Pareto-based Multi-objective Evolutionary Algorithms Research Articles

Optimization of the Steam Alternating Solvent Process Using Pareto-Based Multi-Objective Evolutionary Algorithms

Abstract Steam alternating solvent (SAS) process has been proposed as a more environmentally friendly alternative to traditional steam-based processes for heavy oil production. It consists of injecting steam and a non-condensable gas (solvent) alternatively to reduce the oil viscosity. However, optimizing multiple process design (decision) variables is not trivial since multiple conflicting objectives (i.e., maximize the recovery factor, reduce steam–oil ratio) must be considered. Three different multi-objective evolutionary algorithms (MOEAs) are employed to identify a set of Pareto-optimal operational parameters. A multi-objective optimization (MOO) workflow is developed: first, a 2D reservoir model is constructed based on the Fort McMurray formation. Second, a sensitivity analysis is performed to identify the most impactful decision parameters. Third, two response surface (proxy) models and three different MOEAs are employed and compared. This paper is the first to compare different MOEAs for optimizing a wide range of operational parameters for the SAS process. The results show that if more steam is injected, extending the steam cycle duration is preferable. Conversely, if more solvent is injected, it is recommended to start with injecting a solvent with high propane concentrations over short cycles and switch to lower propane concentrations over long cycles near the end.

Two-stage knowledge-driven evolutionary algorithm for distributed green flexible job shop scheduling with type-2 fuzzy processing time

• The distributed green FJSP with type-2 fuzzy processing time is considered. • A two-stage knowledge-driven evolutionary algorithm is proposed. • An efficient energy-saving strategy is designed. • The results indicate the superior performance of our approach. This study is investigated on multi-objective distributed green flexible job shop scheduling problem with type-2 fuzzy processing time. Minimizing makespan and total energy consumption simultaneously is considered. A mixed integer linearity programming model is developed to describe the considered problem. To solve such a hard problem, a two-stage knowledge-driven evolutionary algorithm is proposed (TS-KEA) which divided evolutionary process into two stage. On the first stage, an initial strategy mixed with five problem-specific heuristics is applied to provide a high-quality initial population. Next, a Pareto-based multi-objective evolutionary algorithm is designed for quickly converging to the high quality solutions. Then, a full-active scheduling strategy is designed to reduce total energy consumption. On the second stage, five problem-specific neighborhood structures are proposed to search the non-dominated solutions around the elite solutions. Finally, to evaluate the performance of the proposed algorithm, a number of experiments are adopted on a benchmark with 20 instances. The experiment results show that the proposed TS-KEA can efficiently solve this problem.

Expensive Multiobjective Optimization Algorithm Based on Equivariate Component Analysis

In order to reduce the cost of candidate solution evaluation in the process of solving expensive optimization problems, an expensive multi-objective optimization algorithm based on equivalence component analysis was proposed to study the influence of decision space equivalence components on the prediction accuracy of agent models. Based on the analysis of the equivalence of decision space attributes, a limit learning network based on the equivalence components was constructed for Pareto dominance prediction among candidate solutions. A multi-objective test problem with equivalent components was selected in Pareto dominance prediction experiments, the results of which showed that the algorithm can effectively improve the accuracy of Pareto dominance prediction among candidate solutions. Successively the candidate solutions were scored with multiple ELM (Extreme Learning Machine) models, selected for evaluation and updated, and integrated into the Pareto-based multi-objective evolutionary algorithm. Through comparative experiments on the test problem, the method could achieve a better Pareto approximation solution under the limitation of a limited number of evaluations, and the goal of reducing the cost of expensive multi-objective optimization calculations.

