Multi-objective Variant Research Articles

Three-dimensional deployment strategy for a multi-BWBUG cooperative system at deep depths

ABSTRACT This study investigates the issue of the three-dimensional deployment for blended-wing-body underwater gliders (BWBUGs) at deep depths. Initially, an underwater three-dimensional deployment optimisation model is formulated, considering factors such as the three-dimensional coverage ratio and the balance of node communication energy consumption. Subsequently, a sine-logistic chaos strategy with excellent ergodicity is proposed. Thereafter, the dynamic decision-assisted heuristic method (DDHM) is proposed based on the dynamic decision framework, sine-logistic chaos strategy, and opposition-based learning. The well-designed dynamic decision framework effectively avoids the premature convergence and local optimum of the algorithm. Additionally, the multi-objective variant of DDHM, referred to as MDDHM, is established utilising the archival mechanism. Lastly, the performance of the DDHM and MDDHM is evaluated by simulation experiments. Statistical analysis demonstrates that DDHM is highly effective for the underwater three-dimensional deployment of the multi-BWBUG cooperative system. Furthermore, its overall performance surpasses that of other comparative methods.

A novel memory-based artificial gorilla troops optimizer for installing biomass distributed generators in unbalanced radial networks

Optimizing unbalanced distribution networks through the strategic integration of distributed generators (DGs) has long been recognized as a significant challenge. Selecting the optimal sizes and locations for these generators is crucial for minimizing network power loss and enhancing voltage profiles. The previously published methods have been plagued by issues such as slow convergence rates, entrapment in local optima, complexity, and extensive computational requirements. Addressing these limitations, this paper introduces an efficient methodology: the Memory-based Artificial Gorilla Troops Optimizer (MGTO). This approach leverages memory-based mechanisms to enhance exploration and decision-making, facilitating the seamless integration of various biomass DGs (BDGs) into unbalanced IEEE 37-bus radial networks. The immigration of gorillas during the exploration phase is enriched through the utilization of stored memories of candidate trajectories within the search space, enabling the silverback to make informed decisions. Furthermore, a multi-objective variant of MGTO is developed in collaboration with Fuzzy Decision-Making (FDM), allowing for the simultaneous optimization of multiple targets. To demonstrate the MGTO effectiveness, it is rigorously compared against a comprehensive set of established optimization algorithms, including the Honey Badger Algorithm (HBA), Runge Kutta Optimizer (RUN), and others. The results proved the dominance of the proposed MGTO by getting minimum power loss and voltage fluctuation of 0.364 % and 15.4 %, respectively, while in the multi-objective problem, the best results are 0.513 % loss and 17.9% voltage fluctuation. The results proved the consistency of the proposed MGTO in installing different BDGs into an unbalanced distribution network.

Generation of black-box adversarial attacks using many independent objective-based algorithm for testing the robustness of deep neural networks

Deep neural networks (DNNs) have become increasingly ubiquitous in our daily lives, finding applications in areas such as image recognition, voice recognition, and natural language processing. However, a growing concern revolves around the vulnerability of DNNs to adversarial examples—malicious inputs that can compromise the safety and accuracy of their outcomes. Existing studies predominantly fall into two categories: white-box and black-box techniques. White-box techniques require detailed internal information about the model, often focusing on gradient-based methods. In contrast, black-box techniques, which emulate real-world scenarios more closely, only rely on input–output knowledge. This study focuses specifically on black-box strategies, with key contributions from Single-Objective Variant of Differential Evolution (Pixel-SOO) and Multi-Objective Variant of Differential Evolution (Pixel-MOO) algorithms. While these approaches show promise, they suffer from drawbacks like long execution times and being unable to generate instances for adversarial purposes. To address these challenges, we introduce a novel archive-based Many Independent Objective (MIO) algorithm for using the first time in this context. Our proposed algorithm identifies the most vulnerable image pixels through the MIO algorithm, enabling efficient label flip attacks with minimized attempts. Furthermore, we balance exploration and exploitation by incorporating an adaptive parameter mechanism. The effectiveness of the proposed algorithm is assessed by employing VGG (VGG16 and VGG19) and ResNet (ResNet50, ResNet101, and ResNet152) architectures, both of which are convolutional neural network (CNN) models. The success criterion for the algorithms is to minimize the number of pixel changes while achieving high flip rates with a minimal number of requests to the network. A comprehensive analysis of the experimental results reveals that our algorithm consistently outperforms Pixel-SOO and Pixel-MOO, exhibiting an average speedup of three times compared to Pixel-SOO and seven times compared to Pixel-MOO. In most runs, adversarial attacks are generated with fewer pixel changes than Pixel-MOO and Pixel-SOO. In addition, our findings are openly accessible on GitHub to ensure transparency and reproducibility and encourage future research efforts.

