Pareto Optimality

In this paper we extend the notion of Pareto efficiency to overlapping generations settings in which fertility decisions are endogenous. The contribution of this paper is threefold. First, we provide two definitions of Pareto dominance and, consequently, of Pareto efficiency referred to Millian efficiency and strong efficiency, differing in the treatment of agents that never get to be born. Second, we provide necessary (static) and sufficient (dynamic) conditions to determine whether or not an allocation is Millian efficient. Third, we characterize Millian efficient allocations as the equilibria of a decentralized price mechanism, and enunciate the Fundamental Welfare Theorems in an environment with endogenous fertility.

In this work both the multimodal hypergraph and the viable hyperpath conceptualizations are presented. The shortest viable hyperpath problem (SVHP) in a multimodal transportation network is defined. We consider a label correcting approach to find the shortest viable hyperpath from an origin to a destination, for different values of the upper limit of modal transfers. Such hyperpaths compose a Pareto-optimal

For the many-to-one matching model in which firms have substitutable and quota q−separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. Therefore, in centralized markets like entry-level professional labor markets if the proposed matching is the workers-optimal stable matching then, no group of workers can never benefit by reporting untruthfully their preference relations. We exhibit an example showing that this property fails if the preferences of firms are substitutable but not quota q−separable.

We consider the problem of simultaneous bitrate allocation for multiple video streams. Current methods for multiplexing video streams often rely on identifying the relative complexity of the video streams to improve the combined overall quality. In such methods, not all the videos benefit from the multiplexing process. Typically, the quality of high motion videos is improved at the expense of a reduction in the quality of low motion videos. In our approach, we use a competitive equilibrium allocation of bitrate to simultaneously improve the quality of all the video streams by finding trades between videos across time. A central controller collects rate-distortion information from each video user and makes a joint bitrate allocation decision. Each user encodes and transmits his video at the allocated bitrate through a shared channel. The proposed method uses information about not only the differing complexity of the video streams at every moment but also the differing complexity of each stream over time. Using the competitive equilibrium bitrate allocation approach for multiple video streams, simulation results show that all the video streams perform better or at least as well as with individual encoding. The results of this research will be useful both for ad hoc networks that employ a cluster head model and for cellular architectures.

1] ESWAT is a simulator that integrates catchment and river water quantity and quality processes. The integration leads to a high number of model parameters, which complicates model calibration. As the model is semidistributed, the water quality and quantity variables at different observation sites inside the catchment can, and should, be used during this process, in order to use all the available information. A simultaneous use of all the different observed series and a high number of free parameters, however, creates a complex mathematical problem. Existing methods such as Pareto-optimization are practically very difficult, if not impossible, to implement. We present therefore a new methodology that reduces the many objective functions to a single global criterion in an objective way, excluding the weighting problem. The global criterion then is minimized using a global search algorithm, i.e., the shuffled complex evolution method. The methodology is applied on the Dender River basin (Belgium), a heavily modified river basin with irregular flows.

In this paper, we consider the problem of permutation flowshop scheduling with the objectives of minimizing the makespan and total flowtime of jobs, and present a Multi-Objective Simulated-annealing Algorithm (MOSA). Two initial sequences are obtained by using simple and fast existing heuristics, supplemented by the implementation of three improvement schemes. Each of the two resultant sequences corresponds to a possible non-dominated solution containing the minimum value of one objective function. These sequences, taken one at a time, are given as the starting sequences to the MOSA. The MOSA seeks to obtain non-dominated solutions through the implementation of a simple probability function that attempts to generate solutions on the Pareto-optimal front. The probability function selects probabilistically a particular objective function, considering which the algorithm uncovers non-dominated solutions. Moreover, the probability function is varied in such a way that the entire objective-function space is covered uniformly so as to obtain as many non-dominated and well-dispersed solutions as possible. The parameters in the proposed MOSA are determined after conducting a pilot study. Two variants of the proposed algorithm, called MOSA-I and MOSA-II, with different parameter settings with respect to the temperature and epoch length, are considered in the performance evaluation of algorithms. In order to evaluate MOSA-I and MOSA-II, we have made use of 90 benchmark problems provided by [Eur. J. Operation. Res. 64 (1993) 278]. After an extensive literature survey, the following flowshop multi-objective scheduling algorithms have been identified as benchmark procedures: (a) MOGLS (Multi-Objective Genetic Local Search) by Ishibuchi and Murata [IEEE Trans. Syst., Man, Cybernet. C: Appl. Rev. 28 (1998) 392]; (b) Elitist Non-dominated sorting Genetic Algorithm (ENGA) by Bagchi [Multi-Objective Scheduling by Genetic Algorithms, Kluwer Academic Publishers, 1999]; (c) GPW (Gradual Priority Weighting) approach by Chang, Hsieh and Lin [Int. J. Prod. Econ. 79 (2002) 171]; and (d) a posteriori approach based heuristic by Framinan, Leisten and Ruiz-Usano [Eur. J. Operation. Res. 141 (2002) 559]. The non-dominated sets obtained from each of the existing bench-0377-2217/$ -see front matter Ó

