Compact relaxations for polynomial programming problems

Reduced RLT constraints are a special class of Reformulation- Linearization Technique (RLT) constraints. They apply to nonconvex (both continuous and mixed-integer) quadratic programming problems subject to systems of linear equality constraints. We present an extension to the general case of polynomial programming problems and discuss the derived convex relaxation. We then show how to perform rRLT constraint generation so as to reduce the number of inequality constraints in the relaxation, thereby making it more compact and faster to solve. We present some computational results validating our approach

On the composition of convex envelopes for quadrilinear terms

International audienceWithin the framework of the spatial Branch-and-Bound algorithm for solving Mixed-Integer Nonlinear Programs, different convex relaxations can be obtained for multilinear terms by applying associativity in different ways. The two groupings ((x1x2)x3)x4 and (x1x2x3)x4 of a quadrilinear term, for example, give rise to two different convex relaxations. In [6] we prove that having fewer groupings of longer terms yields tighter convex relaxations. In this paper we give an alternative proof of the same fact and perform a computational study to assess the impact of the tightened convex relaxation in a spatial Branch-and-Bound setting

Finding and testing network communities by lumped Markov chains

Identifying communities (or clusters), namely groups of nodes with comparatively strong internal connectivity, is a fundamental task for deeply understanding the structure and function of a network. Yet, there is a lack of formal criteria for defining communities and for testing their significance. We propose a sharp definition which is based on a significance threshold. By means of a lumped Markov chain model of a random walker, a quality measure called "persistence probability" is associated to a cluster. Then the cluster is defined as an "$\alpha$-community" if such a probability is not smaller than $\alpha$. Consistently, a partition composed of $\alpha$-communities is an "$\alpha$-partition". These definitions turn out to be very effective for finding and testing communities. If a set of candidate partitions is available, setting the desired $\alpha$-level allows one to immediately select the $\alpha$-partition with the finest decomposition. Simultaneously, the persistence probabilities quantify the significance of each single community. Given its ability in individually assessing the quality of each cluster, this approach can also disclose single well-defined communities even in networks which overall do not possess a definite clusterized structure

Bioactive Sesterterpenes and Triterpenes from Marine Sponges: Occurrence and Pharmacological Significance

Marine ecosystems (>70% of the planet’s surface) comprise a continuous resource of immeasurable biological activities and immense chemical entities. This diversity has provided a unique source of chemical compounds with potential bioactivities that could lead to potential new drug candidates. Many marine-living organisms are soft bodied and/or sessile. Consequently, they have developed toxic secondary metabolites or obtained them from microorganisms to defend themselves against predators [1]. For the last 30–40 years, marine invertebrates have been an attractive research topic for scientists all over the world. A relatively small number of marine plants, animals and microbes have yielded more than 15,000 natural products including numerous compounds with potential pharmaceutical potential. Some of these have already been launched on the pharmaceutical market such as Prialt® (ziconotide; potent analgesic) and Yondelis® (trabectedin or ET-743; antitumor) while others have entered clinical trials, e.g., alpidin and kahalalide F. Amongst the vast array of marine natural products, the terpenoids are one of the more commonly reported and discovered to date. Sesterterpenoids (C25) and triterpenoids (C30) are of frequent occurrence, particularly in marine sponges, and they show prominent bioactivities. In this review, we survey sesterterpenoids and triterpenoids obtained from marine sponges and highlight their bioactivities

Flying safely by bilevel programming

International audiencePreventing aircraft from getting too close to each other is an essential element of safety of the air transportation industry, which becomes ever more important as the air traffic increases. The problem consists in enforcing a minimum distance threshold between flying aircraft, which naturally results in a bilevel formulation with a lower-level subproblem for each pair of aircraft. We propose two single-level reformulations, present a cut generation algorithm which directly solves the bilevel formulation and discuss comparative computational results

Aircraft Trajectory Planning with Dynamical Obstacles by Artificial Evolution and Convex Hull Generations

International audienceAir Traffic Management (ATM) ensures the safety of flights by optimizing flows and maintaining separation between aircraft. Many ATM applications involve some aircraft trajectory optimization in order to improve the performance of the overall system. Trajectories are objects belonging to spaces with infinite dimensions. Widely used approaches are based on discretization, sampling trajectories at some regular points,and then using appropriate representations to reduce the dimension of the search space. We propose an approach in which trajectories in a two-dimensional space are designed with the help of convex hull generation. By using static as well as moving obstacles for which the position and the size are controlled by artificial evolution, we propose a new algorithm for efficient trajectory planning in Terminal Maneuvering Areas