Characterizing Dynamic Optimization Benchmarks for the Comparison of Multi-Modal Tracking Algorithms

Population-based metaheuristics, such as particle swarm optimization (PSO), have been employed to solve many real-world optimization problems. Although it is of- ten sufficient to find a single solution to these problems, there does exist those cases where identifying multiple, diverse solutions can be beneficial or even required. Some of these problems are further complicated by a change in their objective function over time. This type of optimization is referred to as dynamic, multi-modal optimization. Algorithms which exploit multiple optima in a search space are identified as niching algorithms. Although numerous dynamic, niching algorithms have been developed, their performance is often measured solely on their ability to find a single, global optimum. Furthermore, the comparisons often use synthetic benchmarks whose landscape characteristics are generally limited and unknown. This thesis provides a landscape analysis of the dynamic benchmark functions commonly developed for multi-modal optimization. The benchmark analysis results reveal that the mechanisms responsible for dynamism in the current dynamic bench- marks do not significantly affect landscape features, thus suggesting a lack of representation for problems whose landscape features vary over time. This analysis is used in a comparison of current niching algorithms to identify the effects that specific landscape features have on niching performance. Two performance metrics are proposed to measure both the scalability and accuracy of the niching algorithms. The algorithm comparison results demonstrate the algorithms best suited for a variety of dynamic environments. This comparison also examines each of the algorithms in terms of their niching behaviours and analyzing the range and trade-off between scalability and accuracy when tuning the algorithms respective parameters. These results contribute to the understanding of current niching techniques as well as the problem features that ultimately dictate their success.

Optimization of p-cycle protection schemes in optical networks

La survie des réseaux est un domaine d'étude technique très intéressant ainsi qu'une préoccupation critique dans la conception des réseaux. Compte tenu du fait que de plus en plus de données sont transportées à travers des réseaux de communication, une simple panne peut interrompre des millions d'utilisateurs et engendrer des millions de dollars de pertes de revenu. Les techniques de protection des réseaux consistent à fournir une capacité supplémentaire dans un réseau et à réacheminer les flux automatiquement autour de la panne en utilisant cette disponibilité de capacité. Cette thèse porte sur la conception de réseaux optiques intégrant des techniques de survie qui utilisent des schémas de protection basés sur les p-cycles. Plus précisément, les p-cycles de protection par chemin sont exploités dans le contexte de pannes sur les liens. Notre étude se concentre sur la mise en place de structures de protection par p-cycles, et ce, en supposant que les chemins d'opération pour l'ensemble des requêtes sont définis a priori. La majorité des travaux existants utilisent des heuristiques ou des méthodes de résolution ayant de la difficulté à résoudre des instances de grande taille. L'objectif de cette thèse est double. D'une part, nous proposons des modèles et des méthodes de résolution capables d'aborder des problèmes de plus grande taille que ceux déjà présentés dans la littérature. D'autre part, grâce aux nouveaux algorithmes, nous sommes en mesure de produire des solutions optimales ou quasi-optimales. Pour ce faire, nous nous appuyons sur la technique de génération de colonnes, celle-ci étant adéquate pour résoudre des problèmes de programmation linéaire de grande taille. Dans ce projet, la génération de colonnes est utilisée comme une façon intelligente d'énumérer implicitement des cycles prometteurs. Nous proposons d'abord des formulations pour le problème maître et le problème auxiliaire ainsi qu'un premier algorithme de génération de colonnes pour la conception de réseaux protegées par des p-cycles de la protection par chemin. L'algorithme obtient de meilleures solutions, dans un temps raisonnable, que celles obtenues par les méthodes existantes. Par la suite, une formulation plus compacte est proposée pour le problème auxiliaire. De plus, nous présentons une nouvelle méthode de décomposition hiérarchique qui apporte une grande amélioration de l'efficacité globale de l'algorithme. En ce qui concerne les solutions en nombres entiers, nous proposons deux méthodes heurisiques qui arrivent à trouver des bonnes solutions. Nous nous attardons aussi à une comparaison systématique entre les p-cycles et les schémas classiques de protection partagée. Nous effectuons donc une comparaison précise en utilisant des formulations unifiées et basées sur la génération de colonnes pour obtenir des résultats de bonne qualité. Par la suite, nous évaluons empiriquement les versions orientée et non-orientée des p-cycles pour la protection par lien ainsi que pour la protection par chemin, dans des scénarios de trafic asymétrique. Nous montrons quel est le coût de protection additionnel engendré lorsque des systèmes bidirectionnels sont employés dans de tels scénarios. Finalement, nous étudions une formulation de génération de colonnes pour la conception de réseaux avec des p-cycles en présence d'exigences de disponibilité et nous obtenons des premières bornes inférieures pour ce problème.

