Evolutionary Multi Objective Research Articles

SONG: A Multi-Objective Evolutionary Algorithm for Delay and Energy Aware Facility Location in Vehicular Fog Networks.

With the emergence of delay- and energy-critical vehicular applications, forwarding sense-actuate data from vehicles to the cloud became practically infeasible. Therefore, a new computational model called Vehicular Fog Computing (VFC) was proposed. It offloads the computation workload from passenger devices (PDs) to transportation infrastructures such as roadside units (RSUs) and base stations (BSs), called static fog nodes. It can also exploit the underutilized computation resources of nearby vehicles that can act as vehicular fog nodes (VFNs) and provide delay- and energy-aware computing services. However, the capacity planning and dimensioning of VFC, which come under a class of facility location problems (FLPs), is a challenging issue. The complexity arises from the spatio-temporal dynamics of vehicular traffic, varying resource demand from PD applications, and the mobility of VFNs. This paper proposes a multi-objective optimization model to investigate the facility location in VFC networks. The solutions to this model generate optimal VFC topologies pertaining to an optimized trade-off (Pareto front) between the service delay and energy consumption. Thus, to solve this model, we propose a hybrid Evolutionary Multi-Objective (EMO) algorithm called Swarm Optimized Non-dominated sorting Genetic algorithm (SONG). It combines the convergence and search efficiency of two popular EMO algorithms: the Non-dominated Sorting Genetic Algorithm (NSGA-II) and Speed-constrained Particle Swarm Optimization (SMPSO). First, we solve an example problem using the SONG algorithm to illustrate the delay-energy solution frontiers and plotted the corresponding layout topology. Subsequently, we evaluate the evolutionary performance of the SONG algorithm on real-world vehicular traces against three quality indicators: Hyper-Volume (HV), Inverted Generational Distance (IGD) and CPU delay gap. The empirical results show that SONG exhibits improved solution quality over the NSGA-II and SMPSO algorithms and hence can be utilized as a potential tool by the service providers for the planning and design of VFC networks.

Multiobjective Formulation of Multiple Sequence Alignment for Phylogeny Inference.

Multiple sequence alignment (MSA) is a preliminary task for estimating phylogenies. It is used for homology inference among the sequences of a set of species. Generally, the MSA task is handled as a single-objective optimization process. The alignments computed under one criterion may be different from the alignments generated by other criteria, inferring discordant homologies and thus leading to different hypothesized evolutionary histories relating the sequences. The multiobjective (MO) formulation of MSA has recently been advocated by several researchers, to address this issue. An MO approach independently optimizes multiple (often conflicting) objective functions at the same time and outputs a set of competitive alignments. However, no conceptual or experimental rational from a real-world application perspective has been reported so far for any MO formulation of MSA. This article work investigates the impact of MO formulation in the context of an important scientific problem, namely, phylogeny estimation. Employing popular evolutionary MO algorithms, we show that: 1) trees inferred based on alignments produced by the existing MSA methods used in practice are substantially worse in quality than the trees inferred based on the alignment's output by an MO algorithm and 2) even high-quality alignments (according to popular measures available in the literature) may fail to achieve acceptable accuracy in generating phylogenetic trees. Thus, we essentially ask the following natural question: "can a phylogeny-aware (i.e., application-aware) metric guide in selecting appropriate MO formulations to ensure better phylogeny estimation?" Here, we report a carefully designed extensive experimental study that positively answers this question.

Evolutionary Multi–Objective Weather Routing of Sailboats

Abstract The paper presents a multi-objective method, which optimises the route of a sailboat. The presented method makes use of an evolutionary multi-objective (EMO) algorithm, which performs the optimisation according to three objective functions: total passage time, a sum of all course alterations made during the voyage and the average angle of heel. The last two of the objective functions reflect the navigator’s and passenger’s comfort, which may decrease with multiple turns or when experiencing an excessive heel angle for a long time. The optimisation process takes into account static bathymetry-related constraints as well as dynamic constraints related to the sailboat’s safety in changing wind and wave conditions. The method makes use of all of the above and finally returns an approximated Pareto set containing non-dominated solutions to the optimisation problem. The developed method has been implemented as a simulation application. The paper includes selected simulation results followed by their discussion.

