Multi-objective Engineering Design Problems Research Articles

Multi-Objective Search Group Algorithm for engineering design problems

This study proposes a new multi-objective version of the Search Group Algorithm (SGA) called the Multi-Objective Search Group Algorithm (MOSGA). The MOSGA is the combination of the conventional SGA integrated with an elitist non-dominated sorting technique, enabling it to define Pareto optimal solutions via mutation, offspring generation, and selection. The Pareto archive with a selection mechanism is used to preserve and enhance the convergence and diversity of solutions. The MOSGA is validated on twenty-five prominent case studies, including nineteen unconstrained multi-objective benchmark problems, six constrained multi-objective benchmark problems, and five multi-objective engineering design problems to validate its capability and effectiveness. The statistical results are compared to the outcomes of other well-regarded algorithms using the same performance metrics. The comparative results show that MOGSA is robust and superior in handling a wide variety of multi-objective problems.

MOMRFO: Multi-objective Manta ray foraging optimizer for handling engineering design problems

Despite its recent appearance, manta ray foraging optimizer (MRFO) has shown a good ability to deal with single-objective real-world problems, which makes its application in solving problems with multiple objectives an interesting direction. Accordingly, the current paper investigates the MRFO optimizer to develop a new algorithm for handling multi-objective engineering design problems. To achieve this goal, the elitist concept is adopted to save the set of Pareto solutions through the integration of an external archive into the standard MRFO. This archive is considered also as a repository from which a search agent is chosen based on its density degree to control the convergence and diversity of manta rays population. Our algorithm’s efficiency is first validated via extensive experiments on ten test functions, and the results were very satisfactory in terms of convergence and diversity, in almost all cases. Then, it is applied to four multi-objective engineering problems, and it showed a good promise in solving real-world problems with multiple objectives.

MOMPA: Multi-objective marine predator algorithm

In this paper, a multi-objective version of the recently proposed marine predator algorithm (MPA) is presented, which is called the multi-objective marine predator algorithm (MOMPA). In this algorithm, an external archive component is introduced to store the non dominated Pareto optimal solutions found so far. Based on the elite selection method, a top predator selection mechanism is proposed, which selects the effective solutions from the archive as the top predators to simulate the predator’s foraging behavior. The CEC2019 multi-modal multi-objective benchmark functions are utilized to evaluate the performance of the proposed algorithm and compared with nine state-of-the-art multi-objective meta-heuristics algorithms. In addition, seven multi-objective engineering design problems (car side impact problem, gear train design problem, welded beam design problem, disk brake design problem, two bar truss design problem, spring design problem and cantilever beam design problem) are used to further verify the effectiveness of the proposed algorithm. The results demonstrate that the proposed MOMPA algorithm not only provides very competitive results but also outperforms other algorithms.

A symbiotic organisms search algorithm-based design optimization of constrained multi-objective engineering design problems

PurposeIn line with computational technological advances, obtaining optimal solutions for engineering problems has become attractive research topics in various disciplines and real engineering systems having multiple objectives. Therefore, it is aimed to ensure that the multiple objectives are simultaneously optimized by considering them among the trade-offs. Furthermore, the practical means of solving those problems are principally concentrated on handling various complicated constraints. The purpose of this paper is to suggest an algorithm based on symbiotic organisms search (SOS), which mimics the symbiotic reciprocal influence scheme adopted by organisms to live on and breed within the ecosystem, for constrained multi-objective engineering design problems.Design/methodology/approachThough the general performance of SOS algorithm was previously well demonstrated for ordinary single objective optimization problems, its efficacy on multi-objective real engineering problems will be decisive about the performance. The SOS algorithm is, hence, implemented to obtain the optimal solutions of challengingly constrained multi-objective engineering design problems using the Pareto optimality concept.FindingsFour well-known mixed constrained multi-objective engineering design problems and a real-world complex constrained multilayer dielectric filter design problem are tackled to demonstrate the precision and stability of the multi-objective SOS (MOSOS) algorithm. Also, the comparison of the obtained results with some other well-known metaheuristics illustrates the validity and robustness of the proposed algorithm.Originality/valueThe algorithmic performance of the MOSOS on the challengingly constrained multi-objective multidisciplinary engineering design problems with constraint-handling approach is successfully demonstrated with respect to the obtained outperforming final optimal designs.

