On Total Variation Minimization and Surface Evolution Using Parametric Maximum Flows

In a recent paper Boykov et al. (LNCS, Vol. 3953, pp. 409–422, 2006) propose an approach for computing curve and surface evolution using a variational approach and the geo-cuts method of Boykov and Kolmogorov (International conference on computer vision, pp. 26–33, 2003). We recall in this paper how this is related to well-known approaches for mean curvature motion, introduced by Almgren et al. (SIAM Journal on Control and Optimization 31(2):387–438, 1993) and Luckhaus and Sturzenhecker (Calculus of Variations and Partial Differential Equations 3(2):253–271, 1995), and show how the corresponding problems can be solved with sub-pixel accuracy using Parametric Maximum Flow techniques. This provides interesting algorithms for computing crystalline curvature motion, possibly with a forcing term. A. Chambolle’s research supported by ANR project “MICA”, grant ANR-08-BLAN-0082. J. Darbon’s research supported by ONR grant N000140710810.     

Symbolic computation of strongly connected components and fair cycles using saturation

The computation of strongly connected components (SCCs) in discrete-state models is a critical step in formal verification of LTL and fair CTL properties, but the potentially huge number of reachable states and SCCs constitutes a formidable challenge. We consider the problem of computing the set of states in SCCs or terminal SCCs in an asynchronous system. We employ the idea of saturation, which has shown clear advantages in symbolic state-space exploration (Ciardo et al. in Softw Tools Technol Transf 8(1):4–25, 2006; Zhao and Ciardo in Proceedings of 7th international symposium on automated technology for verification and analysis, pp 368–381, 2009), to improve two previously proposed approaches. We use saturation to speed up state exploration when computing each SCC in the Xie-Beerel algorithm, and we compute the transitive closure of the transition relation using a novel algorithm based on saturation. Furthermore, we show that the techniques we developed are also applicable to the computation of fair cycles. Experimental results indicate that the improved algorithms using saturation achieve a substantial speedup over previous BFS algorithms. In particular, with the new transitive closure computation algorithm, up to 10¹⁵⁰ SCCs can be explored within a few seconds.     

Ranking of fuzzy numbers by a new metric

In this paper, a new approach for comparison among fuzzy numbers based on new metric distance (D _TM) is proposed. All reasonable properties of ranking function are proved. At first, the distance on the interval numbers based on convex hall of endpoints is proposed. The existing distance measures for interval numbers, (Bardossy and Duckstein in Fuzzy rule-based modeling with applications to geophysical, biological and engineering systems. CRC press, Boca Raton, 1995; Diamond in Info Sci 46:141–157, 1988; Diamond and Korner in Comput Math Appl 33:15–32, 1997; Tran and Duckstein in Fuzzy Set Syst 130:331–341, 2002; Diamond and Tanaka Fuzzy regression analysis. In: Slowinski R (ed) Fuzzy sets in decision analysis, operations research and statistics. Kluwer, Boston, pp 349–387, 1998) do not satisfy the properties of a metric distance, while the proposed distance does. It is extended to fuzzy numbers and its properties are proved in detail. Finally, we compare the proposed definition with some of the known ones.     

Mode Decomposition Evolution Equations

Partial differential equation (PDE) based methods have become some of the most powerful tools for exploring the fundamental problems in signal processing, image processing, computer vision, machine vision and artificial intelligence in the past two decades. The advantages of PDE based approaches are that they can be made fully automatic, robust for the analysis of images, videos and high dimensional data. A fundamental question is whether one can use PDEs to perform all the basic tasks in the image processing. If one can devise PDEs to perform full-scale mode decomposition for signals and images, the modes thus generated would be very useful for secondary processing to meet the needs in various types of signal and image processing. Despite of great progress in PDE based image analysis in the past two decades, the basic roles of PDEs in image/signal analysis are only limited to PDE based low-pass filters, and their applications to noise removal, edge detection, segmentation, etc. At present, it is not clear how to construct PDE based methods for full-scale mode decomposition. The above-mentioned limitation of most current PDE based image/signal processing methods is addressed in the proposed work, in which we introduce a family of mode decomposition evolution equations (MoDEEs) for a vast variety of applications. The MoDEEs are constructed as an extension of a PDE based high-pass filter (Wei and Jia in Europhys. Lett. 59(6):814–819, 2002) by using arbitrarily high order PDE based low-pass filters introduced by Wei (IEEE Signal Process. Lett. 6(7):165–167, 1999). The use of arbitrarily high order PDEs is essential to the frequency localization in the mode decomposition. Similar to the wavelet transform, the present MoDEEs have a controllable time-frequency localization and allow a perfect reconstruction of the original function. Therefore, the MoDEE operation is also called a PDE transform. However, modes generated from the present approach are in the spatial or time domain and can be easily used for secondary processing. Various simplifications of the proposed MoDEEs, including a linearized version, and an algebraic version, are discussed for computational convenience. The Fourier pseudospectral method, which is unconditionally stable for linearized high order MoDEEs, is utilized in our computation. Validation is carried out to mode separation of high frequency adjacent modes. Applications are considered to signal and image denoising, image edge detection, feature extraction, enhancement etc. It is hoped that this work enhances the understanding of high order PDEs and yields robust and useful tools for image and signal analysis.     