Multi-objective optimisation of software application mappings on heterogeneous MPSoCs: TONPET versus R2-EMOA

For heterogeneous multi-core architectures, efficient development of parallel software is paramount. Fast and accurate compiler technology is required in order to exploit their advantages and to optimise for multiple objectives, such as performance and power.The work at hand presents a heuristic and state-of-the-art Evolutionary Multi Objective Algorithm (EMOA) approach to tackle this problem. The performance and consistency of the population based heuristic TONPET and the indicator based EMOA are compared and thoroughly analysed. For the evaluation, both are integrated into the SLX tool suite. Representative benchmarks and three different MPSoC platforms are chosen for an in-depth realistic analysis. For smaller and medium sized solution spaces, TONPET outperforms the EMOA with 4.7% better Pareto fronts on average, while being 18 × faster in the worst case. In vast solution spaces, the EMOA consistently produces 3% better Pareto fronts on average but TONPET runs 88 × faster in the worst case. Furthermore, for comparison purposes, a full performance consistency analysis on EMOA conducted.

Improved selection in evolutionary multi–objective optimization of multi–skill resource–constrained project scheduling problem

In this paper a modified selection operator is presented in combination with classical Non-dominated Sorting Genetic Algorithm II (NSGA-II). It is shown that various modifications can lead to increased convergence, spread or uniformity of achieved Pareto fronts. A clone prevention method is used to increase the spread of resulting sets. Furthermore a crowding operator is removed from the NSGA-II as it serves a similar purpose as the clone prevention, even though it achieves it in a different manner. The former enforces diversity in a phenotype, while the latter enforces diversity in a genotype. Combinations of multiple selection modifiers are researched and the best configurations are identified. Multiple absolute measures are selected and applied to verify quality of the results. Additionally a relative measure is used to compare the fronts. They indicate that used selection improves convergence and spread of the front at the cost of its uniformity, while at the same time increasing the efficiency of search. Results are compared to the fronts obtained by multiple runs of a single–objective hybrid Differential Evolution with Greedy Algorithm. All experiments are performed on Multi–Skill Resource–Constrained Project Scheduling Problem.

Comparison of evolutionary multi objective optimization algorithms in optimum design of water distribution network

Abstract In this paper, the application of three well-known multi-objective optimization algorithms to water distribution network (WDN) optimum design has been considered. Non-dominated sorting genetic algorithm II (NSGA-II), Multi-objective differential evolution (MODE) and Multi-objective particle swarm optimization (MOPSO) algorithms are applied to benchmark mathematical test function problems for evaluating the performance of these algorithms. The Accuracy and computational runtime are the two indicators used for the comparison of these three algorithms. The optimization results of mathematical test functions show that all three algorithms were able to accurately produce Pareto Front, but the computational time of MODE algorithm to achieve the optimal solutions is lower than the two other algorithms. Then, the discussed algorithms have been used to optimize the WDN design problem. Comparison of the generated solutions on the Pareto Front for WDN design shows that the obtained Pareto Front of MODE is more accurate and faster.

Fling-step ground motions simulation using theoretical-based Green's function technique for structural analysis

The article aims to a. introduce a technique to generate long-period waveforms having fling-step effect at near fault and b. study the effect of fling-step on the structural performance of buildings. The study focuses on the fling-step effect which is related to large co-seismic displacement. For this purpose, seismological parameters of Kocaeli 1999 earthquake have been computed through an evolutionary multi objective approach (MO-GA) and Theoretical-based Green's Function (TGF) method with regard to specific objectives such as permanent displacement, response spectra, and multi-taper spectra. Thereafter many accelerograms were generated at desired near stations and the fling-step effects were removed from the accelerograms by a specific technique. Subsequently, three3-, 9- and 20-story steel frames were modeled in Opensees and the structural responses were obtained using nonlinear time history analyses. Findings from this study demonstrate that fling-step would affect the seismic demand fairly high when the ratio of the fundamental period of the structure to fling rise time (pulse duration) varies from 0.5 to 1.1. Also a good agreement between the responses of the structures subjected to generated ground motions and as-recorded ground motions was observed when this ratio equals 0.5. In most cases, an increase in seismic demand was observed in the absence of fling-step pulse.