This paper integrates elements from the theory of agency, the theory of property rights and the theory of finance to develop a theory of the ownership structure of the firm. We define the concept of agency costs, show its relationship to the 'separation and control' issue, investigate the ...

Understanding the dynamics of two major disrupting frameworks and the ways in which they continue to shape the new law and economic landscape. To do this, I analyzed the current laws, lobbied for by previous oligopolies, showing the inefficient systems that cause increased friction between customer and employee.

The possibility of a normative theory of proportionality in the implementation of the human rights protection have not to lead to be unaware of the specifics of the legal reasoning. A moral and political philosophy discussion can help the concept's analysis and more particularly the analysis of the concept of proportionality, but the philosophical concept of proportionality is not designed for a substitution for the legal reasoning. The paper criticizes as much the normative analysis of proportionality that regards the rights like values to optimize as the juridical analysis that radicalize a strong opposition between rules and principles.

Moral error theorists argue that moral thought and discourse are systematically in error, and that nothing is, or can ever be, morally permissible, required or forbidden. I begin by discussing how error theorists arrive at this conclusion. I then argue that if we accept a moral error theory, we cannot escape a pressing problem – what should we do next, metaethically speaking? I call this problem the ‘what now?’ problem, or WNP for short. I discuss the attempts others have made to respond to the WNP, and in each case I show that the responses fail to be satisfying. I then propose a new response to the WNP, which I call revolutionary relativism. I define revolutionary relativism, explain why it is preferable to the existing responses to the WNP, and defend it against the most problematic objections I anticipate that opponents might raise. I conclude that revolutionary relativism succeeds where previous WNP responses fail, and that if we accept a moral error theory, we should become revolutionary relativists.

Simultaneous consideration of initial construction cost and failure risk in practical design of critical hydraulic structures is a long-standing problem in water resources planning and management. Despite extensive efforts to effectively tackle this problem during recent decades, the traditional rather inefficient technique of return period approach still enjoys being the dominant technique in real-world projects. Accordingly, this article aims at developing an innovative evolutionarycomputation-based multi-objective model as a remedy to shortcomings of existing common methods. This simulation-optimization framework generates a series of uniformly distributed trade-off solutions which represent the compromise between competing objectives of construction cost and failure risk. Hydrologic and hydraulic uncertainties along with flood routing process are considered in the optimization process to provide a more complete picture of the problem. This approach is demonstrated and discussed for flood diversion system of Bakhtiari Dam in Iran and the Pareto optimal fronts are found for different combinations of uncertainties. The presented multi-objective approach can effectively enlarge the decision maker's scope to more efficiently determine the optimum design of the system.