Bidirectional Optimization from Reasoning and Learning in Games

We reopen the investigation into the formal and conceptual relationship between bidirectional optimality theory (Blutner in J Semant 15(2):115–162, 1998, J Semant 17(3):189–216, 2000) and game theory. Unlike a likeminded previous endeavor by Dekker and van Rooij (J Semant 17:217–242, 2000), we consider signaling games not strategic games, and seek to ground bidirectional optimization once in a model of rational step-by-step reasoning and once in a model of reinforcement learning. We give sufficient conditions for equivalence of bidirectional optimality and the former, and show based on numerical simulations that bidirectional optimization may be thought of as a process of reinforcement learning with lateral inhibition.     

On body shapes providing maximum depth of penetration

The problem of maximization of the depth of penetration of rigid impactor into semi-infinite solid media (concrete shield) is investigated analytically and numerically using two-stage model and experimental data of Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997). The shape of the axisymmetric rigid impactor has been taken as an unknown design variable. To solve the formulated optimization problem for nonadditive functional, we expressed the depth of penetration (DOP) under some isoperimetric constraints. We apply approaches based on analytical and qualitative variational methods and numerical optimization algorithm of global search. Basic attention for considered optimization problem was given to constraints on the mass of penetrated bodies, expressed by the volume in the case of penetrated solid body and by the surface area in the case of penetrated thin-walled rigid shell. As a result of performed investigation, based on two-term and three-term two stage models proposed by Forrestal et al. (Int J Impact Eng 15(4):396–405, 1994), Forrestal and Tzou (Int J Solids Struct 34(31–32):4127–4146, 1997) and effectively developed by Ben-Dor et al. (Comp Struct 56:243–248, 2002, Comput Struct 81(1):9–14, 2003a, Int J Solids Struct 40(17):4487–4500, 2003b, Mech Des Struct Mach 34(2): 139–156, 2006), we found analytical and numerical solutions and analyzed singularities of optimal forms.     

All-Pairs Shortest Paths with Real Weights in <Emphasis Type="Italic">O</Emphasis>(<Emphasis Type="Italic">n</Emphasis><Superscript>3</Superscript>/log <Emphasis Type="Italic">n</Emphasis>) Time

We describe an O(n ³/log n)-time algorithm for the all-pairs-shortest-paths problem for a real-weighted directed graph with n vertices. This slightly improves a series of previous, slightly subcubic algorithms by Fredman (SIAM J. Comput. 5:49–60, 1976), Takaoka (Inform. Process. Lett. 43:195–199, 1992), Dobosiewicz (Int. J. Comput. Math. 32:49–60, 1990), Han (Inform. Process. Lett. 91:245–250, 2004), Takaoka (Proc. 10th Int. Conf. Comput. Comb., Lect. Notes Comput. Sci., vol. 3106, pp. 278–289, Springer, 2004), and Zwick (Proc. 15th Int. Sympos. Algorithms and Computation, Lect. Notes Comput. Sci., vol. 3341, pp. 921–932, Springer, 2004). The new algorithm is surprisingly simple and different from previous ones. A preliminary version of this paper appeared in Proc. 9th Workshop Algorithms Data Struct. (WADS), Lect. Notes Comput. Sci., vol. 3608, pp. 318–324, Springer, 2005.     