Tuning of a PID controller using evolutionary multi objective optimization methodologies and application to the pulp and paper industry

Proportional–Integral–Derivative controller technique continues to provide the easiest and effective solutions to most of the industrial applications in recent years. However PID controller is poorly tuned in practice compared to most other tuning methods and is complicated with poor performance. This research presents a multi objective optimization approach involving Genetic Algorithm, Evolutionary Programming, Particle Swarm Optimization and Bacterial foraging optimization. The proposed multi objective optimization algorithm is used to tune the PID controller parameters and their performances have been compared with the conventional methodologies like Ziegler Nichols method. The results proved that the use of multi objective optimization approach based controller tuning improves the performance of process in terms of time domain specifications and performance index, set point tracking and regulatory changes and also provides stability. This paper describes the various multi objective optimization algorithms and its implementation to tune the PID Controller used in paper machine DCS as real time processing of a Pulp and paper industry processes.

Localized Weighted Sum Method for Many-Objective Optimization

Decomposition via scalarization is a basic concept for multiobjective optimization. The weighted sum (WS) method, a frequently used scalarizing method in decomposition-based evolutionary multiobjective (EMO) algorithms, has good features such as computationally easy and high search efficiency, compared to other scalarizing methods. However, it is often criticized by the loss of effect on nonconvex problems. This paper seeks to utilize advantages of the WS method, without suffering from its disadvantage, to solve many-objective problems. A novel decomposition-based EMO algorithm called multiobjective evolutionary algorithm based on decomposition LWS (MOEA/D-LWS) is proposed in which the WS method is applied in a local manner. That is, for each search direction, the optimal solution is selected only amongst its neighboring solutions. The neighborhood is defined using a hypercone. The apex angle of a hypervcone is determined automatically in a priori . The effectiveness of MOEA/D-LWS is demonstrated by comparing it against three variants of MOEA/D, i.e., MOEA/D using Chebyshev method, MOEA/D with an adaptive use of WS and Chebyshev method, MOEA/D with a simultaneous use of WS and Chebyshev method, and four state-of-the-art many-objective EMO algorithms, i.e., preference-inspired co-evolutionary algorithm, hypervolume-based evolutionary, $\boldsymbol {\theta }$ -dominance-based algorithm, and SPEA2+SDE for the WFG benchmark problems with up to seven conflicting objectives. Experimental results show that MOEA/D-LWS outperforms the comparison algorithms for most of test problems, and is a competitive algorithm for many-objective optimization.

An improved biogeography/complex algorithm based on decomposition for many-objective optimization

It is difficult to maintain the balance between convergence and diversity for many-objective optimization problems (MaOPs) in the algorithms of evolutionary multi-objective (EMO). EMO algorithms are useful technology to solve the multi-objective optimization problems (MOPs). However, with the larger of optimization objectives, enough Pareto selection pressure will be loosed, and results in the performance of the algorithms are significantly reduced. The decomposition-based EMO developed for MaOPs have been shown to be effective, and the BBO algorithm is a low-complexity algorithm. In this paper, a hybrid decomposition-based BBO/Complex algorithm (HDB/BBO) for MaOPs is proposed. First, a set of uniformly distributed weight vectors and K-means aggregate method is introduced for decomposing MaOPs into several subsystems. Then, inferior migrated islands will not be chosen unless they pass the Metropolis criterion twice during the within-subsystem migration and cross-subsystem migration. The penalty-based boundary intersection (PBI) distance to calculate neighbor islands distance for balancing the algorithm of convergence and diversity. Finally, after mutation and clear duplication, a uniform distribution Pareto set can be obtained. Experimental results on both DTLZ and WFG benchmarks problems demonstrate the superiority of the proposed algorithm in comparison with three state-of-the-art algorithms in terms of both convergence and diversity.