A guided population archive whale optimization algorithm for solving multiobjective optimization problems

This paper proposes a new multiobjective algorithm by extending the recently Whale Optimization Algorithm (WOA) to solve multiobjective optimization problems. Our algorithm which we shall call Guided Population Archive Whale Optimization Algorithm (GPAWOA) is based on Pareto dominance and uses an external archive to store the non-dominated solutions found during the optimization process. The leaders are selected from the archive to guide the population towards promising regions of the search space, also, the mechanism of crowding distance is incorporated into the standard WOA to maintain the diversity. Our proposed algorithm is evaluated on twelve benchmark functions and is applied to four multi-objective engineering design problems: 4-bar truss design, gear train problem, disk brake design and welded beam design and compared against three well-known algorithms: Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D), Multi-Objective Grey Wolf Optimizer (MOGWO), and Multi-Objective Particle Swarm Optimization (MOPSO). The experimental results indicate that the proposed GPAWOA is highly competitive and outperforms the selected state-of-the-art multiobjective optimization algorithms, being able to provide an excellent approximation of Pareto front in terms of convergence and diversity.

Discrete Sine-Cosine Algorithm (DSCA) with Local Search for Solving Traveling Salesman Problem

One of the new population-based optimization algorithms, named sine-cosine algorithm (SCA), is introduced to solve continuous optimization problems. SCA utilizes the sine and cosine functions to recast a set of potential solutions to balance between exploration and exploitation in the search space. Many researchers have developed and introduced a modified version of SCA to solve engineering problems, multi-objective version of SCA to solve multi-objective engineering design problems, and a binary version of SCA to deal with datasets. Our goal from this work to propose discrete SCA (DSCA) to solve the traveling salesman problem (TSP). The TSP is one of the typical NP-hard problems. DSCA works on the basic concepts of exploration and exploitation. To balance the exploration and exploitation in DSCA, it uses two different mathematical expressions to update the solutions in each generation. DSCA is combined with 2-opt local search method to improve exploitation. To enhance the exploration heuristic crossover, it is united with the proposed DSCA. A benchmarks problem selected from TSPLIB is used to test the algorithm, and the results show that the DSCA algorithm proposed in this article is comparable with the other state-of-the-art algorithms over a wide range of TSP.

An efficient evolutionary algorithm for engineering design problems

This study introduces a multi-objective version of the recently proposed colonial competitive algorithm (CCA) called multi-objective colonial competitive algorithm. In contrast to original CCA, which used the combination of the objective functions to solve multi-objective problems, the proposed algorithm incorporates the Pareto concept to store simultaneously optimal solutions of multiple conflicting functions. Another novelty of this paper is the integration of the variable neighborhood search as an assimilation strategy, in order to improve the performance of the obtained solutions. To prove the effectiveness of the proposed algorithm, a set of standard test functions with high dimensions and some multi-objective engineering design problems are investigated. The results obtained amply demonstrate that the proposed approach is efficient and is able to yield a wide spread of solutions with good convergence to true Pareto fronts, compared with other proposed methods in the literature.

A novel multi-objective optimization algorithm based on artificial algae for multi-objective engineering design problems

There are many diverse fields and applications such as data mining, engineering, operations research, economics, and science can be formulated as multi-objective optimization problems. In this pape...

A novel multi-criteria self-organising migrating algorithm for engineering problems

Solving engineering design and resources optimisation via multi-objective evolutionary algorithms has attracted much attention in the last few years. In this study, an improved Self-Organising Migrating Algorithm (MOSOMA) is developed and investigated to solve multi-objective engineering design problems. The proposed MOSOMA algorithm uses a migration approach for the search of optima. In order to obtain a uniform distribution of Pareto optimal solutions, the crowding distance method is introduced. Pareto dominance is incorporated into the algorithm in order to allow this heuristic to handle problems with several objective functions. The performance of the MOSOMA algorithm is assessed by applying it to a set of multi-objective standard test functions and constrained engineering design problems. The results show that the proposed approach is competitive and effective compared to other algorithms contemplated in this work and it can also find the result with greater precision.

