A multiobjective optimization problem involves several conflicting objectives and has a set of Pareto optimal solutions. By evolving a population of solutions, multiobjective evolutionary algorithms (MOEAs) are able to approximate the Pareto optimal set in a single run. MOEAs have attracted a lot of research effort during the last 20 years, and they are still one of the hottest research areas in the field of evolutionary computation. This paper surveys the development of MOEAs primarily during the last eight years. It covers algorithmic frameworks such as decomposition-based MOEAs (MOEA/Ds), memetic MOEAs, coevolutionary MOEAs, selection and offspring reproduction operators, MOEAs with specific search methods, MOEAs for multimodal problems, constraint handling and MOEAs, computationally expensive multiobjective optimization problems (MOPs), dynamic MOPs, noisy MOPs, combinatorial and discrete MOPs, benchmark problems, performance indicators, and applications. In addition, some future research issues are also presented.

Multiobjective evolutionary algorithms: A survey of the state of the art

Direction of arrival (DOA) estimation is a classical problem in signal processing with many practical applications. Its research has recently been advanced owing to the development of methods based on sparse signal reconstruction. While these methods have shown advantages over conventional ones, there are still difficulties in practical situations where true DOAs are not on the discretized sampling grid. To deal with such an off-grid DOA estimation problem, this paper studies an off-grid model that takes into account effects of the off-grid DOAs and has a smaller modeling error. An iterative algorithm is developed based on the off-grid model from a Bayesian perspective while joint sparsity among different snapshots is exploited by assuming a Laplace prior for signals at all snapshots. The new approach applies to both single snapshot and multi-snapshot cases. Numerical simulations show that the proposed algorithm has improved accuracy in terms of mean squared estimation error. The algorithm can maintain high estimation accuracy even under a very coarse sampling grid.

Off-Grid Direction of Arrival Estimation Using Sparse Bayesian Inference

Wireless Optical Communication Systems addresses the problem of designing efficient signaling and provides a link between the areas of communication theory and modem design for amplitude constrained linear optical intensity channel. Topics include historical perspective, channel impairments, amplitude constraints and the characteristics of popular optoelectronic components. A variety of wireless optical channel topologies are presented along with a survey and analysis of present day signalling techniques employed for these channels. The author provides a unifying framework for signalling design which allows the channel constraints to be represented geometrically and permits the use of modem design principles from electrical channels. Modulation schemes are designed using the formalism of lattice codes and a design process for signalling sets is specified. The use of multiple-input/multiple-output (MIMO) wireless optical channels to improve the spectral efficiency of links is explored. The basic spatio-temporal modem design problem is specified and a spatial multiplexing gain is quantified. New spatial discrete multitone modulation is proposed and the unique features are discussed. Based on measurements on an experimental prototype, a channel model is formulated and a realizable spatio-temporal coding scheme is simulated to quantify performance gains. This volume is organized for professional and academic readers engaged in modem design for wireless optical intensity channels. Significant background material is presented on both the properties as well as on fundamental communications principles. Wireless Optical Communication Systems can be used by physicists and experimentalists as an introduction to signalling design as well as communication systems designers.

Wireless Optical Communication Systems

Traditional multiobjective evolutionary algorithms (MOEAs) consider multiple objectives as a whole when solving multiobjective optimization problems (MOPs). However, this consideration may cause difficulty to assign fitness to individuals because different objectives often conflict with each other. In order to avoid this difficulty, this paper proposes a novel coevolutionary technique named multiple populations for multiple objectives (MPMO) when developing MOEAs. The novelty of MPMO is that it provides a simple and straightforward way to solve MOPs by letting each population correspond with only one objective. This way, the fitness assignment problem can be addressed because the individuals' fitness in each population can be assigned by the corresponding objective. MPMO is a general technique that each population can use existing optimization algorithms. In this paper, particle swarm optimization (PSO) is adopted for each population, and coevolutionary multiswarm PSO (CMPSO) is developed based on the MPMO technique. Furthermore, CMPSO is novel and effective by using an external shared archive for different populations to exchange search information and by using two novel designs to enhance the performance. One design is to modify the velocity update equation to use the search information found by different populations to approximate the whole Pareto front (PF) fast. The other design is to use an elitist learning strategy for the archive update to bring in diversity to avoid local PFs. CMPSO is comprehensively tested on different sets of benchmark problems with different characteristics and is compared with some state-of-the-art algorithms. The results show that CMPSO has superior performance in solving these different sets of MOPs.

Multiple Populations for Multiple Objectives: A Coevolutionary Technique for Solving Multiobjective Optimization Problems

An important consideration of multiobjective optimization (MOO) is the quantitative metrics used for defining the optimality of different solution sets, which is also the basic principle for the design and evaluation of MOO algorithms. Although a plethora of performance metrics have been proposed in the MOO context, there has been a lack of insights on the relationships between metrics. In this paper, we first group the major MOO metrics proposed to date according to four core performance criteria considered in the literature, namely, capacity, convergence, diversity, and convergence-diversity. Then, a comprehensive study is conducted to investigate the relationships among representative group metrics, including generational distance, E-indicator (I
 1
 ∈+
), spread (Δ), generalized spread (Δ*), inverted generational distance, and hypervolume. Experimental results indicated that these six metrics show high consistencies when Pareto fronts (PFs) are convex, whereas they show certain contradictions on concave PFs.