Optimal operation and control of hybrid power systems with stochastic renewables and FACTS devices: An intelligent multi-objective optimization approach

This paper delves into the increasingly complex domain of Optimal Power Flow (OPF) within modern power systems, enhanced by the integration of unpredictable renewable energy sources. The research originally integrates stochastic photovoltaic and wind energy sources, along with a suite of Flexible AC Transmission System (FACTS) components – including thyristor-controlled series compensators, static VAR compensators, and thyristor-controlled phase shifters. The primary objective is to solve the OPF problem by reducing generation costs while accommodating the variable nature of renewable energy sources and load demands. This study prioritizes the examination of both constant and fluctuating load requirements. The inherent variability of PV and wind energy, along with load demand, is captured through the modelling of probability density functions. This approach enables a more detailed optimization process, incorporating not just the cost of thermal energy generation but also the scheduling costs of renewable sources and associated penalty costs. Moreover, the study examines the strategic placement and sizing of FACTS components, an aspect essential in minimizing the overall cost of power production. Employing both single- and multi-objective optimization algorithms, the research addresses the OPF problem in a modified IEEE-30 bus system through various case studies. The application of the recently developed flow direction algorithm, including its multi-objective variant with an ε-based constraint-handling mechanism to OPF problem is the primary contributions of this work. The results, benchmarked against several advanced metaheuristic algorithms, reveal the proposed algorithm's superior performance. This comprehensive study not only underscores the potential of integrating renewable energy sources into the grid but also highlights the efficacy of intelligent optimization strategies in managing the complexities of modern power systems.

MOIMPA: multi-objective improved marine predators algorithm for solving multi-objective optimization problems

This paper introduces a multi-objective variant of the marine predators algorithm (MPA) called the multi-objective improved marine predators algorithm (MOIMPA), which incorporates concepts from Quantum theory. By leveraging Quantum theory, the MOIMPA aims to enhance the MPA’s ability to balance between exploration and exploitation and find optimal solutions. The algorithm utilizes a concept inspired by the Schrödinger wave function to determine the position of particles in the search space. This modification improves both exploration and exploitation, resulting in enhanced performance. Additionally, the proposed MOIMPA incorporates the Pareto dominance mechanism. It stores non-dominated Pareto optimal solutions in a repository and employs a roulette wheel strategy to select solutions from the repository, considering their coverage. To evaluate the effectiveness and efficiency of MOIMPA, tests are conducted on various benchmark functions, including ZDT and DTLZ, as well as using the evolutionary computation 2009 (CEC’09) test suite. The algorithm is also evaluated on engineering design problems. A comparison is made between the proposed multi-objective approach and other well-known evolutionary optimization methods, such as MOMPA, multi-objective ant lion optimizer, and multi-objective multi-verse optimization. The statistical results demonstrate the robustness of the MOIMPA approach, as measured by metrics like inverted generational distance, generalized distance, spacing, and delta. Furthermore, qualitative experimental results confirm that MOIMPA provides highly accurate approximations of the true Pareto fronts.