Investigating the Effect of Imbalance Between Convergence and Diversity in Evolutionary Multi-objective Algorithms

There are two main tasks involved in addressing a multiobjective optimization problem (MOP) by evolutionary multiobjective (EMO) algorithms: 1) make the population converge close to the Pareto-optimal front and 2) maintain adequate population diversity. However, most state-of-the-art EMO algorithms are designed based on the “convergence first and diversity second” principle. It has been observed that although these EMO algorithms have been successful in optimizing many real-world MOPs, they fail to solve certain problems that feature a severe imbalance between diversity preservation and achieving convergence. This paper characterizes an imbalanced MOP by clearly defining properties and indicating the reasons for the existing EMO algorithms’ difficulties in solving them. We then present 14 imbalanced problems, with and without constraints. Computational results using four existing EMO algorithms—elitist non-dominated sorting genetic algorithm (NSGA-II), multiobjective evolutionary algorithm based on decomposition (MOEA/D), strength Pareto evolutionary algorithm 2 (SPEA2), and S metric selection EMO algorithm (SMS-EMOA) and a proposed generalized vector-evaluated genetic algorithm are then presented. It is seen that these EMO algorithms cannot solve these imbalanced problems, but they are able to solve the problems when augmented by multiobjective to multiobjective (M2M), an approach that decomposes the population into several interacting subpopulations. These results and the successful application of the EMO methods with the M2M approach even on standard so-called balanced problems indicate the usefulness of using the M2M approach.

Impact of Number of Interactions, Different Interaction Patterns, and Human Inconsistencies on Some Hybrid Evolutionary Multiobjective Optimization Algorithms*

ABSTRACTWe investigate the impact of the number of human–computer interactions, different interaction patterns, and human inconsistencies in decision maker responses on the convergence of an interactive, evolutionary multiobjective algorithm recently developed by the authors. In our context “an interaction” means choosing the best and worst solutions among a sample of six solutions. By interaction patterns we refer to whether preference questioning is more front‐, center‐, rear‐, or edge‐loaded. As test problems we use two‐ to four‐objective knapsack problems, multicriteria scheduling problems, and multiobjective facility location problems. In the tests, two different preference functions are used to represent actual decision maker preferences, linear and Chebyshev. The results indicate that it is possible to obtain solutions that are very good or even nearly optimal with a reasonable number of interactions. The results also indicate that the algorithm is robust to minor inconsistencies in decision maker responses. There is also surprising robustness toward different patterns of interaction with the decision maker. The results are of interest to the evolutionary multiobjective (EMO) community actively developing hybrid interactive EMO approaches.

Multi objective optimal reactive power dispatch using a new multi objective strategy

This paper presents a new multi objective Chaotic Parallel Vector Evaluated Interactive Honey Bee Mating Optimization (CPVEIHBMO) to find the feasible optimal solution of the multi objective optimal reactive power dispatch (RPD) problem with considering operational constraints of the generators. The optimal RPD problem is an important issue with non-linear structure in power industry that consists of the continuous and discrete control variables. The proposed algorithm is applied to find the settings of continuous and discrete control variables such as tap positions of tap changing transformers, generator voltages, and the amount of reactive compensation devices to optimize three conflicting and non-commensurable objective functions: voltage deviation, the total voltage stability and real power loss. For achieve a good design with different solutions in a multi objective optimization problem, Pareto dominance concept is used to generate and sort the dominated and non-dominated solutions. Also, fuzzy set theory is employed to extract the best compromise solution. The propose method has been individually examined and applied to several test systems. The effectiveness of the proposed approach is demonstrated by comparing its performance with other evolutionary multi objective optimization algorithms. The computational results reveal that the proposed algorithm has excellent convergence characteristics and is superior to other multi objective optimization algorithms. Also, the results confirm its great potential in handling the multi objective problems in power systems.