Approches générales de résolution pour les problèmes multi-attributs de tournées de véhicules et confection d'horaires

Thèse réalisée en cotutelle entre l'Université de Montréal et l'Université de Technologie de Troyes

Improving sampling, optimization and feature extraction in Boltzmann machines

L’apprentissage supervisé de réseaux hiérarchiques à grande échelle connaît présentement un succès fulgurant. Malgré cette effervescence, l’apprentissage non-supervisé représente toujours, selon plusieurs chercheurs, un élément clé de l’Intelligence Artificielle, où les agents doivent apprendre à partir d’un nombre potentiellement limité de données. Cette thèse s’inscrit dans cette pensée et aborde divers sujets de recherche liés au problème d’estimation de densité par l’entremise des machines de Boltzmann (BM), modèles graphiques probabilistes au coeur de l’apprentissage profond. Nos contributions touchent les domaines de l’échantillonnage, l’estimation de fonctions de partition, l’optimisation ainsi que l’apprentissage de représentations invariantes. Cette thèse débute par l’exposition d’un nouvel algorithme d'échantillonnage adaptatif, qui ajuste (de fa ̧con automatique) la température des chaînes de Markov sous simulation, afin de maintenir une vitesse de convergence élevée tout au long de l’apprentissage. Lorsqu’utilisé dans le contexte de l’apprentissage par maximum de vraisemblance stochastique (SML), notre algorithme engendre une robustesse accrue face à la sélection du taux d’apprentissage, ainsi qu’une meilleure vitesse de convergence. Nos résultats sont présent ́es dans le domaine des BMs, mais la méthode est générale et applicable à l’apprentissage de tout modèle probabiliste exploitant l’échantillonnage par chaînes de Markov. Tandis que le gradient du maximum de vraisemblance peut-être approximé par échantillonnage, l’évaluation de la log-vraisemblance nécessite un estimé de la fonction de partition. Contrairement aux approches traditionnelles qui considèrent un modèle donné comme une boîte noire, nous proposons plutôt d’exploiter la dynamique de l’apprentissage en estimant les changements successifs de log-partition encourus à chaque mise à jour des paramètres. Le problème d’estimation est reformulé comme un problème d’inférence similaire au filtre de Kalman, mais sur un graphe bi-dimensionnel, où les dimensions correspondent aux axes du temps et au paramètre de température. Sur le thème de l’optimisation, nous présentons également un algorithme permettant d’appliquer, de manière efficace, le gradient naturel à des machines de Boltzmann comportant des milliers d’unités. Jusqu’à présent, son adoption était limitée par son haut coût computationel ainsi que sa demande en mémoire. Notre algorithme, Metric-Free Natural Gradient (MFNG), permet d’éviter le calcul explicite de la matrice d’information de Fisher (et son inverse) en exploitant un solveur linéaire combiné à un produit matrice-vecteur efficace. L’algorithme est prometteur: en terme du nombre d’évaluations de fonctions, MFNG converge plus rapidement que SML. Son implémentation demeure malheureusement inefficace en temps de calcul. Ces travaux explorent également les mécanismes sous-jacents à l’apprentissage de représentations invariantes. À cette fin, nous utilisons la famille de machines de Boltzmann restreintes “spike & slab” (ssRBM), que nous modifions afin de pouvoir modéliser des distributions binaires et parcimonieuses. Les variables latentes binaires de la ssRBM peuvent être rendues invariantes à un sous-espace vectoriel, en associant à chacune d’elles, un vecteur de variables latentes continues (dénommées “slabs”). Ceci se traduit par une invariance accrue au niveau de la représentation et un meilleur taux de classification lorsque peu de données étiquetées sont disponibles. Nous terminons cette thèse sur un sujet ambitieux: l’apprentissage de représentations pouvant séparer les facteurs de variations présents dans le signal d’entrée. Nous proposons une solution à base de ssRBM bilinéaire (avec deux groupes de facteurs latents) et formulons le problème comme l’un de “pooling” dans des sous-espaces vectoriels complémentaires.