Decomposition is a basic strategy in traditional multiobjective optimization. However, it has not yet been widely used in multiobjective evolutionary optimization. This paper proposes a multiobjective evolutionary algorithm based on decomposition (MOEA/D). It decomposes a multiobjective optimization problem into a number of scalar optimization subproblems and optimizes them simultaneously. Each subproblem is optimized by only using information from its several neighboring subproblems, which makes MOEA/D have lower computational complexity at each generation than MOGLS and nondominated sorting genetic algorithm II (NSGA-II). Experimental results have demonstrated that MOEA/D with simple decomposition methods outperforms or performs similarly to MOGLS and NSGA-II on multiobjective 0-1 knapsack problems and continuous multiobjective optimization problems. It has been shown that MOEA/D using objective normalization can deal with disparately-scaled objectives, and MOEA/D with an advanced decomposition method can generate a set of very evenly distributed solutions for 3-objective test instances. The ability of MOEA/D with small population, the scalability and sensitivity of MOEA/D have also been experimentally investigated in this paper.

This paper integrates elements from the theory of agency, the theory of property rights and the theory of finance to develop a theory of the ownership structure of the firm. We define the concept of agency costs, show its relationship to the 'separation and control' issue, investigate the nature of the agency costs generated by the existence of debt and outside equity, demonstrate who bears costs and why, and investigate the Pareto optimality of their existence. We also provide a new definition of the firm, and show how our analysis of the factors influencing the creation and issuance of debt and equity claims is a special case of the supply side of the completeness of markets problem.

The central composite experimental design and response surface methodology have been employed for statistical modeling and analysis of the results dealing with nickel electroplating process. The empirical models developed in terms of design variables (current density J (A/dm 2 ), temperature T ( • C) and pH) have been found statistically adequate to describe the process responses, i.e. cathode efficiency Y (%), coating thickness U (m), brightness V (%) and hardness W (HV). The graphical representations consisted of 2D contour plots and 3D surface plots have been used for exploring and analysis of response surfaces in order to identify the main, quadratic and interaction effects. The multi-response optimization of nickel electroplating process has been carried out by means of desirability function approach. To this end, a genetic algorithm has been used for mathematical optimization of the multi-response problem. The optimization algorithm has conducted to a set of equivalent solutions named Pareto optimal set. The confirmation runs have been employed in order to make a decision about the optimal solution approved by experiment. Thus, the optimum conditions of nickel electroplating has been defined in this work as J* = 5.35 (A/dm 2 ), T* = 33.44 ( • C) and pH* = 6.22 and respectively the responses confirmed by experiment were Y = 79.12 ± 0.18 (%), U = 52.77 ± 0.48 (m), V = 26.12 ± 0.45 (%) and W = 371.6 ± 1.77 (HV). In such conditions the quality of nickel electroplating deposit was the best one in accordance with experimental results.

A systematic approach is presented to approximate the Pareto optimal front (POF) by a response surface approximation. The data for the POF is obtained by multi-objective evolutionary algorithm. Improvements to address drift in the POF are also presented. The approximated POF can help visualize and quantify trade-offs among objectives to select compromise designs. The bounds of this approximate POF are obtained using multiple convex-hulls. The proposed approach is applied to study trade-offs among objectives of a rocket injector design problem where performance and life objectives compete. The POF is approximated using a quintic polynomial. The compromise region quantifies trade-offs among objectives.

Optimization of the whole plant instead of important individual units is essential for maximizing savings and operational efficiency. Often, there are conflicting objectives for optimizing industrial processes. Many previous studies on multi-objective optimization involved a few critical units (and not complete plants) using models and simulation programs specifically developed for the respective application. Developing rigorous models and a separate code for simulating a complete plant, for the sake of multi-objective optimization is difficult and time consuming. There is potential to make this task easier by employing available process simulators such as Aspen Plus and Hysys. But these simulators do not currently have multi-objective optimization tools. Hence, an interface has been developed between Non-dominated Sorted Genetic Algorithm (NSGA-II) and Hysys. Plant-wide optimization using this interface involves three main steps: (a) development and testing of Hysys model for steady simulation of the process under study; (b) sensitivity analysis and selection of objectives, decision variables and constraints; and (c) optimization of the process for multiple objectives using NSGA-II. This paper describes optimization of a styrene unit/plant for multiple objectives using the interface and compares the obtained results with those obtained using an independently developed simulation program.