Improved Approximation Results for the Minimum Energy Broadcasting Problem

In this paper we present new results on the performance of the Minimum Spanning Tree heuristic for the Minimum Energy Broadcast Routing (MEBR) problem. We first prove that, for any number of dimensions d≥2, the approximation ratio of the heuristic does not increase when the power attenuation coefficient α, that is the exponent to which the coverage distance must be raised to give the emission power, grows. Moreover, we show that, for any fixed instance, as a limit for α going to infinity, the ratio tends to the lower bound of Clementi et al. (Proceedings of the 18th annual symposium on theoretical aspects of computer science (STACS), pp. 121–131, 2001), Wan et al. (Wirel. Netw. 8(6):607–617, 2002) given by the d-dimensional kissing number, thus closing the existing gap between the upper and the lower bound. We then introduce a new analysis allowing to establish a 7.45-approximation ratio for the 2-dimensional case, thus significantly decreasing the previously known 12 upper bound (Wan et al. in Wirel. Netw. 8(6):607–617, 2002) (actually corrected to 12.15 in Klasing et al. (Proceedings of the 3rd IFIP-TC6 international networking conference, pp. 866–877, 2004)). Finally, we extend our analysis to any number of dimensions d≥2 and any α≥d, obtaining a general approximation ratio of 3 ^d −1, again independent of α. The improvements of the approximation ratios are specifically significant in comparison with the lower bounds given by the kissing numbers, as these grow at least exponentially with respect to d. The research was partially funded by the European project COST Action 293, “Graphs and Algorithms in Communication Networks” (GRAAL). Preliminary version of this paper appeared in Flammini et al. (Proceedings of ACM joint workshop on foundations of mobile computing (DIALM-POMC), pp. 85–91, 2004).     

Effect of Stochastic Noise on Superior Julia Sets

Julia sets are considered one of the most attractive fractals and have wide range of applications in science and engineering. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck (Physica D 125(3–4):171–182, 1999) to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter. Argyris et al. (Chaos Solitons Fractals 11(13):2067–2073, 2000) have studied the effect of noise on Julia sets and concluded that Julia sets are stable for noises of low strength, and a small increment in the strength of noise may cause considerable deterioration in the configuration of the Julia sets. It is well-known that the method of function iterates plays a crucial role in discrete dynamics utilizing the techniques of fractal theory. However, recently Rani and Kumar (J. Korea Soc. Math. Edu. Ser. D: Res. Math. Edu. 8(4):261–277, 2004) introduced superior iterations as a generalization of function iterations in the study of Julia sets and studied superior Julia sets. This technique is further utilized to study effectively new Mandelbrot sets and related properties (see, for instance, Negi and Rani, Chaos Solitons Fractals 36(2):237–245, 2008; 36(4):1089–1096, 2008, Rani and Kumar, J. Korea Soc. Math. Edu. Ser. D: Res. Math. Edu. 8(4):279–291, 2004). The intent of this paper is to study certain effects of noise on superior Julia sets. We find that the superior Julia sets are drastically more stable for higher strength of noises than the classical Julia sets. Finally, we make a humble attempt to discuss some applications of superior orbit in discrete dynamics and of superior Julia sets in particle dynamics.     

Linear Time Algorithms for Exact Distance Transform

In 2003, Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) published a paper describing an algorithm that computes the exact distance transform in linear time (with respect to image size) for the rectangular binary images in the k-dimensional space ℝ ^k and distance measured with respect to L _p -metric for 1≤p≤∞, which includes Euclidean distance L ₂. In this paper we discuss this algorithm from theoretical and practical points of view. On the practical side, we concentrate on its Euclidean distance version, discuss the possible ways of implementing it as signed distance transform, and experimentally compare implemented algorithms. We also describe the parallelization of these algorithms and discuss the computational time savings associated with them. All these implementations will be made available as a part of the CAVASS software system developed and maintained in our group (Grevera et al. in J. Digit. Imaging 20:101–118, 2007). On the theoretical side, we prove that our version of the signed distance transform algorithm, GBDT, returns the exact value of the distance from the geometrically defined object boundary. We provide a complete proof (which was not given of Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) that all these algorithms work correctly for L _p -metric with 1<p<∞. We also point out that the precise form of the algorithm from Maurer et al. (IEEE Trans. Pattern Anal. Mach. Intell. 25:265–270, 2003) is not well defined for L ₁ and L _∞ metrics. In addition, we show that the algorithm can be used to find, in linear time, the exact value of the diameter of an object, that is, the largest possible distance between any two of its elements.     

