Downloads & Free Reading Options - Results

An optimization procedure is developed for the simultaneous improvement of the aerodynamic and sonic boom characteristics of high speed aircraft. From a sonic boom perspective, it is desirable to minimize the first peak in the overpressure signal at a specified distance away from the aircraft. From aerodynamic point of view, the aerodynamic drag coefficient ratio must be minimized while maintaining the lift coefficient at desired level. The optimization procedure is applied to wing-body configurations related to high speed aircraft. The objectives of this current research are: (1) development of a multiobjective optimization procedure for aerospace vehicles with the integration of sonic boom and aerodynamic performance criteria; and (2) development of semi-analytical approach for calculating sonic boom design sensitivities.

An approach for reducing the number of variables and constraints, which is combined with System Analysis Equations (SAE), for multiobjective optimization-based design is presented. In order to develop a simplified analysis model, the SAE is computed outside an optimization loop and then approximated for use by an operator. Two examples are presented to demonstrate the approach.

A minimum correction homotopy approach is used to obtain the simultaneous/integrated optimal design of a large flexible structure and its active control system. Instead of the usual method of weighting and summing all desired objectives to form a constrained scalar optimization problem, a vector of objective functions is dealt with directly. The Draper/RPL configuration (a central hub with four symmetric, identical arms) is the design structure. The design seeks to minimize the mass of the arms. Using simple feedback of arm displacements and velocities, the control system seeks to achieve specified closed-loop eigenvalues (frequencies and damping ratios) and control effort. Design variables are the arm dimensions, control system gains, and sensor and actuator locations. Not only can the structural design be accomplished while placing the closed-loop eigenvalues, but a simultaneous 50% reduction in mass and/or control effort can be obtained. Since reduced-order models were used for the structural/control design, the resultant configurations are easily driven unstable by spillover from higher-order unmodeled modes. A modal suppression technique is applied to eliminate observation spillover and provide a decade of deadband above the controller bandwidth. Keywords: Control theory, Combinational analysis.

A quantum cascade (QC) laser is a specific type of semiconductor laser that operates through principles of quantum mechanics. In less than a decade QC lasers are already able to outperform previously designed double heterostructure semiconductor lasers. Because there is a genuine lack of compact and coherent devices which can operate in the far-infrared region the motivation exists for designing a terahertz QC laser. A device operating at this frequency is expected to be more efficient and cost effective than currently existing devices. It has potential applications in the fields of spectroscopy, astronomy, medicine and free-space communication as well as applications to near-space radar and chemical/biological detection. The overarching goal of this research was to find QC laser parameter combinations which can be used to fabricate viable structures. To ensure operation in the THz region the device must conform to the extremely small energy level spacing range from 10-15 meV. The time and expense of the design and production process is prohibitive, so an alternative to fabrication was necessary. To accomplish this goal a model of a QC laser, developed at Worchester Polytechnic Institute with sponsorship from the Air Force Research Laboratory Sensors Directorate, and the General Multiobjective Parallel Genetic Algorithm (GenMOP), developed at the Air Force Institute of Technology, were integrated to form a computer simulation which stochastically searches for feasible solutions.

Multi-objective optimisation is regarded as one of the most promising ways for dealing with constrained optimisation problems in evolutionary optimisation. This paper presents a theoretical investigation of a multi-objective optimisation evolutionary algorithm for solving the 0-1 knapsack problem. Two initialisation methods are considered in the algorithm: local search initialisation and greedy search initialisation. Then the solution quality of the algorithm is analysed in terms of the approximation ratio.

This article is from SpringerPlus , volume 2 . Abstract The multiobjective design of digital filters using spiral optimization technique is considered in this paper. This new optimization tool is a metaheuristic technique inspired by the dynamics of spirals. It is characterized by its robustness, immunity to local optima trapping, relative fast convergence and ease of implementation. The objectives of filter design include matching some desired frequency response while having minimum linear phase; hence, reducing the time response. The results demonstrate that the proposed problem solving approach blended with the use of the spiral optimization technique produced filters which fulfill the desired characteristics and are of practical use.