I argue that John Kenneth Galbraith‟s theory of the “dependence effect” in The  Affluent Society provides a way to rescue A.C. Pigou‟s argument for wealth redistribution from a powerful objection. The objection is based on the unprovability of statements making interpersonal comparisons of utility. Galbraith‟s dependence effect theory allows him to present a version of the Pigovian argument that requires no such statements to be made. I argue that Galbraith‟s main piece of advocacy in The  Affluent Society was for income redistribution, despite the fact that he claimed to be in favour of greater spending in the public sector rather than redistribution as such. I then show how my reading of the dependence effect theory helps to defend it against objections from Hayek and Rothbard. I end by discussing what improvements in economics a proper test of the theory would require and showing how my reading of it helps to reveal the ongoing importance of The Affluent Society to the understanding of political economy.

Skyline Queries have recently received a lot of attention due to their intuitive query capabilities. Following the concept of Pareto optimality all 'best' database objects are returned to the user. However, this often results in unmanageable large result set sizes hampering the success of this innovative paradigm. As an effective remedy for this problem, trade-offs provide a natural concept for dealing with incomparable choices. But such trade-offs are not reflected by the Pareto paradigm. Thus, incorporating them into the users' preference orders and adjusting skyline results accordingly needs special algorithms beyond traditional skylining. For the actual integration of trade-offs into skylines, the problem of ensuring the consistency of arbitrary trade-off sets poses a demanding challenge. Consistency is a crucial aspect when dealing with multi-dimensional trade-offs spanning over several attributes. If the consistency should be violated, cyclic preferences may occur in the result set. But such cyclic preferences cannot be handled by information systems in a sensible way. Often, this problem is circumvented by restricting the trade-offs' expressiveness, e.g. by altogether ignoring some classes of possibly inconsistent tradeoffs. In this paper, we will present a new algorithm capable of efficiently verifying the consistency of any arbitrary set of trade-offs. After motivating its basic concepts and introducing the algorithm itself, we will also show that it exhibits superior average-case performance. The benefits of our approach promise to pave the way towards personalized and cooperative information systems.

This paper describes the use of decision maker preferences in terms of the relative importance of objectives in evolutionary multiobjective optimization. A mathematical model of the relative importance of objectives and an elicitation algorithm are proposed, and three methods of incorporating explicated preference information are described and applied to standard test problems in an empirical study. The axiomatic model proposed here formalizes the notion of relative importance of objectives as a partial order that supports strict preference, equality of importance, and incomparability between objective pairs. Unlike most approaches, the proposed model does not encode relative importance as a set of real-valued parameters. Instead, the approach provides a functional correspondence between a coherent overall preference with a subset of the Pareto-optimal front. An elicitation algorithm is also provided to assist a human decision maker in constructing a coherent overall preference. Besides elicitation of a priori preference, an interactive facility is also furnished to enable modification of overall preference while the search progresses. Three techniques of integrating explicated preference information into the wellknown Non-dominated Sorting Genetic Algorithm (NSGA)-II are also described and validated in a set of empirical investigation. The approach allows a focus on a subset of the Pareto-front. Validations on test problems demonstrate that the preferencebased algorithm gained better convergence as the dimensionality of the problems increased.

The resolution of a Multi-Objective Optimization Problem (MOOP) does not end when the Pareto-optimal set is found. In real problems, a single solution must be selected. Ideally, this solution must belong to the non-dominated solutions set and must take into account the preferences of a Decision Maker (DM). Therefore, the searching for a single solution (or solutions) in MOOP is done in two steps. First, a Pareto optimal set is found. Multi-Objective Evolutionary Algorithms (MOEA), based on the principle of Pareto optimality, are designed to produce the complete set of non-dominated solutions. Second, a methodology able to select a single solution from the set of non-dominated solutions (or a region of the Pareto frontier), and taking into account the preferences of a Decision Maker (DM), can be applied. In this work, a method, based on a weighted stress function, is proposed. It is able to integrate the user's preferences in order to find the best region of the Pareto frontier accordingly with these preferences. This method was tested on some benchmark test problems, with two and three criteria. This methodology is able to select efficiently the best Pareto-frontier region for the specified relative importance of the criteria.