Improved Memetic NSGA-II Using a Deep Neighborhood Search

Elitist non-sorted genetic algorithms as part of Pareto-based multi-objective evolutionary algorithms seems to be one of the most efficient algorithms for multi-objective optimization. However, it has some shortcomings, such as low convergence accuracy, uneven Pareto front distribution, and slow convergence. A number of review papers using memetic technique to improve NSGA-II have been published. Hence, it is imperative to improve memetic NSGA-II by increasing its solving accuracy. In this paper, an improved memetic NSGA-II, called deep memetic non-sorted genetic algorithm (DM-NSGA-II), is proposed, aiming to obtain more non-dominated solutions uniformly distributed and better converged near the true Pareto-optimal front. The proposed algorithm combines the advantages of both exact and heuristic approaches. The effectiveness of DM-NSGA-II is validated using well-known instances taken from the standard literature on multi-objective knapsack problem. As will be shown, the performance of the proposed algorithm is demonstrated by comparing it with M-NSGA-II using hypervolume metric.

Iterative learning-based many-objective history matching using deep neural network with stacked autoencoder

This paper presents an innovative data-integration that uses an iterative-learning method, a deep neural network (DNN) coupled with a stacked autoencoder (SAE) to solve issues encountered with many-objective history matching. The proposed method consists of a DNN-based inverse model with SAE-encoded static data and iterative updates of supervised-learning data are based on distance-based clustering schemes. DNN functions as an inverse model and results in encoded flattened data, while SAE, as a pre-trained neural network, successfully reduces dimensionality and reliably reconstructs geo-models. The iterative-learning method can improve the training data for DNN by showing the error reduction achieved with each iteration step. The proposed workflow shows the small mean absolute percentage error below 4% for all objective functions, while a typical multi-objective evolutionary algorithm fails to significantly reduce the initial population uncertainty. Iterative learning-based many-objective history matching estimates the trends in water cuts that are not reliably included in dynamic-data matching. This confirms the proposed workflow constructs more plausible geo-models. The workflow would be a reliable alternative to overcome the less-convergent Pareto-based multi-objective evolutionary algorithm in the presence of geological uncertainty and varying objective functions.

Modified non-dominated sorting genetic algorithm III with fine final level selection

Dominance resistance is a challenge for Pareto-based multi-objective evolutionary algorithms to solve the high-dimensional optimization problems. The Non-dominated Sorting Genetic Algorithm III (NSGA-III) still has such disadvantage even though it is recognized as an algorithm with good performance for many-objective problems. Thus, a variation of NSGA-III algorithm based on fine final level selection is proposed to improve convergence. The fine final level selection is designed in this way. The θ-dominance relation is used to sort the solutions in the critical layer firstly. Then ISDE index and favor convergence are employed to evaluate convergence of individuals for different situations. And some better solutions are selected finally. The effectiveness of our proposed algorithm is validated by comparing with nine state-of-the-art algorithms on the Deb-Thiele-Laumanns-Zitzler and Walking-Fish-Group test suits. And the optimization objectives are varying from 3 to 15. The performance is evaluated by the inverted generational distance (IGD), hypervolume (HV), generational distance (GD). The simulation results show that the proposed algorithm has an average improvement of 55.4%, 60.0%, 63.1% of 65 test instances for IGD, HV, GD indexes over the original NSGA-III algorithm. Besides, the proposed algorithm obtains the best performance by comparing 9 state-of-art algorithms in HV, GD indexes and ranks third for IGD indicator. Therefore, the proposed algorithm can achieve the advantages over the benchmarks.

An ensemble approach with external archive for multi- and many-objective optimization with adaptive mating mechanism and two-level environmental selection

Based on mating and environmental selections employed, multi-objective evolutionary algorithms (MOEAs) are classified as Pareto-based, decomposition-based and indicator-based approaches that are associated with their own advantages and disadvantages. To benefit from the advantages of different MOEAs, we propose an ensemble framework (ENMOEA) in which mating and environmental selections of diverse MOEAs are combined. ENMOEA is a single-population competitive ensemble, where resource allocation to individual mating operators is done adaptively. In addition, ENMOEA employs a two-level environmental selection where constituent environmental selection operators are first applied to label solutions as “selected” and “non-selected”. Solutions “selected” by most operators are preferred for future evolution. An external archive is employed to facilitate effective usage of function evaluations and achieve a better comprise between convergence and diversity. To demonstrate generality of ENMOEA, we developed two variants: 1) specific case (ENMOEAS - combines different Pareto-based MOEAs) and 2) general case (ENMOEAG - combines Pareto-based, indicator-based and decomposition-based MOEAs). From simulation results on various test suites (DTLZ, WFG and 16 real-world problems), it is evident that ENMOEA is robust to the parameters of the constituent algorithms. In addition, it is evident that the effectiveness of ensemble improves with the diversity of the constituent algorithms.