A multi-objective Chaos Game Optimization algorithm based on decomposition and random learning mechanisms for numerical optimization

Chaos Game Optimization (CGO) is a heuristic optimization approach that estimates global optima for optimization problems using operators based on chaos theory. This paper first proposes a multi-objective variant of this recent algorithm using decomposition. The proposed algorithm is called Multi-Objective CGO based on Decomposition (MOCGO/D), in which the decomposition step employs a Normalized Boundary Intersection (NBI) technique for decomposing the multi-objective problem into single-objective sub-problems. A novel Random Learning (RL) strategy based on the combination of multiple strategies such as Opposition-based learning, Levy flight operator, Orthogonal learning, and the tangent flight operator, is incorporated in the MOCGO/D to propose an enhanced version called MOCGO/DR algorithm. The RL strategy aims to improve the balance between exploitation and exploration of the conventional CGO, leading to better convergence behavior and avoiding getting trapped in local optima. The first set of experimental results demonstrates that MOCGO/DR can perform better than three other variants of MOCGO, namely archive-based MOCGO (MOCGO/A), crowding-distance based MOCGO (MOCGO/CD) and decomposition-based MOCGO (MOCGO/D) on 62% of test cases. A second set of experiments and evaluation shows that the proposed approach provides better results than well-regarded algorithms, including strength pareto evolutionary algorithm (SPEA2), multiobjective evolutionary algorithm based on decomposition (MOEA/D), multi-objective particle swarm optimization algorithm based on decomposition (MPSO/D), multistage evolutionary algorithm (MSEA), and a fast and elitist multi- objective genetic algorithm (NSGAII) when using performance measures such as GD, IGD, HV, Spacing, Spread, and Hausdorff distance on 65% test cases. This two-stage evaluation was conducted on three different benchmark test sets: the Deb–Thiele–Laumanns–Zitzler (DTLZ) test suite, the Zitzler–Deb–Thiele (ZDT) test suite, and the bias test suite (BT). Overall, the Friedman test results for all performance measures show that MOCGO/DR is demonstrated to be a competitive candidate as a multi-objective optimization algorithm in this space.

A multi-objective evolutionary approach towards automated online controlled experiments

Due to the complexity of the web and mobile software applications, engineers rely heavily on A/B testing (i.e., online controlled experiments) to evaluate and measure the impact of the new changes. However, creating and evaluating A/B tests is a time-consuming, error-prone, and costly manual activity. For the problem of automating A/B testing, there is no solution in literature that evaluates A/B testing results as multi-criteria instead of single criteria. The current single criteria based methods overly simplify the A/B test results, as in the web/mobile application industry, a typical A/B test in practice has multiple metrics instead of one metric. In this paper, we describe the Variant Creation and Evaluation (VCE) problem in A/B testing and propose MOVSW (Multi-Objective Variant Selection Wrapper) that utilizes Multi-Objective Evolutionary Algorithm (MOEA) to automate the process of creating and selecting variants as launch candidates in A/B testing. Given a set of parameters we would like to optimize, the control group in the A/B test uses the existing values of these parameters in the system. The MOVSW automatically creates variants of different parameter values and conducts A/B testing to evaluate these variants against the control group with existing parameter values based on multiple measurements. The outputs of the MOVSW are a list of non-dominated candidate variants (also known as Pareto optimal set) that lead to potential improvements on key measures according to the A/B test results. These candidate variants could be then reviewed by stakeholders to determine the final variant to be launched. We designed and conducted a case study to comprehensively evaluate the effectiveness of five MOEAs and three baseline methods on MOVSW for automating A/B tests, using user clicks logging of news articles from the Addressa Dataset. Our results indicate that MOEA/D is the most stable method with fast convergence compared with other MOEAs, produces more high-quality solutions with high precision than the single-objective methods, and thus is promising to be used in the VCE problem of A/B testing.