Production, purification, genetic characterization and application studies of tannase enzyme from marine fungus Aspergillus awamori

Marine fungi remain totally unexplored as a source of industrial enzyme and prospective applications. Further tannase production by a marine organism has so far not been established. The primary objective of this study included the evaluation of the potential of Aspergillus awamori isolated from sea water as part of an earlier study and available in the culture collection of the Microbial technology laboratory for tannase production through different fermentation methods, optimization of bioprocess variables by statistical methods, purification and characterization of the enzyme, genetic study, and assessment of its potential applications.

Mean Squared Residue Based Biclustering Algorithms for the Analysis of Gene Expression Data

Computational Biology is the research are that contributes to the analysis of biological data through the development of algorithms which will address significant research problems.The data from molecular biology includes DNA,RNA ,Protein and Gene expression data.Gene Expression Data provides the expression level of genes under different conditions.Gene expression is the process of transcribing the DNA sequence of a gene into mRNA sequences which in turn are later translated into proteins.The number of copies of mRNA produced is called the expression level of a gene.Gene expression data is organized in the form of a matrix. Rows in the matrix represent genes and columns in the matrix represent experimental conditions.Experimental conditions can be different tissue types or time points.Entries in the gene expression matrix are real values.Through the analysis of gene expression data it is possible to determine the behavioral patterns of genes such as similarity of their behavior,nature of their interaction,their respective contribution to the same pathways and so on. Similar expression patterns are exhibited by the genes participating in the same biological process.These patterns have immense relevance and application in bioinformatics and clinical research.Theses patterns are used in the medical domain for aid in more accurate diagnosis,prognosis,treatment planning.drug discovery and protein network analysis.To identify various patterns from gene expression data,data mining techniques are essential.Clustering is an important data mining technique for the analysis of gene expression data.To overcome the problems associated with clustering,biclustering is introduced.Biclustering refers to simultaneous clustering of both rows and columns of a data matrix. Clustering is a global whereas biclustering is a local model.Discovering local expression patterns is essential for identfying many genetic pathways that are not apparent otherwise.It is therefore necessary to move beyond the clustering paradigm towards developing approaches which are capable of discovering local patterns in gene expression data.A biclusters is a submatrix of the gene expression data matrix.The rows and columns in the submatrix need not be contiguous as in the gene expression data matrix.Biclusters are not disjoint.Computation of biclusters is costly because one will have to consider all the combinations of columans and rows in order to find out all the biclusters.The search space for the biclustering problem is 2 m+n where m and n are the number of genes and conditions respectively.Usually m+n is more than 3000.The biclustering problem is NP-hard.Biclustering is a powerful analytical tool for the biologist.The research reported in this thesis addresses the problem of biclustering.Ten algorithms are developed for the identification of coherent biclusters from gene expression data.All these algorithms are making use of a measure called mean squared residue to search for biclusters.The objective here is to identify the biclusters of maximum size with the mean squared residue lower than a given threshold. All these algorithms begin the search from tightly coregulated submatrices called the seeds.These seeds are generated by K-Means clustering algorithm.The algorithms developed can be classified as constraint based,greedy and metaheuristic.Constarint based algorithms uses one or more of the various constaints namely the MSR threshold and the MSR difference threshold.The greedy approach makes a locally optimal choice at each stage with the objective of finding the global optimum.In metaheuristic approaches particle Swarm Optimization(PSO) and variants of Greedy Randomized Adaptive Search Procedure(GRASP) are used for the identification of biclusters.These algorithms are implemented on the Yeast and Lymphoma datasets.Biologically relevant and statistically significant biclusters are identified by all these algorithms which are validated by Gene Ontology database.All these algorithms are compared with some other biclustering algorithms.Algorithms developed in this work overcome some of the problems associated with the already existing algorithms.With the help of some of the algorithms which are developed in this work biclusters with very high row variance,which is higher than the row variance of any other algorithm using mean squared residue, are identified from both Yeast and Lymphoma data sets.Such biclusters which make significant change in the expression level are highly relevant biologically.

