Showing papers on "Multi-objective optimization published in 2007"

MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition

Abstract: 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.

Covariance Matrix Adaptation for Multi-objective Optimization

Abstract: The covariancematrix adaptation evolution strategy (CMA-ES) is one of themost powerful evolutionary algorithms for real-valued single-objective optimization. In this paper, we develop a variant of the CMA-ES for multi-objective optimization (MOO). We first introduce a single-objective, elitist CMA-ES using plus-selection and step size control based on a success rule. This algorithm is compared to the standard CMA-ES. The elitist CMA-ES turns out to be slightly faster on unimodal functions, but is more prone to getting stuck in sub-optimal local minima. In the new multi-objective CMAES (MO-CMA-ES) a population of individuals that adapt their search strategy as in the elitist CMA-ES is maintained. These are subject to multi-objective selection. The selection is based on non-dominated sorting using either the crowding-distance or the contributing hypervolume as second sorting criterion. Both the elitist single-objective CMA-ES and the MO-CMA-ES inherit important invariance properties, in particular invariance against rotation of the search space, from the original CMA-ES. The benefits of the new MO-CMA-ES in comparison to the well-known NSGA-II and to NSDE, a multi-objective differential evolution algorithm, are experimentally shown.

Advances in Particle Swarm Optimization for Antenna Designs: Real-Number, Binary, Single-Objective and Multiobjective Implementations

Abstract: The particle swarm optimization (PSO) is a recently developed evolutionary algorithm (EA) based on the swarm behavior in the nature. This paper presents recent advances in applying a versatile PSO engine to real-number, binary, single-objective and multiobjective optimizations for antenna designs, with a randomized Newtonian mechanics model developed to describe the swarm behavior. The design of aperiodic (nonuniform and thinned) antenna arrays is presented as an example for the application of the PSO engine. In particular, in order to achieve an improved peak sidelobe level (SLL), element positions in a nonuniform array are optimized by real-number PSO (RPSO). On the other hand, in a thinned array, the on/off state of each element is determined by binary PSO (BPSO). Optimizations for both nonuniform arrays and thinned arrays are also expanded to multiobjective cases. As a result, nondominated designs on the Pareto front enable one to achieve other design factors than the peak SLL. Optimized antenna arrays are compared with periodic arrays and previously presented aperiodic arrays. Selected designs fabricated and measured to validate the effectiveness of PSO in practical electromagnetic problems

An Evolutionary Approach to Multiobjective Clustering

Abstract: The framework of multiobjective optimization is used to tackle the unsupervised learning problem, data clustering, following a formulation first proposed in the statistics literature. The conceptual advantages of the multiobjective formulation are discussed and an evolutionary approach to the problem is developed. The resulting algorithm, multiobjective clustering with automatic k-determination, is compared with a number of well-established single-objective clustering algorithms, a modern ensemble technique, and two methods of model selection. The experiments demonstrate that the conceptual advantages of multiobjective clustering translate into practical and scalable performance benefits

Improved evolutionary optimization from genetically adaptive multimethod search

Abstract: In the last few decades, evolutionary algorithms have emerged as a revolutionary approach for solving search and optimization problems involving multiple conflicting objectives. Beyond their ability to search intractably large spaces for multiple solutions, these algorithms are able to maintain a diverse population of solutions and exploit similarities of solutions by recombination. However, existing theory and numerical experiments have demonstrated that it is impossible to develop a single algorithm for population evolution that is always efficient for a diverse set of optimization problems. Here we show that significant improvements in the efficiency of evolutionary search can be achieved by running multiple optimization algorithms simultaneously using new concepts of global information sharing and genetically adaptive offspring creation. We call this approach a multialgorithm, genetically adaptive multiobjective, or AMALGAM, method, to evoke the image of a procedure that merges the strengths of different optimization algorithms. Benchmark results using a set of well known multiobjective test problems show that AMALGAM approaches a factor of 10 improvement over current optimization algorithms for the more complex, higher dimensional problems. The AMALGAM method provides new opportunities for solving previously intractable optimization problems.