Contingency constrained TCSC and DG coordination in an integrated transmission and distribution network: A multi-objective approach

Transmission System Operators (TSO) deploy Flexible AC Transmission Systems (FACTS) for congestion management in order to meet technical and multilateral power supply transactions. These power commitments are however constrained by thermal, voltage and stability limitations. On the other hand, the campaign to de-carbonize the power supply framework as seen Distribution System Operators (DSO) accommodate an increased penetration of Distributed Generation (DG) within their distribution networks. However, prerogative of system operators for separate planning of FACTS and DG systems can worsen power system’s key performance indicators especially under huge load growth and severe contingencies. Therefore, this paper developed an approach for contingency constrained coordination of Thyristor Controlled Series Compensator (TCSC) and DG through a multi-level optimization, comprising of a hybrid real power flow index and particle swarm in the first level and a multi-objective variant of particle swarm optimization in the second level. The contingency constrained coordination aimed to improve Available Transfer Capability (ATC), power loss and voltage deviation. Two models of DG were coordinated with TCSC under normal and contingency cases. Results indicate that while ATC improvement for various transactions were achieved with TCSC, additional power losses incurred was further reduced with DG deployment in coordination with TCSC. Furthermore, the Pareto front, which establishes the correlation between objectives shows a diving parabola that is partly nonlinear. Also, the TCSC−DGPQ provide superior ATC and power losses compared with TCSC−DGPV. Again, under (N−1) contingencies, the TCSC−DGPQ provides improved ATC compared with other contingency cases under TCSC only.

Multi-objective fitness-dependent optimizer algorithm

This paper proposes the multi-objective variant of the recently-introduced fitness dependent optimizer (FDO). The algorithm is called a multi-objective fitness dependent optimizer (MOFDO) and is equipped with all five types of knowledge (situational, normative, topographical, domain, and historical knowledge) as in FDO. MOFDO is tested on two standard benchmarks for the performance-proof purpose: classical ZDT test functions, which is a widespread test suite that takes its name from its authors Zitzler, Deb, and Thiele, and on IEEE Congress of Evolutionary Computation benchmark (CEC-2019) multi-modal multi-objective functions. MOFDO results are compared to the latest variant of multi-objective particle swarm optimization, non-dominated sorting genetic algorithm third improvement (NSGA-III), and multi-objective dragonfly algorithm. The comparative study shows the superiority of MOFDO in most cases and comparative results in other cases. Moreover, MOFDO is used for optimizing real-world engineering problems (e.g., welded beam design problems). It is observed that the proposed algorithm successfully provides a wide variety of well-distributed feasible solutions, which enable the decision-makers to have more applicable-comfort choices to consider.

Differential Evolution and Its Applications in Image Processing Problems: A Comprehensive Review.

Differential evolution (DE) is one of the highly acknowledged population-based optimization algorithms due to its simplicity, user-friendliness, resilience, and capacity to solve problems. DE has grown steadily since its beginnings due to its ability to solve various issues in academics and industry. Different mutation techniques and parameter choices influence DE's exploration and exploitation capabilities, motivating academics to continue working on DE. This survey aims to depict DE's recent developments concerning parameter adaptations, parameter settings and mutation strategies, hybridizations, and multi-objective variants in the last twelve years. It also summarizes the problems solved in image processing by DE and its variants.

A comprehensive survey on the sine–cosine optimization algorithm

Metaheuristic algorithms based on intelligent rules have been successfully developed and applied to solve many optimization areas over the past few decades. The sine–cosine algorithm (SCA) imitates the behaviour of transcendental functions while the sine and cosine functions are presented to explore and exploit the search space. SCA starts by random population and executes iterative evolution processes to update the standard evolutionary algorithm’s destination or the best location. SCA used linear transition rules to balance the exploration and exploitation searches while searching for the best or optimal solutions. Since Mirjalili proposed it in 2016, SCA has attracted many researchers’ attention to deal with several optimization problems in many fields due to its strengths in solving optimization tasks that include the simple concept, easiness of implementation, and rapid convergence. This paper aims to provide researchers with a relatively comprehensive and extensive overview of the Sine–Cosine optimization algorithm in the literature to inspire further research. It examines the available publications, including improvements, binary, chaotic, hybridizations, multi-objective variants, and different applications. Some optimization formulations regarding single-objective optimization problems, multi-objective optimization problems, binary-objective optimization problems, and more classifications regarding the optimization types are discussed. An extensive bibliography is also included.