Despite major advances in design tools such as engine cycle analysis software and computer aided design, conceptual gas turbine engine design is essentially a trial-and-error process based on the experience of engineers. Modern optimization concepts, such as multidisciplinary optimization (MDO), and multiobjective optimization (MOO), linked with sequential quadratic programming (SQP) methods and genetic algorithms (GA), were applied to the conceptual engine design process to automate the conceptual design phase. Robust integrated computer codes were created to find the optimal values of eight engine parameters in order to minimize fuel usage, aircraft cost and engine annulus area over a given mission. The engine cycle selected for study was the mixed stream, low bypass turbofan. SQP and GA optimization algorithms were integrated with on-design and off- design engine cycle analysis and mission analysis computer codes created by the authors to obtain the optimized conceptual engine design for an imaginary short range interceptor and the Global Strike Aircraft U.S. Air Force concept. The process used a nonspecific approach that can be applied to a wide variety of missions and aircraft. All the codes were written in Matlab, and so operate under the same programming architecture and can be easily upgraded or modified.

A method for the multiobjective optimization of local-scale material topology is presented. The topology optimization scheme is based on a constructive solid geometry-like representation, in which convex polygons---defined as the convex hull of arbitrary-length lists of points---are combined using an overlapping function. This data structure is tree-shaped and so genetic programming is used as the optimizer. The forward problem is solved with a multiscale finite element method with automatic cohesive zone insertion to model damage. As a multiscale method, loads and boundary conditions are applied and objective functions measured at a global scale, while the local scale material structure is optimized. The global scale geometry is assumed fixed. Pareto optimal designs are generated, representing optimal tradeoffs between conflicting goals: quasi-static displacement and dynamic strain energy. Results demonstrate the efficacy of the proposed algorithm.

Book Source: Digital Library of India Item 2015.192764 dc.contributor.author: Mayur Manohar dc.date.accessioned: 2015-07-08T01:35:59Z dc.date.available: 2015-07-08T01:35:59Z dc.date.digitalpublicationdate: 2005-08-31 dc.identifier.barcode: 1990010091159 dc.identifier.origpath: /rawdataupload/upload/0091/159 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/192764 dc.description.scannerno: 12 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 80 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Mechanical Engineering In General. Nuclear Technology. Electrical Engineering. Machinery dc.title: Multiobjective Optimization Of Heat Exchanger Design Geometry An Application Of Evop

This paper gives a concise overview of evolutionary algorithms for multiobjective optimization. A substantial number of evolutionary computation methods for multiobjective problem solving has been proposed so far, and an attempt of unifying existing approaches is here presented. Based on a fine-grained decomposition and following the main issues of fitness assignment, diversity preservation and elitism, a conceptual global model is proposed and is validated by regarding a number of state-of-the-art algorithms as simple variants of the same structure. The presented model is then incorporated into a general-purpose software framework dedicated to the design and the implementation of evolutionary multiobjective optimization techniques: ParadisEO-MOEO. This package has proven its validity and flexibility by enabling the resolution of many real-world and hard multiobjective optimization problems.

Various notions of condition numbers are used to study some sensitivity aspects of scalar optimization problems. The aim of this paper is to introduce a notion of condition number to study the case of a multiobjective optimization problem defined via m convex C^1,1 objective functions on a given closed ball in R^n. Two approaches are proposed: the first one adopts a local point of view around a given solution point, whereas the second one considers the solution set as a whole. A comparison between the two notions of well-conditioned problem is developed. We underline that both the condition numbers introduced in the present work reduce to the same of condition number proposed by Zolezzi in 2003, in the special case of the scalar optimization problem considered there. A pseudodistance between functions is defined such that the condition number provides an upper bound on how far from a well-conditioned function f a perturbed function g can be chosen in order that g is well-conditioned too. For both the local and the global approach an extension of classical Eckart-Young distance theorem is proved, even if only a special class of perturbations is considered.