Two-Level Production Plan Decomposition Based on a Hybrid MOEA for Mineral Processing

This paper addresses the integrated multiobjective production planning and decomposing (P&D) problem for mineral processing. A novel multiobjective 0-1 mixed integer nonlinear programming model is presented for the simultaneous P&D problem (O-model). In order to reduce the computational cost for solving O-model, a rolling horizon-based two-level decomposition approach is proposed to separate O-model into an upper level model (H-model) and a lower level model (L-model). An interactive partition (IP) and multiobjective gradient (MO-G)-based hybrid evolutionary multiobjective (EMO) algorithm named as IG-NSGA-II/IG-SPEA2, which takes the popular NSGA-II/SPEA2 as the basic EA, is proposed to solve both H-model and L-model, where an IP technique is designed to generate the efficient feasible combinational nodes, an ideal solution technique is provided for fathoming the infeasible nodes, an improved multiobjective gradient-based operator is developed to accelerate the evolution process in each selected node, and a cut with all continuous variables is constructed to exclude the previous feasible combination if it is not desired for the decision makers (DMs). The experimental results demonstrate that the presented two-level decomposition strategy can effectively integrate both levels. Moreover, the proposed hybrid method can effectively reduce the combinatorial space so as to concentrate the computing resource on the subspace of most interest, and can generate better feasible solutions than the pure EA in the full-space under computation time limits.

Acceleration of Solving the Dynamic Multi-Objective Network Design Problem Using Response Surface Methods

Optimization of externalities and accessibility using dynamic traffic management measures on a strategic level is a specific example of solving a multi-objective network design problem. Solving this optimization problem is time consuming, because heuristics like evolutionary multi objective algorithms are needed and solving the lower level requires solving the dynamic user equilibrium problem. Using function approximation like response surface methods (RSM) in combination with evolutionary algorithms could accelerate the determination of the Pareto optimal set. Three algorithms in which RSM are used in different ways in combination with the Strength Pareto Evolutionary Algorithm 2+ (SPEA2+) are compared with employing the SPEA2+ without the use of these methods. The results show that the algorithms using RSM methods accelerate the search considerably at the start, but tend to converge more quickly, possibly to a local optimum, and therefore loose their head start. Therefore, usage of function approximation is mainly of interest if a limited number of exact evaluations can be done or this can be used as a pre phase in a hybrid approach.

A generalized automatic clustering algorithm in a multiobjective framework

In this paper a new multiobjective (MO) clustering technique (GenClustMOO) is proposed which can automatically partition the data into an appropriate number of clusters. Each cluster is divided into several small hyperspherical subclusters and the centers of all these small sub-clusters are encoded in a string to represent the whole clustering. For assigning points to different clusters, these local sub-clusters are considered individually. For the purpose of objective function evaluation, these sub-clusters are merged appropriately to form a variable number of global clusters. Three objective functions, one reflecting the total compactness of the partitioning based on the Euclidean distance, the other reflecting the total symmetry of the clusters, and the last reflecting the cluster connectedness, are considered here. These are optimized simultaneously using AMOSA, a newly developed simulated annealing based multiobjective optimization method, in order to detect the appropriate number of clusters as well as the appropriate partitioning. The symmetry present in a partitioning is measured using a newly developed point symmetry based distance. Connectedness present in a partitioning is measured using the relative neighborhood graph concept. Since AMOSA, as well as any other MO optimization technique, provides a set of Pareto-optimal solutions, a new method is also developed to determine a single solution from this set. Thus the proposed GenClustMOO is able to detect the appropriate number of clusters and the appropriate partitioning from data sets having either well-separated clusters of any shape or symmetrical clusters with or without overlaps. The effectiveness of the proposed GenClustMOO in comparison with another recent multiobjective clustering technique (MOCK), a single objective genetic algorithm based automatic clustering technique (VGAPS-clustering), K-means and single linkage clustering techniques is comprehensively demonstrated for nineteen artificial and seven real-life data sets of varying complexities. In a part of the experiment the effectiveness of AMOSA as the underlying optimization technique in GenClustMOO is also demonstrated in comparison to another evolutionary MO algorithm, PESA2.