An Error-Localization, Validation and Optimization Tool for Embedded Code Augmentation: an Architecture Oriented Approach

Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.Embedded systems are usually designed for a single or a specified set of tasks. This specificity means the system design as well as its hardware/software development can be highly optimized. Embedded software must meet the requirements such as high reliability operation on resource-constrained platforms, real time constraints and rapid development. This necessitates the adoption of static machine codes analysis tools running on a host machine for the validation and optimization of embedded system codes, which can help meet all of these goals. This could significantly augment the software quality and is still a challenging field.This dissertation contributes to an architecture oriented code validation, error localization and optimization technique assisting the embedded system designer in software debugging, to make it more effective at early detection of software bugs that are otherwise hard to detect, using the static analysis of machine codes. The focus of this work is to develop methods that automatically localize faults as well as optimize the code and thus improve the debugging process as well as quality of the code.Validation is done with the help of rules of inferences formulated for the target processor. The rules govern the occurrence of illegitimate/out of place instructions and code sequences for executing the computational and integrated peripheral functions. The stipulated rules are encoded in propositional logic formulae and their compliance is tested individually in all possible execution paths of the application programs. An incorrect sequence of machine code pattern is identified using slicing techniques on the control flow graph generated from the machine code.An algorithm to assist the compiler to eliminate the redundant bank switching codes and decide on optimum data allocation to banked memory resulting in minimum number of bank switching codes in embedded system software is proposed. A relation matrix and a state transition diagram formed for the active memory bank state transition corresponding to each bank selection instruction is used for the detection of redundant codes. Instances of code redundancy based on the stipulated rules for the target processor are identified.This validation and optimization tool can be integrated to the system development environment. It is a novel approach independent of compiler/assembler, applicable to a wide range of processors once appropriate rules are formulated. Program states are identified mainly with machine code pattern, which drastically reduces the state space creation contributing to an improved state-of-the-art model checking. Though the technique described is general, the implementation is architecture oriented, and hence the feasibility study is conducted on PIC16F87X microcontrollers. The proposed tool will be very useful in steering novices towards correct use of difficult microcontroller features in developing embedded systems.

Genetic Programming meets Model-Driven Development

Genetic programming is known to provide good solutions for many problems like the evolution of network protocols and distributed algorithms. In such cases it is most likely a hardwired module of a design framework that assists the engineer to optimize specific aspects of the system to be developed. It provides its results in a fixed format through an internal interface. In this paper we show how the utility of genetic programming can be increased remarkably by isolating it as a component and integrating it into the model-driven software development process. Our genetic programming framework produces XMI-encoded UML models that can easily be loaded into widely available modeling tools which in turn posses code generation as well as additional analysis and test capabilities. We use the evolution of a distributed election algorithm as an example to illustrate how genetic programming can be combined with model-driven development. This example clearly illustrates the advantages of our approach – the generation of source code in different programming languages.

From Genetic Algorithms to Efficient Organization

The work described in this thesis began as an inquiry into the nature and use of optimization programs based on "genetic algorithms." That inquiry led, eventually, to three powerful heuristics that are broadly applicable in gradient-ascent programs: First, remember the locations of local maxima and restart the optimization program at a place distant from previously located local maxima. Second, adjust the size of probing steps to suit the local nature of the terrain, shrinking when probes do poorly and growing when probes do well. And third, keep track of the directions of recent successes, so as to probe preferentially in the direction of most rapid ascent. These algorithms lie at the core of a novel optimization program that illustrates the power to be had from deploying them together. The efficacy of this program is demonstrated on several test problems selected from a variety of fields, including De Jong's famous test-problem suite, the traveling salesman problem, the problem of coordinate registration for image guided surgery, the energy minimization problem for determining the shape of organic molecules, and the problem of assessing the structure of sedimentary deposits using seismic data.