Impact of Network Reconfiguration on Loss Allocation of Radial Distribution Systems

Abstract: This paper presents allocation of power losses to consumers connected to radial distribution networks before and after network reconfiguration in a deregulated environment. Loss allocation is made in a quadratic way and it is based on identifying the real and imaginary parts of current in each branch, and losses are allocated to consumers. The network reconfiguration algorithm is based on the fuzzy multiobjective approach and the max-min principle is adopted for the multiobjective optimization in a fuzzy framework. Multiple objectives are considered for real-power loss reduction in which nodes voltage deviation is kept within a range, and an absolute value of branch currents is not allowed to exceed their rated capacities. At the same time, a radial network structure is maintained with all loads energized. The three objectives considered are modeled with fuzzy sets to evaluate their imprecise nature and one can provide his or her anticipated value of each objective. A 69-node example is considered to demonstrate the effectiveness of the proposed method.

Dynamic multi-objective optimization and decision-making using modified NSGA-II: a case study on hydro-thermal power scheduling

Abstract: Most real-world optimization problems involve objectives, constraints, and parameters which constantly change with time Treating such problems as a stationary optimization problem demand the knowledge of the pattern of change a priori and even then the procedure can be computationally expensive Although dynamic consideration using evolutionary algorithms has been made for single-objective optimization problems, there has been a lukewarm interest in formulating and solving dynamic multi-objective optimization problems In this paper, we modify the commonly-used NSGA-II procedure in tracking a new Pareto-optimal front, as soon as there is a change in the problem Introduction of a few random solutions or a few mutated solutions are investigated in detail The approaches are tested and compared on a test problem and a real-world optimization of a hydro-thermal power scheduling problem This systematic study is able to find a minimum frequency of change allowed in a problem for two dynamic EMO procedures to adequately track Pareto-optimal frontiers on-line Based on these results, this paper also suggests an automatic decision-making procedure for arriving at a dynamic single optimal solution on-line

Pareto-, aggregation-, and indicator-based methods in many-objective optimization

Abstract: Research within the area of Evolutionary Multi-objective Optimization (EMO) focused on two- and three-dimensional objective functions, so far. Most algorithms have been developed for and tested on this limited application area. To broaden the insight in the behavior of EMO algorithms (EMOA) in higher dimensional objective spaces, a comprehensive benchmarking is presented, featuring several state-of-the-art EMOA, as well as an aggregative approach and a restart strategy on established scalable test problems with three to six objectives. It is demonstrated why the performance of well-established EMOA (NSGAII, SPEA2) rapidly degradates with increasing dimension. Newer EMOA like Ɛ -MOEA, MSOPS, IBEA and SMS-EMOA cope very well with high-dimensional objective spaces. Their specific advantages and drawbacks are illustrated, thus giving valuable hints for practitioners which EMOA to choose depending on the optimization scenario. Additionally, a new method for the generation of weight vectors usable in aggregation methods is presented.

On the Evolutionary Optimization of Many Conflicting Objectives

Abstract: This study explores the utility of multiobjective evolutionary algorithms (using standard Pareto ranking and diversity-promoting selection mechanisms) for solving optimization tasks with many conflicting objectives. Optimizer behavior is assessed for a grid of mutation and recombination operator configurations. Performance maps are obtained for the dual aims of proximity to, and distribution across, the optimal tradeoff surface. Performance sweet-spots for both variation operators are observed to contract as the number of objectives is increased. Classical settings for recombination are shown to be suitable for small numbers of objectives but correspond to very poor performance for higher numbers of objectives, even when large population sizes are used. Explanations for this behavior are offered via the concepts of dominance resistance and active diversity promotion.