Implicit utility/value maximization and explicit utility/value maximization are identified as two major classes of multiobjective optimization methods. The explicit methods have the advantage that they can fully exploit the power of existing mathematical programming algorithms. Their disadvantage is the high information burden placed on the decision maker. Implicit i.e., interactive)methods have complementary strengths and weaknesses: they require less extensive information but do not lend themselves as easily to optimizing algorithms. The authors developed a hybrid implicit/explicit approach which attempts to combine the advantages of both. The idea is to embed within the implicit method a procedure which periodically formulates an approximate explicit representation of the multiobjective problem, and then optimally solves it without user interaction. Operationally the use of this idea requires frequent solution of two nonlinear programs. This document also reports on the implementation of this method in a forest management decision support system. This is a completely microcomputer based implementation, and is currently undergoing field testing for use in planning the timing and intensity of timber harvest on nonindustrial forests throughout the southeastern U.S. (Author)

The Naval Air Warfare Center - Aircraft Division Warminster, Software and Computer Technology Division, is developing software to allocate tasks to multicomputer nodes such that multiple objectives are optimized. The eventual goal of this project is to allow the decision maker to have design optimization capabilities available to her/him when designing complex system. Two key aspects of the allocation problem are discussed: (1) The techniques used to treat multiple objectives simultaneously and (2) The techniques used to perform the search for the optimal set of model parameters. The report discusses current research reported in the literature and makes several suggestions for continuing the current effort. The current technique being used for treating multiple objectives simultaneously is to use a weighted sum of each of the individual objective functions as the objective function for the search. It is suggested that a vector of objective functions approach be implemented and experimentally compared to the weighted sum approach. Two algorithms are being used in the software: the genetic algorithm and the simulated annealing algorithm.... Complex system engineering, Genetic algorithm, Multicomputer nodes, Multiple objectives, Neural network, Optimization, Searching simulated annealing algorithm, Vector of objective functions.

We introduce a novel multiobjective optimization algorithm based on the conformational space annealing (CSA) algorithm, MOCSA. It has three characteristic features: (a) Dominance relationship and distance between solutions in the objective space are used as the fitness measure, (b) update rules are based on the fitness as well as the distance between solutions in the decision space and (c) it uses a constrained local minimizer. We have tested MOCSA on 12 test problems, consisting of ZDT and DTLZ test suites. Benchmark results show that solutions obtained by MOCSA are closer to the Pareto front and covers a wider range of the objective space than those by the elitist non-dominated sorting genetic system (NSGA2).

One of the major distinguishing features of the dynamic multiobjective optimization problems (DMOPs) is the optimization objectives will change over time, thus tracking the varying Pareto-optimal front becomes a challenge. One of the promising solutions is reusing the "experiences" to construct a prediction model via statistical machine learning approaches. However most of the existing methods ignore the non-independent and identically distributed nature of data used to construct the prediction model. In this paper, we propose an algorithmic framework, called Tr-DMOEA, which integrates transfer learning and population-based evolutionary algorithm for solving the DMOPs. This approach takes the transfer learning method as a tool to help reuse the past experience for speeding up the evolutionary process, and at the same time, any population based multiobjective algorithms can benefit from this integration without any extensive modifications. To verify this, we incorporate the proposed approach into the development of three well-known algorithms, nondominated sorting genetic algorithm II (NSGA-II), multiobjective particle swarm optimization (MOPSO), and the regularity model-based multiobjective estimation of distribution algorithm (RM-MEDA), and then employ twelve benchmark functions to test these algorithms as well as compare with some chosen state-of-the-art designs. The experimental results confirm the effectiveness of the proposed method through exploiting machine learning technology.

In this paper, a new method of H_infinity observer design for Lipschitz nonlinear systems is proposed in the form of an LMI optimization problem. The proposed observer has guaranteed decay rate (exponential convergence) and is robust against unknown exogenous disturbance. In addition, thanks to the linearity of the proposed LMIs in the admissible Lipschitz constant, it can be maximized via LMI optimization. This adds an extra important feature to the observer, robustness against nonlinear uncertainty. Explicit bound on the tolerable nonlinear uncertainty is derived. The new LMI formulation also allows optimizations over the disturbance attenuation level (H_infinity cost). Then, the admissible Lipschitz constant and the disturbance attenuation level of the H_infinity filter are simultaneously optimized through LMI multiobjective optimization.