A Multi-Objective Modified PSO for Inverse Kinematics of a 5-DOF Robotic Arm

In this paper, a new modified particle swarm optimization, m-PSO, is proposed, in which the novelty consists of proposing a fitness-based particle swarm optimization algorithm, PSO, which adapts the particles’ behavior rather than the PSO parameters and where particles evolve differently considering their level of optimality. A multi-objective optimization, MO, approach is then built based on m-PSO. In the proposed method, particles with fitness better than the mean local best are only updated toward the global best, while others keep moving in a classical manner. The proposed m-PSO and its multi-objective version MO-m-PSO are then employed to solve the inverse kinematics of a 5-DOF robotic arm which is 3D-printed for educational use. In the MO-m-PSO approach of inverse kinematics, the arm IK problem is formulated as a multi-objective problem searching for an appropriate solution that takes into consideration the end-effector position and orientation with a Pareto front strategy. The IK problem is addressed as the optimization of the end-effector position and orientation based on the forward kinematics model of the systems which is built using the Denavit–Hartenberg approach. Such an approach allows to avoid classical inverse kinematics solvers challenges such as singularities, which may simply harm the existence of an inverse expression. Experimental investigations included the capacity of the proposal to handle random single points in the workspace and also a circular path planning with a specific orientation. The comparative analysis showed that the mono-objective m-PSO is better than the classical PSO, the CSA, and SSA. The multi-objective variants returned accurate results, fair and better solutions compared to multi-objective variants of MO-PSO, MO-JAYA algorithm, and MO-CSA. Even if the proposed method were applied to solve the inverse kinematics of and educational robotics arms for a single point as well as for a geometric shape, it may be transposed to solve related industrial robotized arms withthe only condition of having their forward kinematics model.

An elitist cooperative evolutionary bi-level multi-objective decomposition-based algorithm for sustainable supply chain

Many real-life applications are modelled using hierarchical decision-making in which: an upper-level optimisation task is constrained by a lower-level one. Such class of optimisation problems is referred in the literature as Bi-Level Optimisation Problems (BLOPs). Most of the proposed methods tackled the single-objective continuous case adhering to some regularity assumptions. This is at odds with real-world problems which involve mainly discrete variables and expensive objective function evaluations. Besides, the optimisation process becomes exorbitantly time-consuming, especially when optimising several objectives at each level. For this reason, the Multi-objective variant (MBLOP) remains relatively less explored and the number of methods tackling the combinatorial case is much reduced. Motivated by these observations, we propose in this work an elitist decomposition-based evolutionary algorithm to solve MBLOPs, called ECODBEMA. The basic idea of our proposal is to handle, decomposition, elitism and multithreading mechanisms to cope with the MBLOP's high complexity. ECODBEMA is applied to the production–distribution problem and to a sustainable end-of-life products disassembly case-study based on real-data of Aix-en-Provence French city. We compared the optimal solutions of an exact method using CPLEX solver with near-optimal solutions obtained by ECODBEMA. The statistical results show the significant outperformance of ECODBEMA against other multi-objective bi-level optimisation algorithms.

A Multi-Objective Anti-Predatory NIA for E-Commerce Logistics Optimization Problem

Nature-inspired algorithms (NIAs) have established their promising performance to solve both single-objective optimization problems (SOOPs) and multi-objective optimization problems (MOOPs). Anti-predatory NIA (APNIA) is one of the recently introduced single-objective algorithm based on the self-defense behavior of frogs. This paper extends APNIA as multi-objective algorithm and presents the first proposal of APNIA to solve MOOPs. The proposed algorithm is a posteriori version of APNIA, which is named as multi-objective anti-predatory NIA (MO-APNIA). It uses the concept of Pareto dominance to determine the non-dominated solutions. The performance of the MO-APNIA is established through the experimental evaluation and statistically verified using the Friedman rank test and Holm-Sidak test. MO-APNIA is also employed to solve a multi-objective variant of hub location problem (HLP) from the perspective of the e-commerce logistics. Results indicate that the MO-APNIA is also capable to finds the non-dominated solutions of HLP. This finds immense use in logistics industry.