Genetic Algorithm (GA) has been used in this paper for a new approach of sub-optimal model reduction in the Nyquist plane and optimal time domain tuning of PID and fractional order (FO) PI λ D μ controllers. Simulation studies show that the Nyquist based new model reduction technique outperforms the conventional H 2 norm based reduced parameter modeling technique. With the tuned controller parameters and reduced order model parameter data-set, optimum tuning rules have been developed with a test-bench of higher order processes via Genetic Programming (GP). The GP performs a symbolic regression on the reduced process parameters to evolve a tuning rule which provides the best analytical expression to map the data. The tuning rules are developed for a minimum time domain integral performance index described by weighted sum of error index and controller effort. From the reported Pareto optimal front of GP based optimal rule extraction technique a trade-off can be made between the complexity of the tuning formulae and the control performance. The efficacy of the single-gene and multi-gene GP based tuning rules has been compared with original GA based control performance for the PID and PI λ D μ controllers, handling four different class of representative higher order processes. These rules are very useful for process control engineers as they inherit the power of the GA based tuning methodology, but can be easily calculated without the requirement for running the computationally intensive GA every time. Three dimensional plots of the required variation in PID/FOPID controller parameters with reduced process parameters have been shown as a guideline for the operator. Parametric robustness of the reported GP based tuning rules has also been shown with credible simulation examples.

In this paper, we deal with the solution of the multicriteria shortest path problem. In particular, we present a class of labeling methods to generate the entire set of Pareto-optimal path-length vectors from an origin node s to all other nodes in a multicriteria network. The proposed methods are supported theoretically by the principle of optimality and they are defined

We propose an iterative algorithm to design optimal linear transmitters and receivers in a K-user frequency-flat MIMO Interference Channel (MIMO IFC) with full channel state information (CSI). The transmitters and receivers are optimized to maximize the Weighted Sum Rate (WSR) of the MIMO IFC. Maximization of WSR is desirable since it allows the system to cover all the rate tuples on the Pareto-optimal rate region boundary for a given MIMO IFC.

In this paper we extend the notion of Pareto efficiency to overlapping generations settings in which fertility decisions are endogenous. The contribution of this paper is threefold. First, we provide two definitions of Pareto dominance and, consequently, of Pareto efficiency referred to Millian efficiency and strong efficiency, differing in the treatment of agents that never get to be born. Second, we provide necessary (static) and sufficient (dynamic) conditions to determine whether or not an allocation is Millian efficient. Third, we characterize Millian efficient allocations as the equilibria of a decentralized price mechanism, and enunciate the Fundamental Welfare Theorems in an environment with endogenous fertility.

In trying to solve multiobjective optimization problems, many traditional methods scalarize the objective vector into a single objective. In those cases, the obtained solution is highly sensitive to the weight vector used in the scalarization process and demands the user to have knowledge about the underlying problem. Moreover, in solving multiobjective problems, designers may be interested in a set of Pareto-optimal points, instead of a single point. Since genetic algorithms(GAs) work with a population of points, it seems natural to use GAs in multiobjective optimization problems to capture a number of solutions simultaneously. Although a vector evaluated GA (VEGA) has been implemented by Scha er and has been tried to solve a number of multiobjective problems, the algorithm seems to have bias towards some regions. In this paper, we investigate Goldberg's notion of nondominated sorting in GAs along with a niche and speciation method to nd multiple Pareto-optimal points simultaneously. The proof-of-principle results obtained on three problems used by Scha er and others suggest that the proposed method can be extended to higher dimensional and more di cult multiobjective problems. A number of suggestions for extension and application of the algorithm is also discussed.

The Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler and Thiele 1999) is a relatively recent technique for finding or approximating the Pareto-optimal set for multiobjective optimization problems. In different studies (Zitzler and Thiele 1999; Zitzler, Deb, and Thiele 2000) SPEA has shown very good performance in comparison to other multiobjective evolutionary algorithms, and therefore it has been a point of reference in various recent investigations, e.g., . Furthermore, it has been used in different applications, e.g., . In this paper, an improved version, namely SPEA2, is proposed, which incorporates in contrast to its predecessor a fine-grained fitness assignment strategy, a density estimation technique, and an enhanced archive truncation method. The comparison of SPEA2 with SPEA and two other modern elitist methods, PESA and NSGA-II, on different test problems yields promising results.

By means of an example, it is shown that the prenucleolus is not the only minimal solution that satisfies nonemptiness, Pareto optimality, covariance, the equal treatment property, and the reduced game property, even if the universe of players is infinite. This example also disproves a conjecture of . As a second result, we prove that the prenucleolus is axiomatized by nonemptiness, covariance, the equal treatment property, and the reconfirmation property, provided the universe of players is infinite.

A special non-TEMA type tubular recuperative heat exchanger used as a regenerator of a gas turbine cycle is considered for multi-criteria optimization. It is assumed that the recuperator is designed for an existing gas turbine cycle to be retrofitted. Three scenarios for optimization of the proposed system have been considered. In one scenario, the objective is minimizing the cost of recuperator; while in another scenario maximizing the cycle exergetic efficiency is considered. In third scenario, both objectives are optimized simultaneously in a multi-objective optimization approach. Geometric specification of the recuperator including tubes length, tubes outside/inside diameters, tube pitch in the tube bundle, inside shell diameter, outer and inner tube limits of the tube bundle and the total number of disc and doughnut baffles are considered as decision variables. Combination of these objectives and decision variables with suitable engineering and physical constraints (including NO x and CO emission limitations) makes a set of MINLP optimization problem. Optimization programming in MATLAB is performed using one of the most powerful and robust multi-objective optimization algorithms namely NSGA-II. This approach which is based on the Genetic Algorithm is applied to find a set of Pareto optimal solutions. Pareto optimal frontier is obtained and a final optimal solution is selected in a decision-making process. It is shown that the multi-objective optimization scenario can be considered as a generalized optimization approach in which balances between economical viewpoints of both heat exchanger manufacturer and end user of recuperator.

Ngoài phần giới thiệu môn học, nội dung cơ bản của chương I: Nêu và giải thích khái niệm "phát triển nông thôn". Theo khái niệm này, phát triển nông thôn là: "một quá trình tất yếu cải thiện một cách bền vững về kinh tế, xã hội, văn hóa và môi trường, nhằm nâng cao chất lượng cuộc sống của dân cư nông thôn. Quá trình này, trước hết chính là do người dân nông thôn với sự hỗ trợ tích cực của Nhà nước và các tổ chức khác".

There has been a considerable body of work on search-based test data generation for branch coverage. However, hitherto, there has been no work on multi-objective branch coverage. In many scenarios a single-objective formulation is unrealistic; testers will want to find test sets that meet several objectives simultaneously in order to maximize the value obtained from the inherently expensive process of running the test cases and examining the output they produce. This paper introduces multi-objective branch coverage. The paper ...

This paper integrates elements from the theory of agency, the theory of property rights and the theory of finance to develop a theory of the ownership structure of the firm. We define the concept of agency costs, show its relationship to the 'separation and control' issue, investigate the nature of the agency costs generated by the existence of debt and outside equity, demonstrate who bears costs and why, and investigate the Pareto optimality of their existence. We also provide a new definition of the firm, and show how our analysis of the factors influencing the creation and issuance of debt and equity claims is a special case of the supply side of the completeness of markets problem.

Motivated by problems of coordination failure observed in weak-link games, we experimentally investigate behavioral spillovers for minimum-and median-effort coordination games. Subjects play these coordination games simultaneously and sequentially. The results show that successful coordination on the Pareto optimal equilibrium in the median game influences behavior in the minimum game when the games are played sequentially. Moreover, this positive, Pareto-improving spillover is present even when group composition changes across games, although the effect is not as strong. We also find that the precedent for uncooperative behavior in the minimum game does not influence play in the median game. These findings suggest guidelines for increasing cooperative behavior within organizations.

