David I. Mester

Active guided evolution strategies for large-scale vehicle routing problems with time windows

We present a new and effective metaheuristic algorithm, active guided evolution strategies, for the vehicle routing problem with time windows. The algorithm combines the strengths of the well-known guided local search and evolution strategies metaheuristics into an iterative two-stage procedure. More precisely, guided local search is used to regulate a composite local search in the first stage and the neighborhood of the evolution strategies algorithm in the second stage. The vehicle routing problem with time windows is a classical problem in operations research, where the objective is to design least cost routes for a fleet of identical capacitated vehicles to service geographically scattered customers within pre-specified time windows. The presented algorithm is specifically designed for large-scale problems. The computational experiments were carried out on an extended set of 302 benchmark problems. The results demonstrate that the suggested method is highly competitive, providing the best-known solutions to 86% of all test instances within reasonable computing times. The power of the algorithm is confirmed by the results obtained on 23 capacitated vehicle routing problems from the literature.

Active-guided evolution strategies for large-scale capacitated vehicle routing problems

We present an adaptation of the active-guided evolution strategies metaheuristic for the capacitated vehicle routing problem. The capacitated vehicle routing problem is a classical problem in operations research in which a set of minimum total cost routes must be determined for a fleet of identical capacitated vehicles in order to service a number of demand or supply points. The applied metaheuristic combines the strengths of the well-known guided local search and evolution strategies metaheuristics into an iterative two-stage procedure. The computational experiments were carried out on a set of 76 benchmark problems. The results demonstrate that the suggested method is highly competitive, providing the best-known solutions to 70 test instances.

Genetic dissection of intermated recombinant inbred lines using a new genetic map of maize.

A new genetic map of maize, ISU–IBM Map4, that integrates 2029 existing markers with 1329 new indel polymorphism (IDP) markers has been developed using intermated recombinant inbred lines (IRILs) from the intermated B73 × Mo17 (IBM) population. The website http://magi.plantgenomics.iastate.edu provides access to IDP primer sequences, sequences from which IDP primers were designed, optimized marker-specific PCR conditions, and polymorphism data for all IDP markers. This new gene-based genetic map will facilitate a wide variety of genetic and genomic research projects, including map-based genome sequencing and gene cloning. The mosaic structures of the genomes of 91 IRILs, an important resource for identifying and mapping QTL and eQTL, were defined. Analyses of segregation data associated with markers genotyped in three B73/Mo17-derived mapping populations (F2, Syn5, and IBM) demonstrate that allele frequencies were significantly altered during the development of the IBM IRILs. The observations that two segregation distortion regions overlap with maize flowering-time QTL suggest that the altered allele frequencies were a consequence of inadvertent selection. Detection of two-locus gamete disequilibrium provides another means to extract functional genomic data from well-characterized plant RILs.

An Effective Multirestart Deterministic Annealing Metaheuristic for the Fleet Size and Mix Vehicle-Routing Problem with Time Windows

This paper presents a new deterministic annealing metaheuristic for the fleet size and mix vehicle-routing problem with time windows. The objective is to service, at minimal total cost, a set of customers within their time windows by a heterogeneous capacitated vehicle fleet. First, we motivate and define the problem. We then give a mathematical formulation of the most studied variant in the literature in the form of a mixed-integer linear program. We also suggest an industrially relevant, alternative definition that leads to a linear mixed-integer formulation. The suggested metaheuristic solution method solves both problem variants and comprises three phases. In Phase 1, high-quality initial solutions are generated by means of a savings-based heuristic that combines diversification strategies with learning mechanisms. In Phase 2, an attempt is made to reduce the number of routes in the initial solution with a new local search procedure. In Phase 3, the solution from Phase 2 is further improved by a set of four local search operators that are embedded in a deterministic annealing framework to guide the improvement process. Some new implementation strategies are also suggested for efficient time window feasibility checks. Extensive computational experiments on the 168 benchmark instances have shown that the suggested method outperforms the previously published results and found 167 best-known solutions. Experimental results are also given for the new problem variant.

A Multi-Parametric Evolution Strategies Algorithm for Vehicle Routing Problems

Vehicle routing problems are at the heart of most decision support systems for real-life distribution problems. In vehicle routing problem a set of routes must be determined at lowest total cost for a number of resources (i.e. fleet of vehicles) located at one or several points (e.g. depots, warehouses) in order to efficiently service a number of demand or supply points. In this paper an efficient evolution strategies algorithm is developed for both capacitated vehicle routing problem and for vehicle routing problem with time window constraints. The algorithm is based on a new multi-parametric mutation procedure that is applied within the 1 + 1 evolution strategies algorithm. Computational testing on six real-life problems and 195 benchmark problems demonstrate that the suggested algorithm is efficient and highly competitive, improving or matching the current best-known solution in 42% of the test cases.

Fast and high precision algorithms for optimization in large-scale genomic problems

There are several very difficult problems related to genetic or genomic analysis that belong to the field of discrete optimization in a set of all possible orders. With n elements (points, markers, clones, sequences, etc.), the number of all possible orders is n!/2 and only one of these is considered to be the true order. A classical formulation of a similar mathematical problem is the well-known traveling salesperson problem model (TSP). Genetic analogues of this problem include: ordering in multilocus genetic mapping, evolutionary tree reconstruction, building physical maps (contig assembling for overlapping clones and radiation hybrid mapping), and others. A novel, fast and reliable hybrid algorithm based on evolution strategy and guided local search discrete optimization was developed for TSP formulation of the multilocus mapping problems. High performance and high precision of the employed algorithm named guided evolution strategy (GES) allows verification of the obtained multilocus orders based on different computing-intensive approaches (e.g., bootstrap or jackknife) for detection and removing unreliable marker loci, hence, stabilizing the resulting paths. The efficiency of the proposed algorithm is demonstrated on standard TSP problems and on simulated data of multilocus genetic maps up to 1000 points per linkage group.