Evolutionary-based prediction interval estimation by blending solar radiation forecasting models using meteorological weather types

Recent research has shown that the integration or blending of different forecasting models is able to improve the predictions of solar radiation. However, most works perform model blending to improve point forecasts, but the integration of forecasting models to improve probabilistic forecasting has not received much attention. In this work the estimation of prediction intervals for the integration of four Global Horizontal Irradiance (GHI) forecasting models (Smart Persistence, WRF-solar, CIADcast, and Satellite) is addressed. Several short-term forecasting horizons, up to one hour ahead, have been analyzed. Within this context, one of the aims of the article is to study whether knowledge about the synoptic weather conditions, which are related to the stability of weather, might help to reduce the uncertainty represented by prediction intervals. In order to deal with this issue, information about which weather type is present at the time of prediction, has been used by the blending model. Four weather types have been considered. A multi-objective variant of the Lower Upper Bound Estimation approach has been used in this work for prediction interval estimation and compared with two baseline methods: Quantile Regression (QR) and Gradient Boosting (GBR). An exhaustive experimental validation has been carried out, using data registered at Seville in the Southern Iberian Peninsula. Results show that, in general, using weather type information reduces uncertainty of prediction intervals, according to all performance metrics used. More specifically, and with respect to one of the metrics (the ratio between interval coverage and width), for high-coverage (0.90, 0.95) prediction intervals, using weather type enhances the ratio of the multi-objective approach by 2%–3%. Also, comparing the multi-objective approach versus the two baselines for high-coverage intervals, the improvement is 11%–17% over QR and 10%–44% over GBR. Improvements for low-coverage intervals (0.85) are smaller.

Evolutionary algorithm hybridized with local search and intelligent seeding for solving multi-objective Euclidian TSP

Multi-objective Euclidian TSP (ETSP) has several practical applications such as mobile computing and maritime surveillance. This problem has complexity not only in terms of combinatorial constraints but also in terms of multiple objectives. The local heuristic-based algorithms are extremely efficient in solving the single-objective ETSPs. However, their efficacy is limited in solving the multi-objective ETSPs due to the presence of multiple objectives. To bridge this gap, a two-stage evolutionary algorithm (TSEA) is developed to solve multi-objective ETSPs. In this algorithm, the first stage involves the use of a hybrid local search evolutionary algorithm (HLS-EA) which incorporates the local heuristic of nearest neighbor and 2-opt in the framework of real-coded NSGA-II to solve the individual objectives of multi-objective ETSP. These individual single-objective solutions which represent the corner solutions of the Pareto optimal front are used in the second stage as seed solutions in seeded HLS-EA (SHLS-EA) for solving the corresponding multi-objective ETSP. The developed algorithm is tested on 17 two-objective, 6 three-objective, and 2 four-objective ETSPs to show the superior performance over multi-objective variants of the Lin-Kernighan algorithm. Also, the developed algorithm is compared with several variants of DE and GA to illustrate the superior performance over the variants of evolutionary algorithms. Further, the algorithm is extended to the multi-objective ETSPs up to 10,000 cities.

A Robust Multi-Objective Feature Selection Model Based on Local Neighborhood Multi-Verse Optimization

Classification tasks often include, among the large number of features to be processed in the datasets, many irrelevant and redundant ones, which can even decrease the efficiency of classifiers. Feature Selection (FS) is the most common preprocessing technique utilized to overcome the drawbacks of the high dimensionality of datasets and often has two conflicting objectives: The first function aims to maximize the classification performance or reduce the error rate of the classifier. In contrast, the second function is designed to minimize the number of features. However, the majority of wrapper FS techniques are developed for single-objective scenarios. Multi-verse optimizer (MVO) is considered as one of the well-regarded optimization approaches in recent years. In this paper, the binary multi-objective variant of MVO (MOMVO) is proposed to deal with feature selection tasks. The standard MOMVO suffers from local optima stagnation, so we propose an improved binary MOMVO to deal with this issue using the memory concept and personal best of the universes. The experimental results and comparisons indicate that the proposed binary MOMVO approach can effectively eliminate irrelevant and/or redundant features and maintain a minimum classification error rate when dealing with different datasets compared with the most popular feature selection techniques. Furthermore, the 14 benchmark datasets showed that the proposed approach outperforms the stat-of-art multi-objective optimization algorithms for feature selection.