In High Dose Rate (HDR) brachytherapy the conventional dose optimization algorithms consider the multiple objectives in the form of an aggregate function which combines individual objectives into a single utility value, As a result, the optimization problem becomes single objective, prior to optimization. Up to 300 parameters must be optimized satisfying objectives which are often competing. We use multiobjective dose optimization methods where the objectives are expressed in terms of quantities derived from dose-volume histograms or in terms of statistical parameters of dose distributions from a small number of sampling points. For the last approach we compare the optimization results of evolutionary multiobjective algorithms with deterministic optimization methods. The deterministic algorithms are very efficient and produce the best results, but they also have the certain limitations. The performance of the multiobjective evolutionary algorithms is improved if a small part of the population is initialized by deterministic algorithms.

The evolution of multidisciplinary design optimization (MDO) over the past several years has been one of rapid expansion and development. In this paper, the evolution of MDO as a field is investigated as well as the evolution of its individual linguistic components: multidisciplinary, design, and optimization. The theory and application of each component have indeed evolved on their own, but the true net gain for MDO is how these piecewise evolutions coalesce to form the basis for MDO, present and future. Originating in structural applications, MDO technology has also branched out into diverse fields and application arenas. The evolution and diversification of MDO as a discipline is explored but details are left to the references cited.

In this paper we present a new methodology for solving multiobjective integer linear programs using tools from algebraic geometry. We introduce the concept of partial Gr\"obner basis for a family of multiobjective programs where the right-hand side varies. This new structure extends the notion of Gr\"obner basis for the single objective case, to the case of multiple objectives, i.e., a partial ordering instead of a total ordering over the feasible vectors. The main property of these bases is that the partial reduction of the integer elements in the kernel of the constraint matrix by the different blocks of the basis is zero. It allows us to prove that this new construction is a test family for a family of multiobjective programs. An algorithm '\`a la Buchberger' is developed to compute partial Gr\"obner bases and two different approaches are derived, using this methodology, for computing the entire set of efficient solutions of any multiobjective integer linear problem (MOILP). Some examples illustrate the application of the algorithms and computational experiments are reported on several families of problems.

Cover title

Cover title

We propose a new nonlinear programming approach for optimization problems with multiple criteria. In the context of no-preference methods, we introduce a new nonlinear nonconvex reformulation of the original multiobjective problem that shows distinctive significant features: computing a (global) solution of our reformulation does not depend on the objectives' scales and provides us with a (global) Pareto optimum of the original problem that "dominates the most" with respect to the objectives space. Furthermore, as for the solvability issue, the problem of finding such Pareto solution, while nonconvex, nonetheless enjoys generalized convexity properties: in turn, this fact allows us to resort to standard nonlinear programming methods in order to calculate a global optimum of our nonconvex reformulation. We show the viability of our ideas by considering portfolio selection: numerical tests prove the effectiveness of our approach.

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

The research proposed in this document investigated multiobjective optimization approaches based upon the Genetic Algorithm (GA). Several versions of the GA have been adopted for multiobjective design, but, prior to this research, there had not been significant comparisons of the most popular strategies. The research effort first generalized the two-branch tournament genetic algorithm in to an N-branch genetic algorithm, then the N-branch GA was compared with a version of the popular Multi-Objective Genetic Algorithm (MOGA). Because the genetic algorithm is well suited to combinatorial (mixed discrete / continuous) optimization problems, the GA can be used in the conceptual phase of design to combine selection (discrete variable) and sizing (continuous variable) tasks. Using a multiobjective formulation for the design of a 50-passenger aircraft to meet the competing objectives of minimizing takeoff gross weight and minimizing trip time, the GA generated a range of tradeoff designs that illustrate which aircraft features change from a low-weight, slow trip-time aircraft design to a heavy-weight, short trip-time aircraft design. Given the objective formulation and analysis methods used, the results of this study identify where turboprop-powered aircraft and turbofan-powered aircraft become more desirable for the 50 seat passenger application. This aircraft design application also begins to suggest how a combinatorial multiobjective optimization technique could be used to assist in the design of morphing aircraft.

