31,074 research outputs found
Minimizing the average distance to a closest leaf in a phylogenetic tree
When performing an analysis on a collection of molecular sequences, it can be
convenient to reduce the number of sequences under consideration while
maintaining some characteristic of a larger collection of sequences. For
example, one may wish to select a subset of high-quality sequences that
represent the diversity of a larger collection of sequences. One may also wish
to specialize a large database of characterized "reference sequences" to a
smaller subset that is as close as possible on average to a collection of
"query sequences" of interest. Such a representative subset can be useful
whenever one wishes to find a set of reference sequences that is appropriate to
use for comparative analysis of environmentally-derived sequences, such as for
selecting "reference tree" sequences for phylogenetic placement of metagenomic
reads. In this paper we formalize these problems in terms of the minimization
of the Average Distance to the Closest Leaf (ADCL) and investigate algorithms
to perform the relevant minimization. We show that the greedy algorithm is not
effective, show that a variant of the Partitioning Among Medoids (PAM)
heuristic gets stuck in local minima, and develop an exact dynamic programming
approach. Using this exact program we note that the performance of PAM appears
to be good for simulated trees, and is faster than the exact algorithm for
small trees. On the other hand, the exact program gives solutions for all
numbers of leaves less than or equal to the given desired number of leaves,
while PAM only gives a solution for the pre-specified number of leaves. Via
application to real data, we show that the ADCL criterion chooses chimeric
sequences less often than random subsets, while the maximization of
phylogenetic diversity chooses them more often than random. These algorithms
have been implemented in publicly available software.Comment: Please contact us with any comments or questions
Bartering integer commodities with exogenous prices
The analysis of markets with indivisible goods and fixed exogenous prices has
played an important role in economic models, especially in relation to wage
rigidity and unemployment. This research report provides a mathematical and
computational details associated to the mathematical programming based
approaches proposed by Nasini et al. (accepted 2014) to study pure exchange
economies where discrete amounts of commodities are exchanged at fixed prices.
Barter processes, consisting in sequences of elementary reallocations of couple
of commodities among couples of agents, are formalized as local searches
converging to equilibrium allocations. A direct application of the analyzed
processes in the context of computational economics is provided, along with a
Java implementation of the approaches described in this research report.Comment: 30 pages, 5 sections, 10 figures, 3 table
Revisiting minimum profit conditions in uniform price day-ahead electricity auctions
We examine the problem of clearing day-ahead electricity market auctions
where each bidder, whether a producer or consumer, can specify a minimum profit
or maximum payment condition constraining the acceptance of a set of bid curves
spanning multiple time periods in locations connected through a transmission
network with linear constraints. Such types of conditions are for example
considered in the Spanish and Portuguese day-ahead markets. This helps
describing the recovery of start-up costs of a power plant, or analogously for
a large consumer, utility reduced by a constant term. A new market model is
proposed with a corresponding MILP formulation for uniform locational price
day-ahead auctions, handling bids with a minimum profit or maximum payment
condition in a uniform and computationally-efficient way. An exact
decomposition procedure with sparse strengthened Benders cuts derived from the
MILP formulation is also proposed. The MILP formulation and the decomposition
procedure are similar to computationally-efficient approaches previously
proposed to handle so-called block bids according to European market rules,
though the clearing conditions could appear different at first sight. Both
solving approaches are also valid to deal with both kinds of bids
simultaneously, as block bids with a minimum acceptance ratio, generalizing
fully indivisible block bids, are but a special case of the MP bids introduced
here. We argue in favour of the MP bids by comparing them to previous models
for minimum profit conditions proposed in the academic literature, and to the
model for minimum income conditions used by the Spanish power exchange OMIE
Differential Evolution for Multiobjective Portfolio Optimization
Financial portfolio optimization is a challenging problem. First, the problem is multiobjective (i.e.: minimize risk and maximize profit) and the objective functions are often multimodal and non smooth (e.g.: value at risk). Second, managers have often to face real-world constraints, which are typically non-linear. Hence, conventional optimization techniques, such as quadratic programming, cannot be used. Stochastic search heuristic can be an attractive alternative. In this paper, we propose a new multiobjective algorithm for portfolio optimization: DEMPO - Differential Evolution for Multiobjective Portfolio Optimization. The main advantage of this new algorithm is its generality, i.e., the ability to tackle a portfolio optimization task as it is, without simplifications. Our empirical results show the capability of our approach of obtaining highly accurate results in very reasonable runtime, in comparison with quadratic programming and another state-of-art search heuristic, the so-called NSGA II.Portfolio Optimization, Multiobjective, Real-world Constraints, Value at Risk, Expected Shortfall, Differential Evolution
Hybrid behavioural-based multi-objective space trajectory optimization
In this chapter we present a hybridization of a stochastic based search approach for multi-objective optimization with a deterministic domain decomposition of the solution space. Prior to the presentation of the algorithm we introduce a general formulation of the optimization problem that is suitable to describe both single and multi-objective problems. The stochastic approach, based on behaviorism, combinedwith the decomposition of the solutions pace was tested on a set of standard multi-objective optimization problems and on a simple but representative case of space trajectory design
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