∊-constraint heat transfer search (∊-HTS) algorithm for solving multi-objective engineering design problems

Abstract In this paper, an effective ∊-constraint heat transfer search (∊-HTS) algorithm for the multi-objective engineering design problems is presented. This algorithm is developed to solve multi-objective optimization problems by evaluating a set of single objective sub-problems. The effectiveness of the proposed algorithm is checked by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as discrete, convex, and non-convex. This algorithm is also tested for several distinctive multi-objective engineering design problems, such as four bar truss problem, gear train problem, multi-plate disc brake design, speed reducer problem, welded beam design, and spring design problem. Moreover, the numerical experimentation shows that the proposed algorithm generates the solution to represent true Pareto front. Highlights A novel multi-objective optimization (MOO) algorithm is proposed. Proposed algorithm is presented to obtain the Pareto-optimal solutions. The multi-objective optimization algorithm compared with other work in the literature. Test performance of proposed algorithm on MOO benchmark/design engineering problems.

Multi-objective sine-cosine algorithm (MO-SCA) for multi-objective engineering design problems

This paper proposes a novel and an effective multi-objective optimization algorithm named multi-objective sine-cosine algorithm (MO-SCA) which is based on the search technique of sine-cosine algorithm (SCA). MO-SCA employs the elitist non-dominated sorting and crowding distance approach for obtaining different non-domination levels and to preserve the diversity among the optimal set of solutions, respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems that have various characteristics of Pareto front such as convex, non-convex and discrete. This proposed algorithm is also checked for the multi-objective engineering design problems with distinctive features. Furthermore, we show the proposed algorithm effectively generates the Pareto front and is easy to implement and algorithmically simple.

Non-dominated sorting moth flame optimization (NS-MFO) for multi-objective problems

This paper proposes an effective non-dominated moth-flame optimization algorithm (NS-MFO) method for solving multi-objective problems. Most of the multi-objective optimization algorithms use different search techniques inspired by different optimization techniques such as genetic algorithms, differential evolutions, particle swarm optimization, cuckoo search etc., but search techniques of recently developed metaheuristics have hardly been investigated. Non-dominated moth-flame optimization algorithm (NS-MFO) is based on the search technique of moth-flame optimization algorithm (MFO) algorithm and utilizes the elitist non-dominated sorting and crowding distance approach for obtaining different non domination levels and to preserve the diversity among the optimal set of solutions respectively. The effectiveness of the method is measured by implementing it on multi-objective benchmark problems and multi-objective engineering design problems with distinctive features. It is shown in this paper that this method effectively generates the Pareto front and also, this method is easy to implement and algorithmically simple.

Artificial Immune System Based Local Search for Solving Multi-Objective Design Problems

In this paper, an artificial intelligent approach based on the clonal selection principle of Artificial Immune System (AIS) and local search (LS) is propose to solve Multiobjective engineering design problems. This paper presents an optimal design of a linear synchronous motor (LSM) considering two objective functions namely, maximum force and minimum saturation and then design of air-cored solenoid with maximum inductance and minimum volume as the objective functions. The proposed approach uses Local search, dominance principle and feasibility to identify solutions that deserve to be cloned.

Multi-objective ant lion optimizer: a multi-objective optimization algorithm for solving engineering problems

This paper proposes a multi-objective version of the recently proposed Ant Lion Optimizer (ALO) called Multi-Objective Ant Lion Optimizer (MOALO). A repository is first employed to store non-dominated Pareto optimal solutions obtained so far. Solutions are then chosen from this repository using a roulette wheel mechanism based on the coverage of solutions as antlions to guide ants towards promising regions of multi-objective search spaces. To prove the effectiveness of the algorithm proposed, a set of standard unconstrained and constrained test functions is employed. Also, the algorithm is applied to a variety of multi-objective engineering design problems: cantilever beam design, brushless dc wheel motor design, disk brake design, 4-bar truss design, safety isolating transformer design, speed reduced design, and welded beam deign. The results are verified by comparing MOALO against NSGA-II and MOPSO. The results of the proposed algorithm on the test functions show that this algorithm benefits from high convergence and coverage. The results of the algorithm on the engineering design problems demonstrate its applicability is solving challenging real-world problems as well.