Optimization of inverse reflector design

Aquesta tesi presenta un nou mètode pel disseny invers de reflectors. Ens hem centrat en tres temes principals: l’ús de fonts de llum reals i complexes, la definició d’un algoritme ràpid pel càlcul de la il•luminació del reflector, i la definició d’un algoritme d’optimització per trobar més eficientment el reflector desitjat. Les fonts de llum estan representades per models near-field, que es comprimeixen amb un error molt petit, fins i tot per fonts de llum amb milions de raigs i objectes a il•luminar molt propers. Llavors proposem un mètode ràpid per obtenir la distribució de la il•luminació d’un reflector i la seva comparació amb la il•luminació desitjada, i que treballa completament en la GPU. Finalment, proposem un nou mètode d’optimització global que permet trobar la solució en menys passos que molts altres mètodes d’optimització clàssics, i alhora evitant mínims locals.

Multi-objective optimization scheme for static and dynamic multicast flows

Muchas de las nuevas aplicaciones emergentes de Internet tales como TV sobre Internet, Radio sobre Internet,Video Streamming multi-punto, entre otras, necesitan los siguientes requerimientos de recursos: ancho de banda consumido, retardo extremo-a-extremo, tasa de paquetes perdidos, etc. Por lo anterior, es necesario formular una propuesta que especifique y provea para este tipo de aplicaciones los recursos necesarios para su buen funcionamiento. En esta tesis, proponemos un esquema de ingeniería de tráfico multi-objetivo a través del uso de diferentes árboles de distribución para muchos flujos multicast. En este caso, estamos usando la aproximación de múltiples caminos para cada nodo egreso y de esta forma obtener la aproximación de múltiples árboles y a través de esta forma crear diferentes árboles multicast. Sin embargo, nuestra propuesta resuelve la fracción de la división del tráfico a través de múltiples árboles. La propuesta puede ser aplicada en redes MPLS estableciendo rutas explícitas en eventos multicast. En primera instancia, el objetivo es combinar los siguientes objetivos ponderados dentro de una métrica agregada: máxima utilización de los enlaces, cantidad de saltos, el ancho de banda total consumido y el retardo total extremo-a-extremo. Nosotros hemos formulado esta función multi-objetivo (modelo MHDB-S) y los resultados obtenidos muestran que varios objetivos ponderados son reducidos y la máxima utilización de los enlaces es minimizada. El problema es NP-duro, por lo tanto, un algoritmo es propuesto para optimizar los diferentes objetivos. El comportamiento que obtuvimos usando este algoritmo es similar al que obtuvimos con el modelo. Normalmente, durante la transmisión multicast los nodos egresos pueden salir o entrar del árbol y por esta razón en esta tesis proponemos un esquema de ingeniería de tráfico multi-objetivo usando diferentes árboles para grupos multicast dinámicos. (en el cual los nodos egresos pueden cambiar durante el tiempo de vida de la conexión). Si un árbol multicast es recomputado desde el principio, esto podría consumir un tiempo considerable de CPU y además todas las comuicaciones que están usando el árbol multicast serán temporalmente interrumpida. Para aliviar estos inconvenientes, proponemos un modelo de optimización (modelo dinámico MHDB-D) que utilice los árboles multicast previamente computados (modelo estático MHDB-S) adicionando nuevos nodos egreso. Usando el método de la suma ponderada para resolver el modelo analítico, no necesariamente es correcto, porque es posible tener un espacio de solución no convexo y por esta razón algunas soluciones pueden no ser encontradas. Adicionalmente, otros tipos de objetivos fueron encontrados en diferentes trabajos de investigación. Por las razones mencionadas anteriormente, un nuevo modelo llamado GMM es propuesto y para dar solución a este problema un nuevo algoritmo usando Algoritmos Evolutivos Multi-Objetivos es propuesto. Este algoritmo esta inspirado por el algoritmo Strength Pareto Evolutionary Algorithm (SPEA). Para dar una solución al caso dinámico con este modelo generalizado, nosotros hemos propuesto un nuevo modelo dinámico y una solución computacional usando Breadth First Search (BFS) probabilístico. Finalmente, para evaluar nuestro esquema de optimización propuesto, ejecutamos diferentes pruebas y simulaciones. Las principales contribuciones de esta tesis son la taxonomía, los modelos de optimización multi-objetivo para los casos estático y dinámico en transmisiones multicast (MHDB-S y MHDB-D), los algoritmos para dar solución computacional a los modelos. Finalmente, los modelos generalizados también para los casos estático y dinámico (GMM y GMM Dinámico) y las propuestas computacionales para dar slución usando MOEA y BFS probabilístico.