An integrated, multiobjective optimization procedure is developed for the design of high speed proprotors with the coupling of aerodynamic, dynamic, aeroelastic, and structural criteria. The objectives are to maximize propulsive efficiency in high speed cruise and rotor figure of merit in hover. Constraints are imposed on rotor blade aeroelastic stability in cruise and on total blade weight. Two different multiobjective formulation procedures, the Min summation of beta and the K-S function approaches are used to formulate the two-objective optimization problems.

A new technique which converts a constrained optimization problem to an unconstrained one where conflicting figures of merit may be simultaneously considered was combined with a complex mission analysis system. The method is compared with existing single and multiobjective optimization methods. A primary benefit from this new method for multiobjective optimization is the elimination of separate optimizations for each objective, which is required by some optimization methods. A typical wide body transport aircraft is used for the comparative studies.

The purpose of this study was to determine the most robust frequency assignment for a search and rescue network. The focus was to assign weights to the transmitter areas of the network to determine which weight sequence produced the most robust frequency assignment. The DoD furnished weight sequences for twelve two-hour time blocks. These weight sequences were compared to a weight sequence with all weights having equal value. Network and linear programming were used to-solve this problem and generate frequency assignments for all weight sequences. Classical and tolerance sensitivity analysis were used to analyze the frequency assignments generated by the different weight sequences. The weight sequence with all weights of equal value produced the most robust frequency assignments for all time blocks.

A new method for developing tradeoffs in the engineering of complex systems is described. The Genetic-Algorithm-Based Normal Boundary Intersection (GANBI) method serves as a preprocessor for conventional genetic-algorithm-based Pareto optimization solvers. The algorithm is based on applying the normal boundary intersection approach of Pareto optimization to genetic solvers. The approach is shown to provide rapid convergence and to provide a better estimate of the Pareto set than existing state-of-the-art methods. A description of Pareto optimization methods for engineering design is included to put the new method in the context of existing solution approaches. The algorithm for the GANBI method is derived and detailed in the report, and numerical examples showing its efficiency in solving an academic problem are presented. The report concludes with an example of how the GANBI method has been used to make tradeoff decisions in the design of large-scale distributed undersea sensor networks.

Book Source: Digital Library of India Item 2015.191724 dc.contributor.author: Mayur Manohar dc.date.accessioned: 2015-07-08T01:09:03Z dc.date.available: 2015-07-08T01:09:03Z dc.date.digitalpublicationdate: 2005-08-31 dc.identifier.barcode: 1990010090215 dc.identifier.origpath: /rawdataupload/upload/0090/215 dc.identifier.copyno: 1 dc.identifier.uri: http://www.new.dli.ernet.in/handle/2015/191724 dc.description.scannerno: 12 dc.description.scanningcentre: IIIT, Allahabad dc.description.main: 1 dc.description.tagged: 0 dc.description.totalpages: 80 dc.format.mimetype: application/pdf dc.language.iso: English dc.publisher: Indian Institute Of Technology Kanpur dc.rights: Out_of_copyright dc.source.library: Indian Institute Of Technology Kanpur dc.subject.classification: Technology dc.subject.classification: Engineering. Technology In General dc.subject.classification: Mechanical Engineering In General. Nuclear Technology. Electrical Engineering. Machinery dc.title: Multiobjective Optimization Of Heat Exchanger Design Geometry An Application Of Evop

This paper deals with the multiobjective version of the optimal spanning tree problem. More precisely, we are interested in determining the optimal spanning tree according to an Ordered Weighted Average (OWA) of its objective values. We first show that the problem is weakly NP-hard. In the case where the weights of the OWA are strictly decreasing, we then propose a mixed integer programming formulation, and provide dedicated optimality conditions yielding an important reduction of the size of the program. Next, we present two bounds that can be used to prune subspaces of solutions either in a shaving phase or in a branch and bound procedure. The validity of these bounds does not depend on specific properties of the weights (apart from non-negativity). All these exact resolution algorithms are compared on the basis of numerical experiments, according to their respective validity scopes.

