proposed model.

show abstract

An improved algorithm for solving biobjective integer programs

Cited by 60 publications

References 41 publications

Optimal duty rostering for toll enforcement inspectors

Optimal duty rostering for toll enforcement inspectors

A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems

Augmented Weighted Tchebycheff Modeling and Robust Design Optimization on a Drug Development Process

Contact Info

Product

Resources

About