RBF equalizer design using directional evolutionary multi-objective optimization

Whilst radial basis function (RBF) equalizers have been employed to combat the linear and nonlinear distortions in modern communication systems, most of them do not take into account the equalizer's generalization capability. In this paper, it is firstly proposed that the. model's generalization capability can be improved by treating the modelling problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets. Then, as a modelling application, a new RBF equalizer learning scheme is introduced based on the directional evolutionary MOO (EMOO). Directional EMOO improves the computational efficiency of conventional EMOO, which has been widely applied in solving MOO problems, by explicitly making use of the directional information. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good performance not only on explaining the training samples but on predicting the unseen samples.

Nonlinear channel equalizer design using directional evolutionary multi-objective optimization

In this paper, a new equalizer learning scheme is introduced based on the algorithm of the directional evolutionary multi-objective optimization (EMOO). Whilst nonlinear channel equalizers such as the radial basis function (RBF) equalizers have been widely studied to combat the linear and nonlinear distortions in the modern communication systems, most of them do not take into account the equalizers' generalization capabilities. In this paper, equalizers are designed aiming at improving their generalization capabilities. It is proposed that this objective can be achieved by treating the equalizer design problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets, followed by deriving equalizers with good capabilities of recovering the signals for all the training sets. Conventional EMOO which is widely applied in the MOO problems suffers from disadvantages such as slow convergence speed. Directional EMOO improves the computational efficiency of the conventional EMOO by explicitly making use of the directional information. The new equalizer learning scheme based on the directional EMOO is applied to the RBF equalizer design. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good generalization capabilities, i.e., good performance on predicting the unseen samples.

Construction of aggregation functions from data using linear programming

This article examines the construction of aggregation functions from data by minimizing the least absolute deviation criterion. We formulate various instances of such problems as linear programming problems. We consider the cases in which the data are provided as intervals, and the outputs ordering needs to be preserved, and show that linear programming formulation is valid for such cases. This feature is very valuable in practice, since the standard simplex method can be used.

Multi-Objective Pipe Smoothing Genetic Algorithm For Water Distribution Network Design

This paper describes the formulation of a Multi-objective Pipe Smoothing Genetic Algorithm (MOPSGA) and its application to the least cost water distribution network design problem. Evolutionary Algorithms have been widely utilised for the optimisation of both theoretical and real-world non-linear optimisation problems, including water system design and maintenance problems. In this work we present a pipe smoothing based approach to the creation and mutation of chromosomes which utilises engineering expertise with the view to increasing the performance of the algorithm whilst promoting engineering feasibility within the population of solutions. MOPSGA is based upon the standard Non-dominated Sorting Genetic Algorithm-II (NSGA-II) and incorporates a modified population initialiser and mutation operator which directly targets elements of a network with the aim to increase network smoothness (in terms of progression from one diameter to the next) using network element awareness and an elementary heuristic. The pipe smoothing heuristic used in this algorithm is based upon a fundamental principle employed by water system engineers when designing water distribution pipe networks where the diameter of any pipe is never greater than the sum of the diameters of the pipes directly upstream resulting in the transition from large to small diameters from source to the extremities of the network. MOPSGA is assessed on a number of water distribution network benchmarks from the literature including some real-world based, large scale systems. The performance of MOPSGA is directly compared to that of NSGA-II with regard to solution quality, engineering feasibility (network smoothness) and computational efficiency. MOPSGA is shown to promote both engineering and hydraulic feasibility whilst attaining good infrastructure costs compared to NSGA-II.

Multi Objective Evolutionary Algorithm Applied to the Optimal Power Flow Problem

This work presents the application of a multiobjective evolutionary algorithm (MOEA) for optimal power flow (OPF) solution. The OPF is modeled as a constrained nonlinear optimization problem, non-convex of large-scale, with continuous and discrete variables. The violated inequality constraints are treated as objective function of the problem. This strategy allows attending the physical and operational restrictions without compromise the quality of the found solutions. The developed MOEA is based on the theory of Pareto and employs a diversity-preserving mechanism to overcome the premature convergence of algorithm and local optimal solutions. Fuzzy set theory is employed to extract the best compromises of the Pareto set. Results for the IEEE-30, RTS-96 and IEEE-354 test systems are presents to validate the efficiency of proposed model and solution technique.