Recent Advances in Optimal Reliability Allocation

Abstract: Reliability has become a greater concern in recent years, because high-tech industrial processes with ever increasing levels of sophistication comprise most engineering systems today. To keep pace with this rapidly developing field, this paper provides a broad overview of recent research on reliability optimization problems and their solution methodologies. In particular, we address issues related to: 1) universal generating-function-based optimal multistate system design; 2) percentile life employed as a system performance measure; 3) multiobjective optimization of reliability systems, especially with uncertain component-reliability estimations; and 4) innovation and improvement in traditional reliability optimization problems, such as fault-tolerance mechanism and cold-standby redundancy-involved system design. New developments in optimization techniques are also emphasized in this paper, especially the methods of ant colony optimization and hybrid optimization. We believe that the interesting problems that are reviewed here are deserving of more attention in the literature. To that end, this paper concludes with a discussion of future challenges related to reliability optimization

Portfolio optimization with linear and fixed transaction costs

Abstract: We consider the problem of portfolio selection, with transaction costs and constraints on exposure to risk. Linear transaction costs, bounds on the variance of the return, and bounds on different shortfall probabilities are efficiently handled by convex optimization methods. For such problems, the globally optimal portfolio can be computed very rapidly. Portfolio optimization problems with transaction costs that include a fixed fee, or discount breakpoints, cannot be directly solved by convex optimization. We describe a relaxation method which yields an easily computable upper bound via convex optimization. We also describe a heuristic method for finding a suboptimal portfolio, which is based on solving a small number of convex optimization problems (and hence can be done efficiently). Thus, we produce a suboptimal solution, and also an upper bound on the optimal solution. Numerical experiments suggest that for practical problems the gap between the two is small, even for large problems involving hundreds of assets. The same approach can be used for related problems, such as that of tracking an index with a portfolio consisting of a small number of assets.

A novel multiple objective optimization framework for constraining conductance-based neuron models by experimental data

Abstract: We present a novel framework for automatically constraining parameters of compartmental models of neurons, given a large set of experimentally measured responses of these neurons. In experiments, intrinsic noise gives rise to a large variability (e.g., in firing pattern) in the voltage responses to repetitions of the exact same input. Thus, the common approach of fitting models by attempting to perfectly replicate, point by point, a single chosen trace out of the spectrum of variable responses does not seem to do justice to the data. In addition, finding a single error function that faithfully characterizes the distance between two spiking traces is not a trivial pursuit. To address these issues, one can adopt a multiple objective optimization approach that allows the use of several error functions jointly. When more than one error function is available, the comparison between experimental voltage traces and model response can be performed on the basis of individual features of interest (e.g., spike rate, spike width). Each feature can be compared between model and experimental mean, in units of its experimental variability, thereby incorporating into the fitting this variability. We demonstrate the success of this approach, when used in conjunction with genetic algorithm optimization, in generating an excellent fit between model behavior and the firing pattern of two distinct electrical classes of cortical interneurons, accommodating and fast-spiking. We argue that the multiple, diverse models generated by this method could serve as the building blocks for the realistic simulation of large neuronal networks.

A survey of recent developments in multiobjective optimization

Abstract: Multiobjective Optimization (MO) has many applications in such fields as the Internet, finance, biomedicine, management science, game theory and engineering. However, solving MO problems is not an easy task. Searching for all Pareto optimal solutions is expensive and a time consuming process because there are usually exponentially large (or infinite) Pareto optimal solutions. Even for simple problems determining whether a point belongs to the Pareto set is \(\mathcal{NP}\) -hard. In this paper, we discuss recent developments in MO. These include optimality conditions, applications, global optimization techniques, the new concept of epsilon Pareto optimal solution, and heuristics.

Controlling dominance area of solutions and its impact on the performance of MOEAs

Abstract: This work proposes a method to control the dominance area of solutions in order to induce appropriate ranking of solutions for the problem at hand, enhance selection, and improve the performance of MOEAs on combinatorial optimization problems. The proposed method can control the degree of expansion or contraction of the dominance area of solutions using a user-defined parameter S. Modifying the dominance area of solutions changes their dominance relation inducing a ranking of solutions that is different to conventional dominance. In this work we use 0/1 multiobjective knapsack problems to analyze the effects on solutions ranking caused by contracting and expanding the dominance area of solutions and its impact on the search performance of a multi-objective optimizer when the number of objectives, the size of the search space, and the complexity of the problems vary. We show that either convergence or diversity can be emphasized by contracting or expanding the dominance area. Also, we show that the optimal value of the area of dominance depends strongly on all factors analyzed here: number of objectives, size of the search space, and complexity of the problems.