Consistencies and contradictions of performance metrics in multiobjective optimization.

In this paper, the source localization problem in wireless sensor networks is investigated where the location of the source is estimated based on the quantized measurements received from sensors in the field. An energy efficient iterative source localization scheme is proposed where the algorithm begins with a coarse location estimate obtained from measurement data from a set of anchor sensors. Based on the available data at each iteration, the posterior probability density function (pdf) of the source location is approximated using an importance sampling based Monte Carlo method and this information is utilized to activate a number of non-anchor sensors. Two sensor selection metrics namely the mutual information and the posterior Cramer-Rao lower bound (PCRLB) are employed and their performance compared. Further, the approximate posterior pdf of the source location is used to compress the quantized data of each activated sensor using distributed data compression techniques. Simulation results show that with significantly less computation, the PCRLB based iterative sensor selection method achieves similar mean squared error (MSE) performance as compared to the state-of-the-art mutual information based sensor selection method. By selecting only the most informative sensors and compressing their data prior to transmission to the fusion center, the iterative source localization method reduces the communication requirements significantly and thereby results in energy savings.

Energy Aware Iterative Source Localization for Wireless Sensor Networks

For distributed detection in a wireless sensor network, sensors arrive at decisions about a specific event that are then sent to a central fusion center that makes global inference about the event. For such systems, the determination of the decision thresholds for local sensors is an essential task. In this paper, we study the distributed detection problem and evaluate the sensor thresholds by formulating and solving a multiobjective optimization problem, where the objectives are to minimize the probability of error and the total energy consumption of the network. The problem is investigated and solved for two types of fusion schemes: 1) parallel decision fusion and 2) serial decision fusion. The Pareto optimal solutions are obtained using two different multiobjective optimization techniques. The normal boundary intersection (NBI) method converts the multiobjective problem into a number of single objective-constrained subproblems, where each subproblem can be solved with appropriate optimization methods and nondominating sorting genetic algorithm-II (NSGA-II), which is a multiobjective evolutionary algorithm. In our simulations, NBI yielded better and evenly distributed Pareto optimal solutions in a shorter time as compared with NSGA-II. The simulation results show that, instead of only minimizing the probability of error, multiobjective optimization provides a number of design alternatives, which achieve significant energy savings at the cost of slightly increasing the best achievable decision error probability. The simulation results also show that the parallel fusion model achieves better error probability, but the serial fusion model is more efficient in terms of energy consumption.

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A Multiobjective Optimization Approach to Obtain Decision Thresholds for Distributed Detection in Wireless Sensor Networks

Equalizer design typically requires careful modeling of the underlying storage channel. The aim of this paper is to present an efficient ISI model for volume hololgraphic storage channels (VHSC) in which we consider the frequency plane aperture, spatial light modulator (SLM) and CCD fill factors, and SLM finite contrast ratio as the main sources of ISI.

Efficient modeling of volume holographic storage channels (VHSC)

Although patterned media storage (PMS) is a promising candidate for ultrahigh-capacity magnetic data storage, as the capacity of PMS increases, the bit error rate (BER) performance of the system is degraded by increased two-dimensional intersymbol interference (2D-ISI), which results from intertrack interference (ITI), intersymbol interference (ISI), and noise. To improve the system performance under these adverse effects and to increase the capacity, in this paper, we propose to use and/or devise two-dimensional equalization/detection techniques: iterative decision feedback detection (IDFD) and two-dimensional generalized partial response equalization, which is optimized in minimum mean square error (MMSE), followed by one-dimensional Viterbi algorithm (2D-GPR/1D-VA). We evaluate the performance of the proposed methods by using numerical experiments under different amounts of 2D-ISI and noise. Simulation results suggest that under high storage density, the performance of the IDFD is improved by using more iterations and that under the same computational load, 2D-GPR/1D-VA performs better than IDFD. 2D-GPR/1D-VA, therefore, is a good candidate for ultrahigh-capacity PMS.

Two-Dimensional Equalization/Detection for Patterned Media Storage

As storage density increases, the performance of volume holographic storage channels is degraded, because intersymbol interference and noise also increase. Equalization and detection methods must be employed to mitigate the effects of intersignal interference and noise. However, the output detector array in a holographic storage system detects the intensity of the incident light's wave front, leading to loss of sign information. This sign loss precludes the applicability of conventional equalization and detection schemes. We first address channel modeling under quadratic nonlinearity and develop an efficient model named the discrete magnitude-squared channel model. We next introduce an advanced equalization method called the iterative magnitude-squared decision feedback equalization (IMSDFE), which takes the channel nonlinearity into account. The performance of IMSDFE is quantified for optical-noise-dominated channels as well as for electronic-noise-dominated channels. Results indicate that IMSDFE is a good candidate for a high-density, high-intersignal-interference volume holographic storage channel.

Mehmet Keskinoz

Papers

Energy Aware Iterative Source Localization for Wireless Sensor Networks

A Multiobjective Optimization Approach to Obtain Decision Thresholds for Distributed Detection in Wireless Sensor Networks

Efficient modeling of volume holographic storage channels (VHSC)

Two-Dimensional Equalization/Detection for Patterned Media Storage

Discrete magnitude-squared channel modeling, equalization, and detection for volume holographic storage channels