MOEO-EED: A multi-objective equilibrium optimizer with exploration–exploitation​ dominance strategy

The work proposes multi-objective variants of the recently-proposed equilibrium optimizer (EO) using an archive to obtain Pareto optimal solutions and a crowding distance approach to preserve the diversity among the non-dominated solutions. However, due to the use of constant values for the controlling parameters of EO, the exploration and exploitation of multi-objective EO (MOEO) are not accelerated, so the first variant is proposed with a number of linear and non-linear equations to generate increasing and decreasing values proportional to the number of iterations that will eventually improve exploratory and exploitative behaviors of MOEO. In the second proposed variant of MOEO with exploration–exploitation​ dominance strategy (MOEO-EED), solutions are updated according to the number of dominated solutions. If a solution has a high number of dominated solutions, it will go through fewer abrupt changes, while others will undergo major changes. In addition, a novel strategy known as a Gaussian-based mutation (G) strategy is proposed to use the Gaussian distribution to generate two different step sizes: small step sizes that are generated under a small sigma value for the Gaussian distribution to promote the exploitation capability, and high step sizes under a high sigma value to increase the exploration operator. The tradeoff between those two-step sizes is predefined through experimentation. This strategy is integrated to generate the third variant, namely MOEO-EED-G. In the fourth variant (OMOEO-EED-G), the tradeoff between the best solution selected from the archive and its opposite is achieved with a probability to increase the diversity and accelerate the convergence of MOEO-EED-G. Finally, the efficacy of the proposed algorithms is tested on four benchmark multi-objective functions to show that the proposed algorithms, especially OMOEO-EED-G, are superior to selected state-of-the-art multi-objective algorithms.

MOSMA: Multi-Objective Slime Mould Algorithm Based on Elitist Non-Dominated Sorting

This paper proposes a multi-objective Slime Mould Algorithm (MOSMA), a multi-objective variant of the recently-developed Slime Mould Algorithm (SMA) for handling the multi-objective optimization problems in industries. Recently, for handling optimization problems, several meta-heuristic and evolutionary optimization techniques have been suggested for the optimization community. These methods tend to suffer from low-quality solutions when evaluating multi-objective optimization (MOO) problems than addressing the objective functions of identifying Pareto optimal solutions’ accurate estimation and increasing the distribution throughout all objectives. The SMA method follows the logic gained from the oscillation behaviors of slime mould in the laboratory experiments. The SMA algorithm shows a powerful performance compared to other well-established methods, and it is designed by incorporating the optimal food path using the positive-negative feedback system. The proposed MOSMA algorithm employs the same underlying SMA mechanisms for convergence combined with an elitist non-dominated sorting approach to estimate Pareto optimal solutions. As a posteriori method, the multi-objective formulation is maintained in the MOSMA, and a crowding distance operator is utilized to ensure increasing the coverage of optimal solutions across all objectives. To verify and validate the performance of MOSMA, 41 different case studies, including unconstrained, constrained, and real-world engineering design problems are considered. The performance of the MOSMA is compared with Multiobjective Symbiotic-Organism Search (MOSOS), Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), and Multiobjective Water-Cycle Algorithm (MOWCA) in terms of different performance metrics, such as Generational Distance (GD), Inverted Generational Distance (IGD), Maximum Spread (MS), Spacing, and Run-time. The simulation results demonstrated the superiority of the proposed algorithm in realizing high-quality solutions to all multi-objective problems, including linear, nonlinear, continuous, and discrete Pareto optimal front. The results indicate the effectiveness of the proposed algorithm in solving complicated multi-objective problems. This research will be backed up with extra online service and guidance for the paper’s source code at https://premkumarmanoharan.wixsite.com/mysite and https://aliasgharheidari.com/SMA.html . Also, the source code of SMA is shared with the public at https://aliasgharheidari.com/SMA.html .

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.