Multiobjective Optimization in Bioinformatics and Computational Biology

Abstract: This paper reviews the application of multiobjective optimization in the fields of bioinformatics and computational biology. A survey of existing work, organized by application area, forms the main body of the review, following an introduction to the key concepts in multiobjective optimization. An original contribution of the review is the identification of five distinct "contexts,” giving rise to multiple objectives: These are used to explain the reasons behind the use of multiobjective optimization in each application area and also to point the way to potential future uses of the technique.

Substitute distance assignments in NSGA-II for handling many-objective optimization problems

Abstract: Many-objective optimization refers to optimization problems with a number of objectives considerably larger than two or three. In this paper, a study on the performance of the Fast Elitist Nondominated Sorting Genetic Algorithm (NSGA-II) for handling such many-objective optimization problems is presented. In its basic form, the algorithm is not well suited for the handling of a larger number of objectives. The main reason for this is the decreasing probability of having Pareto-dominated solutions in the initial external population. To overcome this problem, substitute distance assignment schemes are proposed that can replace the crowding distance assignment, which is normally used in NSGA-II. These distances are based on measurement procedures for the highest degree, to which a solution is nearly Pareto-dominated by any other solution: like the number of smaller objectives, the magnitude of all smaller or larger objectives, or a multi-criterion derived from the former ones. For a number of many-objective test problems, all proposed substitute distance assignments resulted into a strongly improved performance of the NSGA-II.

A genetic algorithms based multi-objective neural net applied to noisy blast furnace data

Abstract: A genetic algorithms based multi-objective optimization technique was utilized in the training process of a feed forward neural network, using noisy data from an industrial iron blast furnace. The number of nodes in the hidden layer, the architecture of the lower part of the network, as well as the weights used in them were kept as variables, and a Pareto front was effectively constructed by minimizing the training error along with the network size. A predator-prey algorithm efficiently performed the optimization task and several important trends were observed.

Congestion Management Using Multiobjective Particle Swarm Optimization

Abstract: This paper presents an effective method of congestion management in power systems. Congestions or overloads in transmission network are alleviated by generation rescheduling and/or load shedding of participating generators and loads. The two conflicting objectives 1) alleviation of overload and 2) minimization of cost of operation are optimized to provide pareto-optimal solutions. A multiobjective particle swarm optimization (MOPSO) method is used to solve this complex nonlinear optimization problem. A realistic frequency and voltage dependent load flow method which considers the voltage and frequency dependence of loads and generator regulation characteristics is used to solve this problem. The proposed algorithm is tested on IEEE 30-bus system, IEEE 118-bus system, and Northern Region Electricity Board, India (NREB) 390-bus system with smooth as well as nonsmooth cost functions due to valve point loading effect.

Multiobjective Optimization and Hybrid Evolutionary Algorithm to Solve Constrained Optimization Problems

Abstract: This paper presents a novel evolutionary algorithm (EA) for constrained optimization problems, i.e., the hybrid constrained optimization EA (HCOEA). This algorithm effectively combines multiobjective optimization with global and local search models. In performing the global search, a niching genetic algorithm based on tournament selection is proposed. Also, HCOEA has adopted a parallel local search operator that implements a clustering partition of the population and multiparent crossover to generate the offspring population. Then, nondominated individuals in the offspring population are used to replace the dominated individuals in the parent population. Meanwhile, the best infeasible individual replacement scheme is devised for the purpose of rapidly guiding the population toward the feasible region of the search space. During the evolutionary process, the global search model effectively promotes high population diversity, and the local search model remarkably accelerates the convergence speed. HCOEA is tested on 13 well-known benchmark functions, and the experimental results suggest that it is more robust and efficient than other state-of-the-art algorithms from the literature in terms of the selected performance metrics, such as the best, median, mean, and worst objective function values and the standard deviations