Design and management optimization of trickle irrigation systems using non-linear programming

A non-linear model is presented which optimizes the lay-out, as well as the design and management of trickle irrigation systems, to achieve maximum net benefit. The model consists of an objective function that maximizes profit at the farm level, subject to appropriate geometric and hydraulic constraints. It can be applied to rectangular shaped fields, with uniform or zero slope. The software used is the Gams-Minos package. The basic inputs are the crop-water-production function, the cost function and cost of system components, and design variables. The main outputs are the annual net benefit and pipe diameters and lengths. To illustrate the capability of the model, a sensitivity analysis of the annual net benefit for a citrus field is evaluated with respect to irrigated area, ground slope, micro-sprinkler discharge and shape of the field. The sensitivity analysis suggests that the greatest benefit is obtained with the smallest microsprinkler discharge, the greatest area, a square field and zero ground slope. The costs of the investment and energy are the components of the objective function that had the greatest effect in the 120 situations evaluated. (C) 1996 Academic Press Limited

A mixed-integer linear programming approach for optimal type, size and allocation of distributed generation in radial distribution systems

This paper presents a mixed-integer linear programming approach to solving the problem of optimal type, size and allocation of distributed generators (DGs) in radial distribution systems. In the proposed formulation, (a) the steady-state operation of the radial distribution system, considering different load levels, is modeled through linear expressions; (b) different types of DGs are represented by their capability curves; (c) the short-circuit current capacity of the circuits is modeled through linear expressions; and (d) different topologies of the radial distribution system are considered. The objective function minimizes the annualized investment and operation costs. The use of a mixed-integer linear formulation guarantees convergence to optimality using existing optimization software. The results of one test system are presented in order to show the accuracy as well as the efficiency of the proposed solution technique.© 2012 Elsevier B.V. All rights reserved.

A new method for decision making in multi-objective optimization problems

Many engineering sectors are challenged by multi-objective optimization problems. Even if the idea behind these problems is simple and well established, the implementation of any procedure to solve them is not a trivial task. The use of evolutionary algorithms to find candidate solutions is widespread. Usually they supply a discrete picture of the non-dominated solutions, a Pareto set. Although it is very interesting to know the non-dominated solutions, an additional criterion is needed to select one solution to be deployed. To better support the design process, this paper presents a new method of solving non-linear multi-objective optimization problems by adding a control function that will guide the optimization process over the Pareto set that does not need to be found explicitly. The proposed methodology differs from the classical methods that combine the objective functions in a single scale, and is based on a unique run of non-linear single-objective optimizers.

Multi-objective evolutionary algorithm for single and multiple fault service restoration in large-scale distribution systems

Network reconfiguration for service restoration (SR) in distribution systems is a complex optimization problem. For large-scale distribution systems, it is computationally hard to find adequate SR plans in real time since the problem is combinatorial and non-linear, involving several constraints and objectives. Two Multi-Objective Evolutionary Algorithms that use Node-Depth Encoding (NDE) have proved able to efficiently generate adequate SR plans for large distribution systems: (i) one of them is the hybridization of the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) with NDE, named NSGA-N; (ii) the other is a Multi-Objective Evolutionary Algorithm based on subpopulation tables that uses NDE, named MEAN. Further challenges are faced now, i.e. the design of SR plans for larger systems as good as those for relatively smaller ones and for multiple faults as good as those for one fault (single fault). In order to tackle both challenges, this paper proposes a method that results from the combination of NSGA-N, MEAN and a new heuristic. Such a heuristic focuses on the application of NDE operators to alarming network zones according to technical constraints. The method generates similar quality SR plans in distribution systems of significantly different sizes (from 3860 to 30,880 buses). Moreover, the number of switching operations required to implement the SR plans generated by the proposed method increases in a moderate way with the number of faults.