This paper deals with the multiobjective version of the optimal spanning tree problem. More precisely, we are interested in determining the optimal spanning tree according to an Ordered Weighted Average (OWA) of its objective values. We first show that the problem is weakly NP-hard. In the case where the weights of the OWA are strictly decreasing, we then propose a mixed integer programming formulation, and provide dedicated optimality conditions yielding an important reduction of the size of the program. Next, we present two bounds that can be used to prune subspaces of solutions either in a shaving phase or in a branch and bound procedure. The validity of these bounds does not depend on specific properties of the weights (apart from non-negativity). All these exact resolution algorithms are compared on the basis of numerical experiments, according to their respective validity scopes.

We present several new results about smoothed analysis of multiobjective optimization problems. Motivated by the discrepancy between worst-case analysis and practical experience, this line of research has gained a lot of attention in the last decade. We consider problems in which d linear and one arbitrary objective function are to be optimized over a subset S of {0,1}^n of feasible solutions. We improve the previously best known bound for the smoothed number of Pareto-optimal solutions to O(n^{2d} phi^d), where phi denotes the perturbation parameter. Additionally, we show that for any constant c the c-th moment of the smoothed number of Pareto-optimal solutions is bounded by O((n^{2d} phi^d)^c). This improves the previously best known bounds significantly. Furthermore, we address the criticism that the perturbations in smoothed analysis destroy the zero-structure of problems by showing that the smoothed number of Pareto-optimal solutions remains polynomially bounded even for zero-preserving perturbations. This broadens the class of problems captured by smoothed analysis and it has consequences for non-linear objective functions. One corollary of our result is that the smoothed number of Pareto-optimal solutions is polynomially bounded for polynomial objective functions.

This report addresses the development of a multidisciplinary optimization procedure using an efficient semi-analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles. A semi-analytical sensitivity analysis procedure is developed for calculating computational grid sensitivities and aerodynamic design sensitivities. Accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique. The developed sensitivity analysis technique are then used within a multidisciplinary optimization procedure for designing aerospace vehicles. The optimization problem, with the integration of aerodynamics and structures, is decomposed into two levels. Optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level. Aerodynamic analysis is performed by solving the three-dimensional parabolized Navier Stokes equations. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The proceduredeveloped is applied to design the wing of a high speed aircraft. Results obtained show significant improvements in the aircraft aerodynamic and structural performance when compared to a reference or baseline configuration. The use of the semi-analytical sensitivity technique provides significant computational savings.

We present results from a study comparing a recently developed coevolutionary genetic algorithm (CGA) against a set of evolutionary algorithms using a suite of multiobjective optimization benchmarks. The CGA embodies competitive coevolution and employs a simple, straightforward target population representation and fitness calculation based on developmental theory of learning. Because of these properties, setting up the additional population is trivial making implementation no more difficult than using a standard GA. Empirical results using a suite of two-objective test functions indicate that this CGA performs well at finding solutions on convex, nonconvex, discrete, and deceptive Pareto-optimal fronts, while giving respectable results on a nonuniform optimization. On a multimodal Pareto front, the CGA finds a solution that dominates solutions produced by eight other algorithms, yet the CGA has poor coverage across the Pareto front.

Many complex systems obey to optimality conditions that are usually not simple. Conflicting traits often interact making a Multi Objective Optimization (MOO) approach necessary. Recent MOO research on complex systems report about the Pareto front (optimal designs implementing the best trade-off) in a qualitative manner. Meanwhile, research on traditional Simple Objective Optimization (SOO) often finds phase transitions and critical points. We summarize a robust framework that accounts for phase transitions located through SOO techniques and indicates what MOO features resolutely lead to phase transitions. These appear determined by the shape of the Pareto front, which at the same time is deeply related to the thermodynamic Gibbs surface. Indeed, thermodynamics can be written as an MOO from where its phase transitions can be parsimoniously derived; suggesting that the similarities between transitions in MOO-SOO and Statistical Mechanics go beyond mere coincidence.

Differential Evolution is a simple, fast, and robust evolutionary algorithm that has proven effective in determining the global optimum for several difficult single-objective optimization problems. In this paper, the Differential Evolution algorithm is extended to multiobjective optimization problems by using a Pareto-based approach. The algorithm performs well when applied to several test optimization problems from the literature.