A parallel naive approach for non-dominated sorting: a theoretical study considering PRAM CREW model

Pareto-based multi-objective evolutionary algorithms use non-dominated sorting as an intermediate step. These algorithms are easy to parallelize as various steps of these algorithms are independent of each other. Researchers have focused on the parallelization of non-dominated sorting in order to reduce the execution time of these algorithms. In this paper, we focus on one of the initial approaches for non-dominated sorting also known as naive approach, proposed by Srinivas et al. and explore the scope of parallelism in this approach. Parallelism is explored in the considered approach in three different ways considering Parallel Random Access Machine, Concurrent Read Exclusive Write model. The time and space complexities of three different parallel versions are also analyzed. Analysis of parallel algorithms is usually carried out under the assumption that an unbounded number of processors are available. Thus, the same assumption has been considered in our analysis too and we have obtained the maximum number of processors required for three parallel versions.

Multi-Objective Evolutionary Algorithms to Find Community Structures in Large Networks

Real-world complex systems are often modeled by networks such that the elements are represented by vertices and their interactions are represented by edges. An important characteristic of these networks is that they contain clusters of vertices densely linked amongst themselves and more sparsely connected to nodes outside the cluster. Community detection in networks has become an emerging area of investigation in recent years, but most papers aim to solve single-objective formulations, often focused on optimizing structural metrics, including the modularity measure. However, several studies have highlighted that considering modularityas a unique objective often involves resolution limit and imbalance inconveniences. This paper opens a new avenue of research in the study of multi-objective variants of the classical community detection problem by applying multi-objective evolutionary algorithms that simultaneously optimize different objectives. In particular, they analyzed two multi-objective variants involving not only modularity but also the conductance metric and the imbalance in the number of nodes of the communities. With this aim, a new Pareto-based multi-objective evolutionary algorithm is presented that includes advanced initialization strategies and search operators. The results obtained when solving large-scale networks representing real-life power systems show the good performance of these methods and demonstrate that it is possible to obtain a balanced number of nodes in the clusters formed while also having high modularity and conductance values.

Optimization of Fuzzy Energy-Management System for Grid-Connected Microgrid Using NSGA-II.

This article proposes a fuzzy logic-based energy-management system (FEMS) for a grid-connected microgrid with renewable energy sources (RESs) and energy storage system (ESS). The objectives of the FEMS are reducing the average peak load (APL) and operating cost through arbitrage operation of the ESS. These objectives are achieved by controlling the charge and discharge rate of the ESS based on the state of charge of ESS, the power difference between load and RES, and electricity market price. The effectiveness of the fuzzy logic greatly depends on the membership functions (MFs). The fuzzy MFs of the FEMS are optimized offline using a Pareto-based multiobjective evolutionary algorithm, nondominated sorting genetic algorithm (NSGA-II). The best compromise solution is selected as the final solution and implemented in the fuzzy-logic controller. A comparison with other control strategies with similar objectives is carried out at a simulation level. The proposed FEMS is experimentally validated on a real microgrid in the energy storage test bed at Newcastle University, U.K.

Merge Nondominated Sorting Algorithm for Many-Objective Optimization.