Ranking efficient decision-making units in data envelopment analysis using fuzzy concept

This paper introduces a new mathematical method for improving the discrimination power of data envelopment analysis and to completely rank the efficient decision-making units (DMUs). Fuzzy concept is utilised. For this purpose, first all DMUs are evaluated with the CCR model. Thereafter, the resulted weights for each output are considered as fuzzy sets and are then converted to fuzzy numbers. The introduced model is a multi-objective linear model, endpoints of which are the highest and lowest of the weighted values. An added advantage of the model is its ability to handle the infeasibility situation sometimes faced by previously introduced models.

A novel adaptive weight selection algorithm for multi-objective multi-agent reinforcement learning

To solve multi-objective problems, multiple reward signals are often scalarized into a single value and further processed using established single-objective problem solving techniques. While the field of multi-objective optimization has made many advances in applying scalarization techniques to obtain good solution trade-offs, the utility of applying these techniques in the multi-objective multi-agent learning domain has not yet been thoroughly investigated. Agents learn the value of their decisions by linearly scalarizing their reward signals at the local level, while acceptable system wide behaviour results. However, the non-linear relationship between weighting parameters of the scalarization function and the learned policy makes the discovery of system wide trade-offs time consuming. Our first contribution is a thorough analysis of well known scalarization schemes within the multi-objective multi-agent reinforcement learning setup. The analysed approaches intelligently explore the weight-space in order to find a wider range of system trade-offs. In our second contribution, we propose a novel adaptive weight algorithm which interacts with the underlying local multi-objective solvers and allows for a better coverage of the Pareto front. Our third contribution is the experimental validation of our approach by learning bi-objective policies in self-organising smart camera networks. We note that our algorithm (i) explores the objective space faster on many problem instances, (ii) obtained solutions that exhibit a larger hypervolume, while (iii) acquiring a greater spread in the objective space.

Exposing market mechanism design trade-offs via multi-objective evolutionary search

Market mechanisms are a means by which resources in contention can be allocated between contending parties, both in human economies and those populated by software agents. Designing such mechanisms has traditionally been carried out by hand, and more recently by automation. Assessing these mechanisms typically involves them being evaluated with respect to multiple conflicting objectives, which can often be nonlinear, noisy, and expensive to compute. For typical performance objectives, it is known that designed mechanisms often fall short on being optimal across all objectives simultaneously. However, in all previous automated approaches, either only a single objective is considered, or else the multiple performance objectives are combined into a single objective. In this paper we do not aggregate objectives, instead considering a direct, novel application of multi-objective evolutionary algorithms (MOEAs) to the problem of automated mechanism design. This allows the automatic discovery of trade-offs that such objectives impose on mechanisms. We pose the problem of mechanism design, specifically for the class of linear redistribution mechanisms, as a naturally existing multi-objective optimisation problem. We apply a modified version of NSGA-II in order to design mechanisms within this class, given economically relevant objectives such as welfare and fairness. This application of NSGA-II exposes tradeoffs between objectives, revealing relationships between them that were otherwise unknown for this mechanism class. The understanding of the trade-off gained from the application of MOEAs can thus help practitioners with an insightful application of discovered mechanisms in their respective real/artificial markets.

