Total vertex-edge domination in graphs: Complexity and algorithms

Let [Formula: see text] be a simple, undirected and connected graph. A vertex [Formula: see text] of a simple, undirected graph [Formula: see text]-dominates all edges incident to at least one vertex in its closed neighborhood [Formula: see text]. A set [Formula: see text] of vertices is a vertex-edge dominating set of [Formula: see text], if every edge of graph [Formula: see text] is [Formula: see text]-dominated by some vertex of [Formula: see text]. A vertex-edge dominating set [Formula: see text] of [Formula: see text] is called a total vertex-edge dominating set if the induced subgraph [Formula: see text] has no isolated vertices. The total vertex-edge domination number [Formula: see text] is the minimum cardinality of a total vertex-edge dominating set of [Formula: see text]. In this paper, we prove that the decision problem corresponding to [Formula: see text] is NP-complete for chordal graphs, star convex bipartite graphs, comb convex bipartite graphs and planar graphs. The problem of determining [Formula: see text] of a graph [Formula: see text] is called the minimum total vertex-edge domination problem (MTVEDP). We prove that MTVEDP is linear time solvable for chain graphs and threshold graphs. We also show that MTVEDP can be approximated within approximation ratio of [Formula: see text]. It is shown that the domination and total vertex-edge domination problems are not equivalent in computational complexity aspects. Finally, an integer linear programming formulation for MTVEDP is presented.

Learning Feedback Molecular Network Models Using Integer Linear Programming

Analysis of intracellular molecular networks has many applications in understanding of the molecular bases of some complex diseases and finding the effective therapeutic targets for drug development. To perform such analyses, the molecular networks need to be converted into computational models. In general, network models constructed using literature and pathway databases may not accurately predict and reproduce experimental network data. This can be due to the incompleteness of literature on molecular pathways, the resources used to construct the networks, or some conflicting information in the resources. In this paper, we propose a network learning approach via an integer linear programming formulation that can efficiently incorporate biological dynamics and regulatory mechanisms of molecular networks in the learning process. Moreover, we present a method to properly take into account the feedback paths, while learning the network from data. Examples are also provided to show how one can apply the proposed learning approach to a network of interest. Overall, the proposed methods are useful for reducing the gap between the curated networks and experimental network data, and result in calibrated networks that are more reliable for making biologically meaningful predictions.

A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

In this paper, we investigate the resource-constrained order acceptance and scheduling on unrelated parallel machines that arise in make-to-order systems. The objective of this problem is to simultaneously select a subset of orders to be processed and schedule the accepted orders on unrelated machines in such a way that the resources are not overutilized at any time. We first propose two formulations for the problem: mixed integer linear programming formulation and set partitioning. In view of the complexity of the problem, we then develop a column generation approach based on the set partitioning formulation. In the proposed column generation approach, a differential evolution algorithm is designed to solve subproblems efficiently. Extensive numerical experiments on different-sized instances are conducted, and the results demonstrate that the proposed column generation algorithm reports optimal or near-optimal solutions that are evidently better than the solutions obtained by solving the mixed integer linear programming formulation.

A linear programming-based strategy to save pipette tips in automated DNA assembly

Laboratory automation and mathematical optimisation are key to improving the efficiency of synthetic biology research. While there are algorithms optimising the construct designs and synthesis strategies for DNA assembly, the optimisation of how DNA assembly reaction mixes are prepared remains largely unexplored. Here, we focus on reducing the pipette tip consumption of a liquid-handling robot as it delivers DNA parts across a multi-well plate where several constructs are being assembled in parallel. We propose a linear programming formulation of this problem based on the capacitated vehicle routing problem, along with an algorithm which applies a linear programming solver to our formulation, hence providing a strategy to prepare a given set of DNA assembly mixes using fewer pipette tips. The algorithm performed well in randomly generated and real-life scenarios concerning several modular DNA assembly standards, proving capable of reducing the pipette tip consumption by up to 61% in large-scale cases. Combining automatic process optimisation and robotic liquid-handling, our strategy promises to greatly improve the efficiency of DNA assembly, either used alone or in combination with other algorithmic methods.