Solving multi-mode resource-constrained project scheduling problem using two multi objective evolutionary algorithms

The aim of this research is to present a new mathematical model for a multi-mode resource-constrained project scheduling problem (MRCPSP) with discounted cash flows. The objective is to minimize the project makespan and maximize the net present value (NPV), simultaneously, which are the two common objectives of this problem in the literature. Two evolutionary algorithms, NSGA-II and MOPSO are applied to find the set of Pareto solutions for this bi-objective scheduling problem. Furthermore, a new policy is proposed to have feasible solutions for both algorithms. To show the superiority and applicability of the algorithms, different metrics are applied and the graphical comparisons are also considered. Finally, the computational results illustrate the superior performance of the NSGA-II algorithm with regard to the proposed metrics. Key words: Resource-constraint, multi-mode project scheduling, net present value, makespan, evolutionary multi objective optimization.

Evolutionary multi objective optimization for rule mining: a review

Evolutionary multi objective optimization (EMOO) systems are evolutionary systems which are used for optimizing various measures of the evolving system. Rule mining has gained attention in the knowledge discovery literature. The problem of discovering rules with specific properties is treated as a multi objective optimization problem. The objectives to be optimized being the metrics like accuracy, comprehensibility, surprisingness, novelty to name a few. There are a variety of EMOO algorithms in the literature. The performance of these EMOO algorithms is influenced by various characteristics including evolutionary technique used, chromosome representation, parameters like population size, number of generations, crossover rate, mutation rate, stopping criteria, Reproduction operators used, objectives taken for optimization, the fitness function used, optimization strategy, the type of data, number of class attributes and the area of application. This study reviews EMOO systems taking the above criteria into consideration. There are other hybridization strategies like use of intelligent agents, fuzzification, meta data and meta heuristics, parallelization, interactiveness with the user, visualization, etc., which further enhance the performance and usability of the system. Genetic Algorithms (GAs) and Genetic Programming (GPs) are two widely used evolutionary strategies for rule knowledge discovery in Data mining. Thus the proposed study aims at studying the various characteristics of the EMOO systems taking into consideration the two evolutionary strategies of Genetic Algorithm and Genetic programming.

Multi Objective Optimization Model for Collaborative Multi{Echelon Inventory Control in Supply Chain

The use of single objective model in which only the cost is considered in multi-echelon inventory systems does not suffice to raise the total performance of a supply chain. In this paper, we propose an optimization model in which the cost, elapsing time and the demand satisfaction rate are considered in a combined way. For the case where the capacity and supply are limited under the condition of multi classes, random demand and complex link relationships, a two-level solution algorithm is presented. This algorithm enables us to find out the optimal strategy of sites and at the same time deal with the logistic structure using a evolutionary multi objective optimization method and simulation approach. Numerical examples were designed to demonstrate the validity of the algorithm, and the results show that the multi objective optimization model can significantly improve the total performance of supply chains.

Optimal Design of Alloy Steels Using Multiobjective Genetic Algorithms

ABSTRACT Determining the optimal heat treatment regimen and the required weight percentages for the chemical composites to obtain the desired mechanical properties of steel is a challenging problem for the steel industry. To tackle what is in essence an optimization problem, several neural network-based models, which were developed in the early stage of this research work, are used to predict the mechanical properties of steel such as the tensile strength (TS), the reduction of area (ROA), and the elongation. Because these predictive models are generally data driven, such predictions should be treated carefully. In this research work, evolutionary multiobjective (EMO) optimization algorithms are exploited not only to obtain the targeted mechanical properties but also to consider the reliability of the predictions. To facilitate the implementation of a broad range of single-objective and multi-objective algorithms, a versatile Windows 2000®-based application is developed. The obtained results from the single-objective and the multiobjective optimization algorithms are presented and compared, and it is shown that the EMO techniques can be effectively used to deal with such optimization problems.