Two-Phase Analysis in Consensus Genetic Mapping

Numerous mapping projects conducted on different species have generated an abundance of mapping data. Consequently, many multilocus maps have been constructed using diverse mapping populations and marker sets for the same organism. The quality of maps varies broadly among populations, marker sets, and software used, necessitating efforts to integrate the mapping information and generate consensus maps. The problem of consensus genetic mapping (MCGM) is by far more challenging compared with genetic mapping based on a single dataset, which by itself is also cumbersome. The additional complications introduced by consensus analysis include inter-population differences in recombination rate and exchange distribution along chromosomes; variations in dominance of the employed markers; and use of different subsets of markers in different labs. Hence, it is necessary to handle arbitrary patterns of shared sets of markers and different level of mapping data quality. In this article, we introduce a two-phase approach for solving MCGM. In phase 1, for each dataset, multilocus ordering is performed combined with iterative jackknife resampling to evaluate the stability of marker orders. In this phase, the ordering problem is reduced to the well-known traveling salesperson problem (TSP). Namely, for each dataset, we look for order that gives minimum sum of recombination distances between adjacent markers. In phase 2, the optimal consensus order of shared markers is selected from the set of allowed orders and gives the minimal sum of total lengths of nonconflicting maps of the chromosome. This criterion may be used in different modifications to take into account the variation in quality of the original data (population size, marker quality, etc.). In the foregoing formulation, consensus mapping is considered as a specific version of TSP that can be referred to as “synchronized TSP.” The conflicts detected after phase 1 are resolved using either a heuristic algorithm over the entire chromosome or an exact/heuristic algorithm applied subsequently to the revealed small non-overlapping regions with conflicts separated by non-conflicting regions. The proposed approach was tested on a wide range of simulated data and real datasets from maize.

Building Ultra-Dense Genetic Maps in the Presence of Genotyping Errors and Missing Data

Recent advances of genomic technologies have opened unprecedented possibilities in building high-quality ultra-dense genetic maps. However, with very large numbers of markers available for a mapping population, most of the markers will remain inseparable by recombination. Real situations are also complicated by genotyping errors, which “diversify” a certain part of the markers that would be identical in error-free situations. The higher the error rate the more difficult is the problem of building a reliable map. In our algorithm, we assume that error-free markers can be selected based on the presence of “twins”. There is also a probability of an opposite effect, when non-identical markers may become “twins” because of genotyping errors. Thus, a certain threshold is introduced for the selection of markers with a sufficient number of twins. The developed algorithm (implemented in MultiPoint software) enables mapping big sets of markers (~105–106). Unlike some other algorithms used in building ultra-dense genetic maps, the proposed “twins” approach does not need any prior information (e.g., anchor markers), and hence can be applied to genetically poorly studied organisms.

Looking for Organization Patterns of Highly Expressed Genes: Purine-Pyrimidine Composition of Precursor mRNAs

We analyzed precursor messenger RNAs (pre-mRNAs) of 12 eukaryotic species. In each species, three groups of highly expressed genes, ribosomal proteins, heat shock proteins, and amino-acyl tRNA synthetases, were compared with a control group (randomly selected genes). The purine-pyrimidine (R-Y) composition of pre-mRNAs of the three targeted gene groups proved to differ significantly from the control. The exons of the three groups tested have higher purine contents and R-tract abundance and lower abundance of Y-tracts compared to the control (R-tract—tract of sequential purines with Rn ≥ 5; Y-tract—tract of sequential pyrimidines with Yn ≥ 5). In species widely employing “intron definition” in the splicing process, the Y content of introns of the three targeted groups appeared to be higher compared to the control group. Furthermore, in all examined species, the introns of the targeted genes have a lower abundance of R-tracts compared to the control. We hypothesized that the R-Y composition of the targeted gene groups contributes to high rate and efficiency of both splicing and translation, in addition to the mRNA coding role. This is presumably achieved by (1) reducing the possibility of the formation of secondary structures in the mRNA, (2) using the R-tracts and R-biased sequences as exonic splicing enhancers, (3) lowering the amount of targets for pyrimidine tract binding protein in the exons, and (4) reducing the amount of target sequences for binding of serine/arginine-rich (SR) proteins in the introns, thereby allowing SR proteins to bind to proper (exonic) targets.

Building Ultra-high Density Linkage Maps Based on Efficient Filtering of Trustable Markers

This study concerns building high-density genetic maps in situations with intrachromosomal recombination rate heterogeneity and differences in genotyping The study is focused on addressing the problem of building genetic maps in the presence of ∼103–104 of markers per chromosome. We consider a spectrum of situations with intrachromosomal heterogeneity of recombination rate, different level of genotyping errors, and missing data. In the ideal scenario of the absence of errors and missing data, the majority of markers should appear as groups of cosegregating markers (“twins”) representing no challenge for map construction. The central aspect of the proposed approach is to take into account the structure of the marker space, where each twin group (TG) and singleton markers are represented as points of this space. The confounding effect of genotyping errors and missing data leads to reduction of TG size, but upon a low level of these effects surviving TGs can still be used as a source of reliable skeletal markers. Increase in the level of confounding effects results in a considerable decrease in the number or even disappearance of usable TGs and, correspondingly, of skeletal markers. Here, we show that the paucity of informative markers can be compensated by detecting kernels of markers in the marker space using a clustering procedure, and demonstrate the utility of this approach for high-density genetic map construction on simulated and experimentally obtained genotyping datasets.