Temperature management for heterogeneous multi-core FPGAs using adaptive evolutionary multi-objective approaches

Heterogeneous multi-core FPGAs contain different types of cores, which can improve efficiency when used with an effective online task scheduler. However, it is not easy to find the right cores for tasks when there are multiple objectives or dozens of cores. Inappropriate scheduling may cause hot spots which decrease the reliability of the chip. Given that, our research builds a simulating platform to evaluate all kinds of scheduling algorithms on a variety of architectures. On this platform, we provide an online scheduler which uses multi-objective evolutionary algorithm (EA). Comparing the EA and current algorithms such as Predictive Dynamic Thermal Management (PDTM) and Adaptive Temperature Threshold Dynamic Thermal Management (ATDTM), we find some drawbacks in previous work. First, current algorithms are overly dependent on manually set constant parameters. Second, those algorithms neglect optimization for heterogeneous architectures. Third, they use single-objective methods, or use linear weighting method to convert a multi-objective optimization into a single-objective optimization. Unlike other algorithms, the EA is adaptive and does not require resetting parameters when workloads switch from one to another. EAs also improve performance when used on heterogeneous architecture. A efficient Pareto front can be obtained with EAs for the purpose of multiple objectives.

Hybrid multi-objective optimization and hybridized self-organizing response surface method

Numerical optimization is a technique where a computer is used to explore design parameter combinations to find extremes in performance factors. In multi-objective optimization several performance factors can be optimized simultaneously. The solution to multi-objective optimization problems is not a single design, but a family of optimized designs referred to as the Pareto frontier. The Pareto frontier is a trade-off curve in the objective function space composed of solutions where performance in one objective function is traded for performance in others. A Multi-Objective Hybridized Optimizer (MOHO) was created for the purpose of solving multi-objective optimization problems by utilizing a set of constituent optimization algorithms. MOHO tracks the progress of the Pareto frontier approximation development and automatically switches amongst those constituent evolutionary optimization algorithms to speed the formation of an accurate Pareto frontier approximation. Aerodynamic shape optimization is one of the oldest applications of numerical optimization. MOHO was used to perform shape optimization on a 0.5-inch ballistic penetrator traveling at Mach number 2.5. Two objectives were simultaneously optimized: minimize aerodynamic drag and maximize penetrator volume. This problem was solved twice. The first time the problem was solved by using Modified Newton Impact Theory (MNIT) to determine the pressure drag on the penetrator. In the second solution, a Parabolized Navier-Stokes (PNS) solver that includes viscosity was used to evaluate the drag on the penetrator. The studies show the difference in the optimized penetrator shapes when viscosity is absent and present in the optimization. In modern optimization problems, objective function evaluations may require many hours on a computer cluster to perform these types of analysis. One solution is to create a response surface that models the behavior of the objective function. Once enough data about the behavior of the objective function has been collected, a response surface can be used to represent the actual objective function in the optimization process. The Hybrid Self-Organizing Response Surface Method (HYBSORSM) algorithm was developed and used to make response surfaces of objective functions. HYBSORSM was evaluated using a suite of 295 non-linear functions. These functions involve from 2 to 100 variables demonstrating robustness and accuracy of HYBSORSM.

Defining efficient policies in a general equilibrium model: a multi-objective approach

Macroeconomic policy makers are typically concerned with several indicators of economic performance. We thus propose to tackle the design of macroeconomic policy using Multicriteria Decision Making (MCDM) techniques. More specifically, we employ Multiobjective Programming (MP) to seek so-called efficient policies. The MP approach is combined with a computable general equilibrium (CGE) model. We chose use of a CGE model since they have the dual advantage of being consistent with standard economic theory while allowing one to measure the effect(s) of a specific policy with real data. Applying the proposed methodology to Spain (via the 1995 Social Accounting Matrix) we first quantified the trade-offs between two specific policy objectives: growth and inflation, when designing fiscal policy. We then constructed a frontier of efficient policies involving real growth and inflation. In doing so, we found that policy in 1995 Spain displayed some degree of inefficiency with respect to these two policy objectives. We then offer two sets of policy recommendations that, ostensibly, could have helped Spain at the time. The first deals with efficiency independent of the importance given to both growth and inflation by policy makers (we label this set: general policy recommendations). A second set depends on which policy objective is seen as more important by policy makers: increasing growth or controlling inflation (we label this one: objective-specific recommendations).