Political districting without geography

Geographical considerations such as contiguity and compactness are necessary elements of political districting in practice. Yet an analysis of the problem without such constraints yields mathematical insights that can inform real-world model construction. In particular, it clarifies the sharp contrast between proportionality and competitiveness and how it might be overcome in a properly formulated objective function. It also reveals serious weaknesses of the much-discussed efficiency gap as a criterion for gerrymandering.Published versio

Exploiting the Power of mip Solvers in maxsat

Abstract. maxsat is an optimization version of satisfiability. Since many practical problems involve optimization, there are a wide range of potential applications for effective maxsat solvers. In this paper we present an extensive empirical evaluation of a number of maxsat solvers. In addition to traditional maxsat solvers, we also evaluate the use of a state-of-the-art Mixed Integer Program (mip) solver, cplex, for solving maxsat. mip solvers are the most popular technology for solving opti-mization problems and are also theoretically more powerful than sat solvers. In fact, we show that cplex is quite effective on a range of maxsat instances. Based on these observations we extend a previously developed hybrid approach for solving maxsat, that utilizes both a sat solver and a mip solver. Our extensions aim to take better advantage of the power of the mip solver. The resulting improved hybrid solver is shown to be quite effective.

Orbital Shrinking: A New Tool for Hybrid MIP/CP Methods

Abstract. Orbital shrinking is a newly developed technique in the MIP community to deal with symmetry issues, which is based on aggregation rather than on symmetry breaking. In a recent work, a hybrid MIP/CP scheme based on orbital shrinking was developed for the multi-activity shift scheduling problem, showing significant improvements over previ-ous pure MIP approaches. In the present paper we show that the scheme above can be extended to a general framework for solving arbitrary sym-metric MIP instances. This framework naturally provides a new way for devising hybrid MIP/CP decompositions. Finally, we specialize the above framework to the multiple knapsack problem. Computational re-sults show that the resulting method can be orders of magnitude faster than pure MIP approaches on hard symmetric instances.

Cost-based domain filtering for stochastic constraint programming

Cost-based filtering is a novel approach that combines techniques from Operations Research and Constraint Programming to filter from decision variable domains values that do not lead to better solutions [7]. Stochastic Constraint Programming is a framework for modeling combinatorial optimization problems that involve uncertainty [9]. In this work, we show how to perform cost-based filtering for certain classes of stochastic constraint programs. Our approach is based on a set of known inequalities borrowed from Stochastic Programming ¿ a branch of OR concerned with modeling and solving problems involving uncertainty. We discuss bound generation and cost-based domain filtering procedures for a well-known problem in the Stochastic Programming literature, the static stochastic knapsack problem. We also apply our technique to a stochastic sequencing problem. Our results clearly show the value of the proposed approach over a pure scenario-based Stochastic Constraint Programming formulation both in terms of explored nodes and run time

The genera Melanothamnus Bornet & Falkenberg and Vertebrata S.F. Gray constitute well-defined clades of the red algal tribe Polysiphonieae (Rhodomelaceae, Ceramiales).

Polysiphonia is the largest genus of red algae, and several schemes subdividing it into smaller taxa have been proposed since its original description. Most of these proposals were not generally accepted, and currently the tribe Polysiphonieae consists of the large genus Polysiphonia (190 species), the segregate genus Neosiphonia (43 species), and 13 smaller genera (< 10 species each). In this paper, phylogenetic relationships of the tribe Polysiphonieae are analysed, with particular emphasis on the genera Carradoriella, Fernandosiphonia, Melanothamnus, Neosiphonia, Polysiphonia sensu stricto, Streblocladia and Vertebrata. We evaluated the consistency of 14 selected morphological characters in the identified clades. Based on molecular phylogenetic (rbcL and 18S genes) and morphological evidence, two speciose genera are recognized: Vertebrata (including the type species of the genera Ctenosiphonia, Enelittosiphonia, Boergeseniella and Brongniartella) and Melanothamnus (including the type species of the genera Fernandosiphonia and Neosiphonia). Both genera are distinguished from other members of the Polysiphonieae by synapomorphic characters, the emergence of which could have provided evolutionarily selective advantages for these two lineages. In Vertebrata trichoblast cells are multinucleate, possibly associated with the development of extraordinarily long, photoprotective, trichoblasts. Melanothamnus has 3-celled carpogonial branches and plastids lying exclusively on radial walls of the pericentral cells, which similarly may improve resistance to damage caused by excessive light. Other relevant characters that are constant in each genus are also shared with other clades. The evolutionary origin of the genera Melanothamnus and Vertebrata is estimated as 75.7-95.78 and 90.7-138.66 Ma, respectively. Despite arising in the Cretaceous, before the closure of the Tethys Seaway, Melanothamnus is a predominantly Indo-Pacific genus and its near-absence from the northeastern Atlantic is enigmatic. The nomenclatural implications of this work are that 46 species are here transferred to Melanothamnus, six species are transferred to Vertebrata and 13 names are resurrected for Vertebrata

Research trends in combinatorial optimization

Acknowledgments This work has been partially funded by the Spanish Ministry of Science, Innovation, and Universities through the project COGDRIVE (DPI2017-86915-C3-3-R). In this context, we would also like to thank the Karlsruhe Institute of Technology. Open access funding enabled and organized by Projekt DEAL.Peer reviewedPublisher PD

Planning and scheduling to minimize tardiness

Abstract. We combine mixed integer linear programming (MILP) and constraint programming (CP) to minimize tardiness in planning and scheduling. Tasks are allocated to facilities using MILP and scheduled using CP, and the two are linked via logic-based Benders decomposition. We consider two objectives: minimizing the number of late tasks, and minimizing total tardiness. Our main theoretical contribution is a relaxation of the cumulative scheduling subproblem, which is critical to performance. We obtain substantial computational speedups relative to the state of the art in both MILP and CP. We also obtain much better solutions for problems that cannot be solved to optimality. We address a planning and scheduling problem that occurs frequently in manufacturing and supply chain contexts. Tasks must be assigned to facilities and scheduled on each facility subject to release dates and due dates. Tasks assigned to a given facility may run in parallel if desired, subject to a resource constraint (cumulative scheduling). We consider two objectives: minimizing th