Review of Reactive Power Planning: Objectives, Constraints, and Algorithms

Abstract: The key of reactive power planning (RPP), or Var planning, is the optimal allocation of reactive power sources considering location and size. Traditionally, the locations for placing new Var sources were either simply estimated or directly assumed. Recent research works have presented some rigorous optimization-based methods in RPP. This paper will first review various objectives of RPP. The objectives may consider many cost functions such as variable Var cost, fixed Var cost, real power losses, and fuel cost. Also considered may be the deviation of a given voltage schedule, voltage stability margin, or even a combination of different objectives as a multi-objective model. Secondly, different constraints in RPP are discussed. These different constraints are the key of various optimization models, identified as optimal power flow (OPF) model, security-constrained OPF (SCOPF) model, and SCOPF with voltage-stability consideration. Thirdly, the optimization-based models will be categorized as conventional algorithms, intelligent searches, and fuzzy set applications. The conventional algorithms include linear programming, nonlinear programming, mixed-integer nonlinear programming, etc. The intelligent searches include simulated annealing, evolutionary algorithms, and tabu search. The fuzzy set applications in RPP address the uncertainties in objectives and constraints. Finally, this paper will conclude the discussion with a summary matrix for different objectives, models, and algorithms.

Prediction-based population re-initialization for evolutionary dynamic multi-objective optimization

Abstract: Optimization in changing environment is a challenging task, especially when multiple objectives are to be optimized simultaneously. The basic idea to address dynamic optimization problems is to utilize history information to guide future search. In this paper, two strategies for population re-initialization are introduced when a change in the environment is detected. The first strategy is to predict the new location of individuals from the location changes that have occurred in the history. The current population is then partially or completely replaced by the new individuals generated based on prediction. The second strategy is to perturb the current population with a Gaussian noise whose variance is estimated according to previous changes. The prediction based population re-initialization strategies, together with the random re-initialization method, are then compared on two bi-objective test problems. Conclusions on the different re-initialization strategies are drawn based on the preliminary empirical results.

A Model for the Multiperiod Multiobjective Power Generation Expansion Problem

Abstract: A long-term multiobjective model for the power generation expansion planning of electric systems is described and evaluated in this paper. The model optimizes simultaneously multiple objectives (i.e., minimizes costs, environmental impact, imported fuel and fuel price risks) and decides the location of the planned generation units in a multiperiod planning horizon. Among the attributes considered in the model are the investment and operation cost of the units, the environmental impact, the amount of imported fuel, and the portfolio investment risk. The approach to solve this problem is based on multiobjective linear programming and the analytical hierarchy process. A case study from the Mexican Electric Power System is used to illustrate the proposed framework

A framework for Visually Interactive Decision-making and Design using Evolutionary Multi-objective Optimization (VIDEO)

Abstract: This study presents a framework for Visually Interactive Decision-making and Design using Evolutionary Multi-objective Optimization (VIDEO). The VIDEO framework allows users to visually navigate large multi-objective solution sets while aiding decision makers in identifying one or more optimal designs. Specifically, the interactive visualization framework is intended to provide an innovative exploration tool for high-order Pareto-optimal solution sets (i.e., solution sets for three or more objectives). The framework is demonstrated for a long-term groundwater monitoring (LTM) application in which users can explore and visualize tradeoffs for up to four design objectives, simultaneously. Interactive functionality within the framework allows the user to select solutions within the objective space and visualize the corresponding monitoring plan's performance in the design space. This functionality provides the user with a holistic picture of the information provided by a particular solution, ultimately allowing them to make a more informed decision. In addition, the ease with which the framework allows users to navigate and compare solutions as well as design tradeoffs leads to a time efficient analysis, even when there are thousands of potential solutions.

Optimal security hardening using multi-objective optimization on attack tree models of networks

Abstract: Researchers have previously looked into the problem of determining if a given set of security hardening measures can effectively make a networked system secure. Many of them also addressed the problem of minimizing the total cost of implementing these hardening measures, given costs for individual measures. However, system administrators are often faced with a more challenging problem since they have to work within a fixed budget which may be less than the minimum cost of system hardening. Their problem is how to select a subset of security hardening measures so as to be within the budget and yet minimize the residual damage to the system caused by not plugging all required security holes. In this work, we develop a systematic approach to solve this problem by formulating it as a multi-objective optimization problem on an attack tree model of the system and then use an evolutionary algorithm to solve it.