A new technique which converts a constrained optimization problem to an unconstrained one where conflicting figures of merit may be simultaneously considered was combined with a complex mission analysis system. The method is compared with existing single and multiobjective optimization methods. A primary benefit from this new method for multiobjective optimization is the elimination of separate optimizations for each objective, which is required by some optimization methods. A typical wide body transport aircraft is used for the comparative studies.

Genetic Algorithm are capable of handling a large number of design parameters and work for optimization problems that have discontinues or non-differentiable multidimensional solution spaces, making them ideal for optimization of machining parameters. Current paper is based on Genetic Algorithm (GA) for optimization of process parameters (e.g. feed and speed) for multi-objective multi pass end milling. GA has been implemented using the MATLAB environment on the objective function, which is a hybrid function of cost and time, feed and speed. The results of optimum cost, feed and speed have been calculated after GA based implementation with PSO based implementation and conventional results. The GA results are found better in terms of the objective function as compared with PSO results for the multi-objective multipass end milling process.

Genetic Algorithm are capable of handling a large number of design parameters and work for optimization problems that have discontinues or non-differentiable multidimensional solution spaces, making them ideal for optimization of machining parameters. Current paper is based on Genetic Algorithm (GA) for optimization of process parameters (e.g. feed and speed) for multi-objective multi pass end milling. GA has been implemented using the MATLAB environment on the objective function, which is a hybrid function of cost and time, feed and speed. The results of optimum cost, feed and speed have been calculated after GA based implementation with PSO based implementation and conventional results. The GA results are found better in terms of the objective function as compared with PSO results for the multi-objective multipass end milling process.

An appropriate visualization of multiobjective non-dominated solutions is a valuable asset for decision making. Although there are methods for visualizing the solutions in the design space, they do not provide any information about their relationship. In this work, we propose a novel methodology that allows the visualization of the non-dominated solutions in the design space and their relationships by means of a network. The nodes represent the solutions in the objective space, while the edges show the relationships between the solutions in the design space. Our proposal (called moGrams) thus provides a joint visualization of both objective and design spaces. It aims at helping the decision maker to get more understanding of the problem so that (s)he can choose the more appropriate final solution. moGrams can be applied to any multicriteria problem in which the solutions are related by a similarity metric. Besides, the decision maker interaction is facilitated by modifying the network based on the current preferences to obtain a clearer view. An exhaustive experimental study is performed using three multiobjective problems in order to show both the usefulness and versatility of moGrams. The results exhibit interesting characteristics of our methodology for visualizing and analyzing solutions of multiobjective problems.

Purpose: Current inverse planning methods for IMRT are limited because they are not designed to explore the trade-offs between the competing objectives between the tumor and normal tissues. Our goal was to develop an efficient multiobjective optimization algorithm that was flexible enough to handle any form of objective function and that resulted in a set of Pareto optimal plans. Methods: We developed a hierarchical evolutionary multiobjective algorithm designed to quickly generate a diverse Pareto optimal set of IMRT plans that meet all clinical constraints and reflect the trade-offs in the plans. The top level of the hierarchical algorithm is a multiobjective evolutionary algorithm (MOEA). The genes of the individuals generated in the MOEA are the parameters that define the penalty function minimized during an accelerated deterministic IMRT optimization that represents the bottom level of the hierarchy. The MOEA incorporates clinical criteria to restrict the search space through protocol objectives and then uses Pareto optimality among the fitness objectives to select individuals. Results: Acceleration techniques implemented on both levels of the hierarchical algorithm resulted in short, practical runtimes for optimizations. The MOEA improvements were evaluated for example prostate cases with one target and two OARs. The modified MOEA dominated 11.3% of plans using a standard genetic algorithm package. By implementing domination advantage and protocol objectives, small diverse populations of clinically acceptable plans that were only dominated 0.2% by the Pareto front could be generated in a fraction of an hour. Conclusions: Our MOEA produces a diverse Pareto optimal set of plans that meet all dosimetric protocol criteria in a feasible amount of time. It optimizes not only beamlet intensities but also objective function parameters on a patient-specific basis.