Improved multi-processor scheduling for?flow time and?energy

Energy usage has been an important concern in recent research on online scheduling. In this paper, we study the tradeoff between flow time and energy (Albers and Fujiwara in ACM Trans. Algorithms 3(4), 2007; Bansal et al. in Proceedings of ACM-SIAM Symposium on Discrete Algorithms, pp. 805–813, 2007b, Bansal et al. in Proceedings of International Colloquium on Automata, Languages and Programming, pp. 409–420, 2008; Lam et al. in Proceedings of European Symposium on Algorithms, pp. 647–659, 2008b) in the multi-processor setting. Our main result is an enhanced analysis of a simple non-migratory online algorithm called CRR (classified round robin) on m≥2 processors, showing that its flow time plus energy is within O(1) times of the optimal non-migratory offline algorithm, when the maximum allowable speed is slightly relaxed. The result still holds even if the comparison is made against the optimal migratory offline algorithm. This improves previous analysis that CRR is O(log P)-competitive where P is the ratio of the maximum job size to the minimum job size.     

New Results on the Most Significant Bit of Integer Multiplication

Integer multiplication as one of the basic arithmetic functions has been in the focus of several complexity theoretical investigations and ordered binary decision diagrams (OBDDs) are one of the most common dynamic data structures for Boolean functions. Analyzing the limits of symbolic graph algorithms for the reachability problem Sawitzki (Proc. of LATIN, LNCS, vol. 3887, pp. 781–792, Springer, Berlin, 2006) has presented the first exponential lower bound on the π-OBDD size for the most significant bit of integer multiplication according to one predefined variable order π. Since the choice of the variable order is a main issue to obtain OBDDs of small size the investigation is continued. As a result a new upper bound method and the first non-trivial upper bound on the size of OBDDs according to an arbitrary variable order is presented. Furthermore, Sawitzki’s lower bound is improved.     

On the Behavior of True and False

Uzquiano (Analysis 70:39–44, 2010) showed that the Hardest Logic Puzzle Ever (HLPE) [in its amended form due to Rabern and Rabern (Analysis 68:105–112, 2008)] has a solution in only two questions. Uzquiano concludes his paper by noting that his solution strategy naturally suggests a harder variation of the puzzle which, as he remarks, he does not know how to solve in two questions. Wheeler and Barahona (J Philos Logic, to appear, 2011) formulated a three question solution to Uzquiano’s puzzle and gave an information theoretic argument to establish that a two question solution for Uzquiano’s puzzle does not exist. However, their argument crucially relies on a certain conception of what it means to answer self-referential yes–no questions truly and falsely. We propose an alternative such conception which, as we show, allows one to solve Uzquiano’s puzzle in two questions. The solution strategy adopted suggests an even harder variation of Uzquiano’s puzzle which, as we will show, can also be solved in two questions. Just as all previous solutions to versions of HLPE, our solution is presented informally. The second part of the paper investigates the prospects of formally representing solutions to HLPE by exploiting theories of truth.     