Many Pareto-based multiobjective evolutionary algorithms require ranking the solutions of the population in each iteration according to the dominance principle, which can become a costly operation particularly in the case of dealing with many-objective optimization problems. In this article, we present a new efficient algorithm for computing the nondominated sorting procedure, called merge nondominated sorting (MNDS), which has a best computational complexity of O(NlogN) and a worst computational complexity of O(MN2) , with N being the population size and M being the number of objectives. Our approach is based on the computation of the dominance set, that is, for each solution, the set of solutions that dominate it, by taking advantage of the characteristics of the merge sort algorithm. We compare MNDS against six well-known techniques that can be considered as the state-of-the-art. The results indicate that the MNDS algorithm outperforms the other techniques in terms of the number of comparisons as well as the total running time.

An Indicator-Based Many-Objective Evolutionary Algorithm With Boundary Protection.

Many-objective optimization problems (MaOPs) pose a big challenge to the traditional Pareto-based multiobjective evolutionary algorithms (MOEAs). As the number of objectives increases, the number of mutually nondominated solutions explodes and MOEAs become invalid due to the loss of Pareto-based selection pressure. Indicator-based many-objective evolutionary algorithms (MaOEAs) have been proposed to address this issue by enhancing the environmental selection. Indicator-based MaOEAs are easy to implement and of good versatility, however, they are unlikely to maintain the population diversity and coverage very well. In this article, a new indicator-based MaOEA with boundary protection, namely, MaOEA-IBP, is presented to relieve this weakness. In MaOEA-IBP, a worst elimination mechanism based on the Iϵ+ indicator and boundary protection strategy is devised to enhance the balance of population convergence, diversity, and coverage. Specifically, a pair of solutions with the smallest Iϵ+ value are first identified from the population. If one solution dominates the other, the dominated solution is eliminated. Otherwise, one solution is eliminated by the boundary protection strategy. MaOEA-IBP is compared with four indicator-based algorithms (i.e., I SDE+ , SRA, MaOEAIGD, and ARMOEA) and other five state-of-the-art MaOEAs (i.e., KnEA, MaOEA-CSS, 1by1EA, RVEA, and EFR-RR) on various benchmark MaOPs. The experimental results demonstrate that MaOEA-IBP can achieve competitive performance with the compared algorithms.

A Pareto Based Multi-Objective Evolutionary Algorithm Approach to Military Installation Rail Infrastructure Investment

Decision making for military railyard infrastructure is an inherently multi-objective problem, balancing cost versus capability. In this research, a Pareto-based Multi-Objective Evolutionary Algorithm is compared to a military rail inventory and decision support tool (RAILER). The problem is formulated as a multi-objective evolutionary algorithm in which the overall railyard condition is increased while decreasing cost to repair and maintain. A prioritization scheme for track maintenance is introduced that takes into account the volume of materials transported over the track and each rail segment’s primary purpose. Available repair options include repairing current 90 gauge rail, upgrade of rail segments to 115 gauge rail, and the swapping of rail removed during the upgrade. The proposed Multi-Objective Evolutionary Algorithm approach provides several advantages to the RAILER approach. The MOEA methodology allows decision makers to incorporate additional repair options beyond the current repair or do nothing options. It was found that many of the solutions identified by the evolutionary algorithm were both lower cost and provide a higher overall condition that those generated by DoD’s rail inventory and decision support system, RAILER. Additionally, the MOEA methodology generates lower cost, higher capability solutions when reduced sets of repair options are considered. The collection of non-dominated solutions provided by this technique gives decision makers increased flexibility and the ability to evaluate whether an additional cost repair solution is worth the increase in facility rail condition.