This collection of matlab scripts and functions was used to design and optimize shaped pulses for CEST MRI

One of the most common approaches for multiobjective optimization is to generate a solution set that well approximates the whole Pareto-optimal frontier to facilitate the later decision-making process. However, how to evaluate and compare the quality of different solution sets remains challenging. Existing measures typically require additional problem knowledge and information, such as a reference point or a substituted set of the Pareto-optimal frontier. In this paper, we propose a quality measure, called dominance move (DoM), to compare solution sets generated by multiobjective optimizers. Given two solution sets, DoM measures the minimum sum of move distances for one set to weakly Pareto dominate the other set. DoM can be seen as a natural reflection of the difference between two solutions, capturing all aspects of solution sets' quality, being compliant with Pareto dominance, and does not need any additional problem knowledge and parameters. We present an exact method to calculate the DoM in the biobjective case. We show the necessary condition of constructing the optimal partition for a solution set's minimum move, and accordingly propose an efficient algorithm to recursively calculate the DoM. Finally, DoM is evaluated on several groups of artificial and real test cases as well as by a comparison with two well-established quality measures.

We consider a recent coinfection model for Tuberculosis (TB), Human Immunodeficiency Virus (HIV) infection and Acquired Immunodeficiency Syndrome (AIDS) proposed in [Discrete Contin. Dyn. Syst. 35 (2015), no. 9, 4639--4663]. We introduce and analyze a multiobjective formulation of an optimal control problem, where the two conflicting objectives are: minimization of the number of HIV infected individuals with AIDS clinical symptoms and coinfected with AIDS and active TB; and costs related to prevention and treatment of HIV and/or TB measures. The proposed approach eliminates some limitations of previous works. The results of the numerical study provide comprehensive insights about the optimal treatment policies and the population dynamics resulting from their implementation. Some nonintuitive conclusions are drawn. Overall, the simulation results demonstrate the usefulness and validity of the proposed approach.

We study output-sensitive algorithms and complexity for multiobjective combinatorial optimization problems. In this computational complexity framework, an algorithm for a general enumeration problem is regarded efficient if it is output-sensitive, i.e., its running time is bounded by a polynomial in the input and the output size. We provide both practical examples of MOCO problems for which such an efficient algorithm exists as well as problems for which no efficient algorithm exists under mild complexity theoretic assumptions.

This paper contains selected applications of the new tangential extremal principles and related results developed in Part I to calculus rules for infinite intersections of sets and optimality conditions for problems of semi-infinite programming and multiobjective optimization with countable constraints

The proximal point method for a special class of nonconvex multiobjective functions is studied in this paper. We show that the method is well defined and that the accumulation points of any generated sequence, if any, are Pareto--Clarke critical points. Moreover, under additional assumptions, we show the full convergence of the generated sequence.

This report presents the multiobjective optimization methodology suitable to the preliminary design of large scale aircraft structures. The algorithm is based on generalized compound scaling techniques to reach the intersection of multiple functions. Multiobjective functions are treated similar to the behavior constraints by generating pseudo targets on objectives. This algorithm is very efficient due to the fact that it does not solve many single objective optimization problems in reaching the Pareto set. The Pareto set gives several optimum solutions, and the designer has to use additional decision criteria in selecting the best design. In this work a reliability index based concept is used as the decision criterion. System reliability of the Pareto designs is calculated-due to the random nature of material properties, fabrication tolerances, and service loads, where the random parameters influencing the design appear through their mean and covariance values.

We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main difference with existing techniques is that we optimize a single (extended) optimization problem that provides a polynomial approximation whereas existing methods iteratively construct a piecewise linear approximation. One of the advantages of the proposed method is that it is more useful for visualizing the Pareto set.

Design problems in industrial engineering often involve a large number of design variables with multiple objectives, under complex nonlinear constraints. The algorithms for multiobjective problems can be significantly different from the methods for single objective optimization. To find the Pareto front and non-dominated set for a nonlinear multiobjective optimization problem may require significant computing effort, even for seemingly simple problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we extend the recently developed firefly algorithm to solve multiobjective optimization problems. We validate the proposed approach using a selected subset of test functions and then apply it to solve design optimization benchmarks. We will discuss our results and provide topics for further research.