Robust optimal classification trees under noisy labels

In this paper we propose a novel methodology to construct Optimal Classification Trees that takes into account that noisy labels may occur in the training sample. The motivation of this new methodology is based on the superaditive effect of combining together margin based classifiers and outlier detection techniques. Our approach rests on two main elements: (1) the splitting rules for the classification trees are designed to maximize the separation margin between classes applying the paradigm of SVM; and (2) some of the labels of the training sample are allowed to be changed during the construction of the tree trying to detect the label noise. Both features are considered and integrated together to design the resulting Optimal Classification Tree. We present a Mixed Integer Non Linear Programming formulation for the problem, suitable to be solved using any of the available off-the-shelf solvers. The model is analyzed and tested on a battery of standard datasets taken from UCI Machine Learning repository, showing the effectiveness of our approach. Our computational results show that in most cases the new methodology outperforms both in accuracy and AUC the results of the benchmarks provided by OCT and OCT-H.

Optimal Taxes in Atomic Congestion Games

How can we design mechanisms to promote efficient use of shared resources? Here, we answer this question in relation to the well-studied class of atomic congestion games, used to model a variety of problems, including traffic routing. Within this context, a methodology for designing tolling mechanisms that minimize the system inefficiency (price of anarchy) exploiting solely local information is so far missing in spite of the scientific interest. In this article, we resolve this problem through a tractable linear programming formulation that applies to and beyond polynomial congestion games. When specializing our approach to the polynomial case, we obtain tight values for the optimal price of anarchy and corresponding tolls, uncovering an unexpected link with load balancing games. We also derive optimal tolling mechanisms that are constant with the congestion level, generalizing the results of Caragiannis et al. [8] to polynomial congestion games and beyond. Finally, we apply our techniques to compute the efficiency of the marginal cost mechanism. Surprisingly, optimal tolling mechanism using only local information perform closely to existing mechanism that utilize global information, e.g., Bilò and Vinci [6], while the marginal cost mechanism, known to be optimal in the continuous-flow model, has lower efficiency than that encountered levying no toll. All results are tight for pure Nash equilibria and extend to coarse correlated equilibria.

A Matheuristic approach for the maximum balanced subgraph of a signed graph

A graph G=(V,E) with its edges labeled in the set {+, -} is called a signed graph. It is balanced if its set of vertices V can be partitioned into two sets V 1 and V 2 , such that all positive edges connect nodes within V 1 or V 2 , and all negative edges connect nodes between V 1 and V 2 . The maximum balanced subgraph problem (MBSP) for a signed graph is the problem of finding a balanced subgraph with the maximum number of vertices. In this work, we present the first polynomial integer linear programming formulation for this problem and a matheuristic to obtain good quality solutions in a short time. The results obtained for different sets of instances show the effectiveness of the matheuristic, optimally solving several instances and finding better results than the exact method in a much shorter computational time.

The Role of Biowaste: A Multi-Objective Optimization Platform for Combined Heat, Power and Fuel

Biomass, bioenergy and negative emission technologies are inherent to the future design of energy systems. Urban clusters have a growing demand for fuel, heat and electricity, which is both a challenge and an opportunity for biomass-based technologies. Their deployment should meet demand, while minimizing environmental impact and staying cost-competitive. We develop a systematic approach for the design, evaluation and ranking of biomass-to-X production strategies under uncertain market conditions. We assemble state-of-the-art and innovative conversion technologies, based on feedstock, by-products and waste characteristics. Technical specifications, as well as economic and environmental aspects are estimated based on literature values and industry experts input. Embedded into a bi-level mixed-integer linear programming formulation, the framework identifies and assesses current and promising strategies, while establishing the most robust and resilient designs. The added value of this approach is the inclusion of sub-optimal routes which might outperform competing strategies under different market assumptions. The methodology is illustrated in the anaerobic digestion of food and green waste biomass used as a case study in the current Swiss market. By promoting a fair comparison between alternatives it highlights the benefits of energy integration and poly-generation in the energy transition, showing how biomass-based technologies can be deployed to achieve a more sustainable future.

Integrated Train Timetabling and Rolling Stock Circulation Planning for a Metro Line with Multiple Depots

With the expansion of metro networks, it is common that a metro line is equipped with multiple depots. The operation costs of rail operators and the passenger satisfaction are highly dependent on train timetables and rolling stock circulation plans, which are closely related to each other. Therefore, it is important to investigate the integrated train timetabling and rolling stock circulation planning problem for metro lines with multiple depots. A mixed integer linear programming formulation is proposed to generate train timetables and rolling stock circulation plans simultaneously for a metro line with multiple depots, in which the capacity of each depot and the rolling stock balances between depots are considered. Several numerical experiments based on real-world data of Beijing Subway Line 5 and Beijing Subway Line 6 are carried out to demonstrate the effectiveness of the presented model.