A Multi-Objective Emergency Rescue Facilities Location Model for Catastrophic Interlocking Chemical Accidents in Chemical Parks

Catastrophic interlocking chemical accidents (CICAs) are the most frequent hazardous events that occur in chemical parks, and they result in severe human casualties and property losses. Emergency rescue facilities play an important role in ensuring the safety of chemical parks, as their locations determine the efficiency and effectiveness of the emergency management process. This paper proposes a multi-objective emergency rescue facilities location (ERFsL) model for emergency management of CICAs. Due to the special characteristics of CICAs, the proposed model considers not only the spatial characteristics of the facilities but also the potential risks associated with CICAs. A quantitative area risk assessment (QARA) approach based on domino effect and grid partition is involved to delineate the potential negative impacts of CICAs on different demand points. Moreover, a matrix encoding scheme is coupled with Pareto-based multi-objective evolutionary algorithms (MOEAs) for model solving. A case study is presented to demonstrate the methodology. A set of reasonable and non-dominated solutions indicate that the matrix encoding scheme and the corresponding evolutionary operators can be successfully coupled with the MOEAs to produce feasible child solutions. We also find that the involvement of risk analysis has a significant effect on the location decision. The findings show that our work has the potential to ensure the safety and long-term development of the parks.

A Pareto-based many-objective evolutionary algorithm using space partitioning selection and angle-based truncation

Evolutionary algorithms (EAs) have shown to be efficient in dealing with many-objective optimization problems (MaOPs) due to their ability to obtain a set of compromising solutions which not only converge toward the Pareto front (PF), but also distribute well. The Pareto-based multi-objective evolutionary algorithms are valid for solving optimization problems with two and three objectives. Nevertheless, when they encounter many-objective problems, they lose their effectiveness due to the weakening of selection pressure based on the Pareto dominance relation. Our major purpose is to develop more effective diversity maintenance mechanisms which cover convergence besides dominance in order to enhance the Pareto-based many-objective evolutionary algorithms. In this paper, we propose a Pareto-based many-objective evolutionary algorithm using space partitioning selection and angle-based truncation, abbreviated as SPSAT. The space partitioning selection increases selection pressure and maintains diversity simultaneously, which we realize through firstly dividing the normalized objective space into many subspaces and then selecting only one individual with the best proximity estimation value in each subspace. To further enhance convergence and diversity, the angle-based truncation calculates the angle values of any pair of individuals in the critical layer and then gradually removes the individuals with the minimum angle values. From the comparative experimental results with six state-of-the-art algorithms on a series of well-defined optimization problems with up to 20 objectives, the proposed algorithm shows its competitiveness in solving many-objective optimization problems.

A divide-and-conquer based efficient non-dominated sorting approach

Abstract In general, evolutionary algorithms are very prevalent in solving multi-objective optimization problems. Pareto-based multi-objective evolutionary algorithms are popularly used in solving different multi-objective optimization problems. These algorithms work using several steps, non-dominated sorting being the most salient one. However, this non-dominated sorting step is associated with a high computational complexity. In the past, different approaches have been proposed for non-dominated sorting. In this paper, to address the problem of non-dominated sorting, a framework called DCNS (Divide-and-conquer based non-dominated sorting) is developed. Based on this DCNS framework, four different approaches are proposed. The best case time complexity of our proposed DCNS framework is proved to be O ( N log N + M N ) for M ≥ 2 where N is the number of solutions and M is the number of objectives. This best case time complexity is better than the best case time complexities of various other approaches. The number of dominance comparisons performed by the proposed framework is lower than those from other state-of-the-art approaches in different scenarios. The proposed framework has the parallelism property and the scope of parallelism is also discussed.

A hybrid ensemble pruning approach based on consensus clustering and multi-objective evolutionary algorithm for sentiment classification