Evolutionary algorithms (EA's) are often well-suited for optimization problems involving several, often conflicting objectives. Since 1985, various evolutionary approaches to multiobjective optimization have been developed that are capable of searching for multiple solutions concurrently in a single run. However, the few comparative studies of different methods presented up to now remain mostly qualitative and are often restricted to a few approaches. In this paper, four multiobjective EA's are compared quantitatively where an extended 0/1 knapsack problem is taken as a basis. Furthermore, we introduce a new evolutionary approach to multicriteria optimization, the Strength Pareto EA (SPEA), that combines several features of previous multiobjective EA's in a unique manner. It is characterized by a) storing nondominated solutions externally in a second, continuously updated population, b) evaluating an individual's fitness dependent on the number of external nondominated points that dominate it, c) preserving population diversity using the Pareto dominance relationship, and d) incorporating a clustering procedure in order to reduce the nondominated set without destroying its characteristics. The proof-of-principle results obtained on two artificial problems as well as a larger problem, the synthesis of a digital hardware-software multiprocessor system, suggest that SPEA can be very effective in sampling from along the entire Pareto-optimal front and distributing the generated solutions over the tradeoff surface. Moreover, SPEA clearly outperforms the other four multiobjective EA's on the 0/1 knapsack problem.

The prediction of optimal machining conditions for required surface finish and dimensional accuracy plays a very important role in process planning of wire electrical discharge machining. The present work deals with the features of trim cutting operation of wire electrical discharge machining of ␥-titanium aluminide. A second-order mathematical model, in terms of machining parameters, was developed for surface roughness, dimensional shift and cutting speed using response surface methodology (RSM). The experimental plan was based on the face centered, central composite design (CCD). The residual analysis and experimental results indicate that the proposed models could adequately describe the performance indicators within the limits of the factors that are being investigated. Finally the trim cutting operation has been optimized for a given machining condition by desirability function approach and Pareto optimization algorithm. It was observed that performance of the developed Pareto optimization algorithm is superior compared to desirability function approach.

We consider the problem of how to select an investment project according to a two-criterion technique and illustrate this issue by the transportation-and- logistic center project for the Novosibirsk Oblast. We also analyze how regular the investments are made and show the minimal discounted costs and an algorithm and the mechanism to select Parettos optimal investments.

A criticism of Evolutionary Algorithms might be the lack of efficient and robust generic methods to handle constraints. The most widespread approach for constrained search problems is to use penalty methods, because of their simplicity and ease of implementation. Nonetheless, the most difficult aspect of the penalty function approach is to find an appropriate penalty parameters. In this paper, a method combining the new Non-dominated Ranked Genetic Algorithm (NRGA), with a parameterless penalty approach are exploited to devise the search to find Pareto optimal set of solutions. The new Parameterless Penalty and the Nondominated Ranked Genetic Algorithm (PP-NRGA) continuously find better Pareto optimal set of solutions. This new algorithm have been evaluated by solving four test problems, reported in the multi-objective evolutionary algorithm (MOEA) literature. Performance comparisons based on quantitative metrics for accuracy, coverage, and spread are presented.

Evolutionary multiobjective optimization (EMO) methodologies have gained popularity in finding a representative set of Pareto optimal solutions in the past decade and beyond. Several techniques have been proposed in the specialized literature to ensure good convergence and diversity of the obtained solutions. However, in real world applications, the decision maker is not interested in the overall Pareto optimal front since the final decision is a unique solution. Recently, there has been an increased emphasis in addressing the decision-making task in searching for the most preferred alternatives. In this paper, we introduce a new variant of the Pareto dominance relation, called r-dominance, which has the ability to create a strict partial order among Pareto-equivalent solutions. This fact makes such a relation able to guide the search toward the interesting parts of the Pareto optimal region based on the decision maker's preferences expressed as a set of aspiration levels. After integrating the new dominance relation in the NSGA-II methodology, the efficacy and the usefulness of the modified procedure are assessed through two to ten-objective test problems a priori and interactively. Moreover, the proposed approach provides competitive and better results when compared to other recently proposed preferencebased EMO approaches.