Representable good EQ-algebras

Recently, a special algebra called EQ-algebra (we call it here commutative EQ-algebra since its multiplication is assumed to be commutative) has been introduced by Novák (Proceedings of the Czech-Japan seminar, ninth meeting, Kitakyushu and Nagasaki, 18–22 August, 2006), which aims at becoming the algebra of truth values for fuzzy type theory. Its implication and multiplication are no more closely tied by the adjunction and so, this algebra generalizes commutative residuated lattice. One of the outcomes is the possibility to relax the commutativity of the multiplication. This has been elaborated by El-Zekey et al. (Fuzzy Sets Syst 2009, submitted). We continue in this paper the study of EQ-algebras (i.e., those with multiplication not necessarily commutative). We introduce prelinear EQ-algebras, in which the join-semilattice structure is not assumed. We show that every prelinear and good EQ-algebra is a lattice EQ-algebra. Moreover, the $\{\wedge,\vee,\rightarrow,1\}Recently, a special algebra called EQ-algebra (we call it here commutative EQ-algebra since its multiplication is assumed to be commutative) has been introduced by Novák (Proceedings of the Czech-Japan seminar, ninth meeting, Kitakyushu and Nagasaki, 18–22 August, 2006), which aims at becoming the algebra of truth values for fuzzy type theory. Its implication and multiplication are no more closely tied by the adjunction and so, this algebra generalizes commutative residuated lattice. One of the outcomes is the possibility to relax the commutativity of the multiplication. This has been elaborated by El-Zekey et al. (Fuzzy Sets Syst 2009, submitted). We continue in this paper the study of EQ-algebras (i.e., those with multiplication not necessarily commutative). We introduce prelinear EQ-algebras, in which the join-semilattice structure is not assumed. We show that every prelinear and good EQ-algebra is a lattice EQ-algebra. Moreover, the {ù,ú,?,1}\{\wedge,\vee,\rightarrow,1\}-reduct of a prelinear and separated lattice EQ-algebra inherits several lattice-related properties from product of linearly ordered and separated EQ-algebras. We show that prelinearity alone does not characterize the representable class of all good (commutative) EQ-algebras. One of the main results of this paper is to characterize the representable good EQ-algebras. This is mainly based on the fact that {?,1}\{\rightarrow,1\}-reducts of good EQ-algebras are BCK-algebras and run on lines of van Alten’s (J Algebra 247:672–691, 2002) characterization of representable integral residuated lattices. We also supply a number of potentially useful results, leading to this characterization.     

Graph Spanners in the Streaming Model: An Experimental Study

This article reports the results of an extensive experimental analysis of efficient algorithms for computing graph spanners in the data streaming model, where an (α,β)-spanner of a graph G is a subgraph S⊆G such that for each pair of vertices the distance in S is at most α times the distance in G plus β. To the best of our knowledge, this is the first computational study of graph spanner algorithms in a streaming setting. We compare experimentally the randomized algorithms proposed by Baswana () and by Elkin (In: Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP 2007), Wroclaw, Poland, pp. 716–727, 9–13 July 2007) for general stretch factors with the deterministic algorithm presented by Ausiello et al. (In: Proceedings of the 15th Annual European Symposium on Algorithms (ESA 2007), Engineering and Applications Track, Eilat, Israel, 8–10 October 2007. LNCS, vol. 4698, pp. 605–617, 2007), designed for building small stretch spanners. All the algorithms we implemented work in a data streaming model where the input graph is given as a stream of edges in arbitrary order, and all of them need a single pass over the data. Differently from the algorithm in Ausiello et al., the algorithms in Baswana () and Elkin (In: Proceedings of the 34th International Colloquium on Automata, Languages and Programming (ICALP 2007), Wroclaw, Poland, pp. 716–727, 9–13 July 2007) need to know in advance the number of vertices in the graph. The results of our experimental investigation on several input families confirm that all these algorithms are very efficient in practice, finding spanners with stretch and size much smaller than the theoretical bounds and comparable to those obtainable by off-line algorithms. Moreover, our experimental findings confirm that small values of the stretch factor are the case of interest in practice, and that the algorithm by Ausiello et al. tends to produce spanners of better quality than the algorithms by Baswana and Elkin, while still using a comparable amount of time and space resources. Work partially supported by the Italian Ministry of University and Research under Project MAINSTREAM “Algorithms for Massive Information Structures and Data Streams”. A preliminary version of this paper was presented at the 15th Annual European Symposium on Algorithms (ESA 2007) 5.     

Robust scalability analysis and SPM case studies

Scalability has become an attribute of paramount importance for computer systems used in business, scientific and engineering applications. Although scalability has been widely discussed, especially for pure parallel computer systems, it conveniently focuses on improving performance when increasing the number of computing processors. In fact, the term “scalable” is so much abused that it has become a marketing tool for computer vendors independent of the system’s technical qualifications. Since the primary objective of scalability analysis is to determine how well a system can work on larger problems with an increase in its size, we introduce here a generic definition of scalability. For illustrative purposes only, we apply this definition to PC clusters, a rather difficult subject due to their long communication latencies. Since scalability does not solely depend on the system architecture but also on the application programs and their actual management by the run-time environment, for the sake of illustration, we evaluate scalability for programs developed under the super-programming model (SPM) (Jin and Ziavras in IEEE Trans. Parallel Distrib. Syst. 15(9):783–794, 2004; J. Parallel Distrib. Comput. 65(10):1281–1289, 2005; IEICE Trans. Inf. Syst. E87-D(7):1774–1781, 2004).     