Sentiment analysis is a critical task of extracting subjective information from online text documents. Ensemble learning can be employed to obtain more robust classification schemes. However, most approaches in the field incorporated feature engineering to build efficient sentiment classifiers.The purpose of our research is to establish an effective sentiment classification scheme by pursuing the paradigm of ensemble pruning. Ensemble pruning is a crucial method to build classifier ensembles with high predictive accuracy and efficiency. Previous studies employed exponential search, randomized search, sequential search, ranking based pruning and clustering based pruning. However, there are tradeoffs in selecting the ensemble pruning methods. In this regard, hybrid ensemble pruning schemes can be more promising.In this study, we propose a hybrid ensemble pruning scheme based on clustering and randomized search for text sentiment classification. Furthermore, a consensus clustering scheme is presented to deal with the instability of clustering results. The classifiers of the ensemble are initially clustered into groups according to their predictive characteristics. Then, two classifiers from each cluster are selected as candidate classifiers based on their pairwise diversity. The search space of candidate classifiers is explored by the elitist Pareto-based multi-objective evolutionary algorithm.For the evaluation task, the proposed scheme is tested on twelve balanced and unbalanced benchmark text classification tasks. In addition, the proposed approach is experimentally compared with three ensemble methods (AdaBoost, Bagging and Random Subspace) and three ensemble pruning algorithms (ensemble selection from libraries of models, Bagging ensemble selection and LibD3C algorithm). Results demonstrate that the consensus clustering and the elitist pareto-based multi-objective evolutionary algorithm can be effectively used in ensemble pruning. The experimental analysis with conventional ensemble methods and pruning algorithms indicates the validity and effectiveness of the proposed scheme.

A benchmark test suite for evolutionary many-objective optimization

In the real world, it is not uncommon to face an optimization problem with more than three objectives. Such problems, called many-objective optimization problems (MaOPs), pose great challenges to the area of evolutionary computation. The failure of conventional Pareto-based multi-objective evolutionary algorithms in dealing with MaOPs motivates various new approaches. However, in contrast to the rapid development of algorithm design, performance investigation and comparison of algorithms have received little attention. Several test problem suites which were designed for multi-objective optimization have still been dominantly used in many-objective optimization. In this paper, we carefully select (or modify) 15 test problems with diverse properties to construct a benchmark test suite, aiming to promote the research of evolutionary many-objective optimization (EMaO) via suggesting a set of test problems with a good representation of various real-world scenarios. Also, an open-source software platform with a user-friendly GUI is provided to facilitate the experimental execution and data observation.

Designing multi-period supply chain network considering risk and emission: a multi-objective approach

This research formulates a multi-objective problem (MOP) for supply chain network (SCN) design by incorporating the issues of social relationship, carbon emissions, and supply chain risks such as disruption and opportunism. The proposed MOP includes three conflicting objectives: maximization of total profit, minimization of supply disruption and opportunism risks, and minimization of carbon emission considering a number of supply chain constraints. Furthermore, this research analyses the effect of social relationship levels between different tiers of SCN on the profitability, risk, and emission over the time. In this regard, we focus on responding to the following questions. (1) How does the evolving social relationship affect the objectives of the supply chain (SC)? (2) How do the upstream firms’ relationships affect the relationships of downstream firms, and how these relationships influence the objectives of the SC? (3) How does the supply disruption risk interact with the opportunism risk through supply chain relationships, and how these risks affect the objectives of the SC? (4) How do these three conflicting objectives trade-off? A Pareto-based multi-objective evolutionary algorithm–non-dominated sorting genetic algorithm-II (NSGA-II) has been employed to solve the presented problem. In order to improve the quality of solutions, tuning parameters of the NSGA-II are modulated using Taguchi approach. An illustrative example is presented to manifest the capability of the model and the algorithm. The results obtained evince the robust performance of the proposed MOP.

Memory-based adaptive partitioning (MAP) of search space for the enhancement of convergence in Pareto-based multi-objective evolutionary algorithms

A new algorithm, dubbed memory-based adaptive partitioning (MAP) of search space, which is intended to provide a better accuracy/speed ratio in the convergence of multi-objective evolutionary algorithms (MOEAs) is presented in this work. This algorithm works by performing an adaptive-probabilistic refinement of the search space, with no aggregation in objective space. This work investigated the integration of MAP within the state-of-the-art fast and elitist non-dominated sorting genetic algorithm (NSGAII). Considerable improvements in convergence were achieved, in terms of both speed and accuracy. Results are provided for several commonly used constrained and unconstrained benchmark problems, and comparisons are made with standalone NSGAII and hybrid NSGAII-efficient local search (eLS).