Algorithm for generating defective graphene sheets

An algorithm is presented for the generation of molecular models of defective graphene fragments, containing a majority of 6-membered rings with a small number of 5- and 7-membered rings as defects. The structures are generated from an initial random array of points in 2D space, which are then subject to Delaunay triangulation. The dual of the triangulation forms a Voronoi tessellation of polygons with a range of ring sizes. An iterative cycle of refinement, involving deletion and addition of points followed by further triangulation, is performed until the user-defined criteria for the number of defects are met. The array of points and connectivities are then converted to a molecular structure and subject to geometry optimization using a standard molecular modeling package to generate final atomic coordinates. On the basis of molecular mechanics with minimization, this automated method can generate structures, which conform to user-supplied criteria and avoid the potential bias associated with the manual building of structures. One application of the algorithm is the generation of structures for the evaluation of the reactivity of different defect sites. Ab initio electronic structure calculations on a representative structure indicate preferential fluorination close to 5-ring defects.

Genetic analysis of complex demographic scenarios: Spatially expanding populations of the cane toad, Bufo marinus

Inferring the spatial expansion dynamics of invading species from molecular data is notoriously difficult due to the complexity of the processes involved. For these demographic scenarios, genetic data obtained from highly variable markers may be profitably combined with specific sampling schemes and information from other sources using a Bayesian approach. The geographic range of the introduced toad Bufo marinus is still expanding in eastern and northern Australia, in each case from isolates established around 1960. A large amount of demographic and historical information is available on both expansion areas. In each area, samples were collected along a transect representing populations of different ages and genotyped at 10 microsatellite loci. Five demographic models of expansion, differing in the dispersal pattern for migrants and founders and in the number of founders, were considered. Because the demographic history is complex, we used an approximate Bayesian method, based on a rejection-regression algorithm. to formally test the relative likelihoods of the five models of expansion and to infer demographic parameters. A stepwise migration-foundation model with founder events was statistically better supported than other four models in both expansion areas. Posterior distributions supported different dynamics of expansion in the studied areas. Populations in the eastern expansion area have a lower stable effective population size and have been founded by a smaller number of individuals than those in the northern expansion area. Once demographically stabilized, populations exchange a substantial number of effective migrants per generation in both expansion areas, and such exchanges are larger in northern than in eastern Australia. The effective number of migrants appears to be considerably lower than that of founders in both expansion areas. We found our inferences to be relatively robust to various assumptions on marker. demographic, and historical features. The method presented here is the only robust, model-based method available so far, which allows inferring complex population dynamics over a short time scale. It also provides the basis for investigating the interplay between population dynamics, drift, and selection in invasive species.

Search space pruning and global optimization of multiple gravity assist trajectories with deep space manoeuvres

This paper deals with the design of optimal multiple gravity assist trajectories with deep space manoeuvres. A pruning method which considers the sequential nature of the problem is presented. The method locates feasible vectors using local optimization and applies a clustering algorithm to find reduced bounding boxes which can be used in a subsequent optimization step. Since multiple local minima remain within the pruned search space, the use of a global optimization method, such as Differential Evolution, is suggested for finding solutions which are likely to be close to the global optimum. Two case studies are presented.

Optimization algorithms in FMRF model-based segmentation for LIDAR data and co-registered bands

In this paper, a fuzzy Markov random field (FMRF) model is used to segment land-objects into free, grass, building, and road regions by fusing remotely, sensed LIDAR data and co-registered color bands, i.e. scanned aerial color (RGB) photo and near infra-red (NIR) photo. An FMRF model is defined as a Markov random field (MRF) model in a fuzzy domain. Three optimization algorithms in the FMRF model, i.e. Lagrange multiplier (LM), iterated conditional mode (ICM), and simulated annealing (SA), are compared with respect to the computational cost and segmentation accuracy. The results have shown that the FMRF model-based ICM algorithm balances the computational cost and segmentation accuracy in land-cover segmentation from LIDAR data and co-registered bands.