Semi-Lagrangian Runge-Kutta Exponential Integrators for Convection Dominated Problems

In this paper we consider the case of nonlinear convection-diffusion problems with a dominating convection term and we propose exponential integrators based on the composition of exact pure convection flows. These methods can be applied to the numerical integration of the considered PDEs in a semi-Lagrangian fashion. Semi-Lagrangian methods perform well on convection dominated problems (Pironneau in Numer. Math. 38:309–332, 1982; Hockney and Eastwood in Computer simulations using particles. McGraw-Hill, New York, 1981; Rees and Morton in SIAM J. Sci. Stat. Comput. 12(3):547–572, 1991; Baines in Moving finite elements. Monographs on numerical analysis. Clarendon Press, Oxford, 1994). In these methods linear convective terms can be integrated exactly by first computing the characteristics corresponding to the gridpoints of the adopted discretization, and then producing the numerical approximation via an interpolation procedure.     

Efficient scheme of verifying integrity of application binaries in embedded operating systems

Currently, embedded systems have been widely used for ubiquitous computing environments including digital setup boxes, mobile phones, and USN (Ubiquitous Sensor Networks). The significance of security has been growing as it must be necessarily embedded in all these systems. Up until now, many researchers have made efforts to verify the integrity of applied binaries downloaded in embedded systems. The research of problem solving is organized into hardware methods and software-like methods. In this research, the basic approach to solving problems from the software perspective was employed. From the software perspective, unlike in the existing papers (Seshadri et al., Proc. the IEEE symposium on security and privacy, 2004; Seshadri et al., Proc. the symposium on operating systems principals, 2005) based on the standardized model (TTAS.KO-11.0054. 2006) publicized in Korea, there is no extra verifier and conduct for the verification function in the target system. Contrary to the previous schemes (Jung et al. , 2008; Lee et al., LNCS, vol. 4808, pp. 346–355, 2007), verification results are stored in 1 validation check bit, instead of storing signature value for application binary files in the i-node structure for the purpose of reducing run-time execution overhead. Consequently, the proposed scheme is more efficient because it dramatically reduces overhead in storage space, and when it comes to computing, it performs one hash algorithm for initial execution and thereafter compares 1 validation check bit only, instead of signature and hash algorithms for every application binary. Furthermore, in cases where there are frequent changes in the i-node structure or file data depending on the scheme application, the scheme can provide far more effective verification performance compared to the previous schemes.     

Topology design with negative masks using gradient search

Previous implementations of the Material Mask Overlay Scheme (MMOS) (Saxena, ASME J Mech Des 130(8):1–9, 2009, 2010; Jain and Saxena, ASME J Mech Des 132(6):1–10, 2010) use stochastic search to achieve well connected, perfectly binary topologies but are computationally expensive. Here, a gradient search is employed to lay the negative masks over the design region. A continuous material assignment model is presented and studied. This investigation is motivated by the following goals: (a) reduction in the number of evaluations thereby making the search computationally efficient compared to the previous implementations, (b) obtaining as close to well-connected binary topologies as possible, and (c) influence of various parameters on the quality of solutions and existence of gray cells.     

Comparison of parallel multi-objective approaches to protein structure prediction

Protein structure prediction (PSP) is an open problem with many useful applications in disciplines such as medicine, biology and biochemistry. As this problem presents a vast search space and the analysis of each protein structure requires a significant amount of computing time, it is necessary to take advantage of high-performance parallel computing platforms as well as to define efficient search procedures in the space of possible protein conformations. In this paper we compare two parallel procedures for PSP which are based on different multi-objective optimization approaches, i.e. PAES (Knowles and Corne in Proc. Congr. Evol. Comput. 1:98–105, 1999) and NSGA2 (Deb et al. in IEEE Trans. Evol. Comput. 6:182–197, 2002). Although both procedures include techniques to take advantage of known protein structures and strategies to simplify the search space through the so-called rotamer library and adaptive mutation operators, they present different profiles with respect to their implicit parallelism.