Optimal Golomb Ruler Sequences Generation for Optical WDM Systems: A Novel Parallel Hybrid Multi-objective Bat Algorithm

In real-life, multi-objective engineering design problems are very tough and time consuming optimization problems due to their high degree of nonlinearities, complexities and inhomogeneity. Nature-inspired based multi-objective optimization algorithms are now becoming popular for solving multi-objective engineering design problems. This paper proposes original multi-objective Bat algorithm (MOBA) and its extended form, namely, novel parallel hybrid multi-objective Bat algorithm (PHMOBA) to generate shortest length Golomb ruler called optimal Golomb ruler (OGR) sequences at a reasonable computation time. The OGRs found their application in optical wavelength division multiplexing (WDM) systems as channel-allocation algorithm to reduce the four-wave mixing (FWM) crosstalk. The performances of both the proposed algorithms to generate OGRs as optical WDM channel-allocation is compared with other existing classical computing and nature-inspired algorithms, including extended quadratic congruence (EQC), search algorithm (SA), genetic algorithms (GAs), biogeography based optimization (BBO) and big bang-big crunch (BB-BC) optimization algorithms. Simulations conclude that the proposed parallel hybrid multi-objective Bat algorithm works efficiently as compared to original multi-objective Bat algorithm and other existing algorithms to generate OGRs for optical WDM systems. The algorithm PHMOBA to generate OGRs, has higher convergence and success rate than original MOBA. The efficiency improvement of proposed PHMOBA to generate OGRs up to 20-marks, in terms of ruler length and total optical channel bandwidth (TBW) is 100 %, whereas for original MOBA is 85 %. Finally the implications for further research are also discussed.

An improved imperialist competitive algorithm for multi-objective optimization

This article proposes an improved imperialistic competitive algorithm to solve multi-objective optimization problems. The proposed multi-objective imperialistic competitive algorithm (MOICA) uses the elitist strategy, based on the mutation and crossover as in genetic algorithms, and the Pareto concept to store simultaneously optimal solutions of multiple conflicting functions. Three performance metrics are used to evaluate the performance of the new algorithm: convergence to the true Pareto-optimal set, solution diversity and robustness, characterized by the variance over 10 runs. To validate the efficiency of the proposed algorithm, several multi-objective standard test functions with true solutions are used. The obtained results show that the MOICA outperforms most of the methods available in the literature. The proposed algorithm can also handle multi-objective engineering design problems with high dimensions.

Self-adaptive differential evolution algorithm with α-constrained-domination principle for constrained multi-objective optimization

Real-world problems are inherently constrained optimization problems often with multiple conflicting objectives. To solve such constrained multi-objective problems effectively, in this paper, we put forward a new approach which integrates self-adaptive differential evolution algorithm with α-constrained-domination principle, named SADE-αCD. In SADE-αCD, the trial vector generation strategies and the DE parameters are gradually self-adjusted adaptively based on the knowledge learnt from the previous searches in generating improved solutions. Furthermore, by incorporating domination principle into α-constrained method, α-constrained-domination principle is proposed to handle constraints in multi-objective problems. The advantageous performance of SADE-αCD is validated by comparisons with non-dominated sorting genetic algorithm-II, a representative of state-of-the-art in multi-objective evolutionary algorithms, and constrained multi-objective differential evolution, over fourteen test problems and four well-known constrained multi-objective engineering design problems. The performance indicators show that SADE-αCD is an effective approach to solving constrained multi-objective problems, which is basically enabled by the integration of self-adaptive strategies and α-constrained-domination principle.

A particle swarm optimizer for constrained multi-objective engineering design problems

This article presents a particle swarm optimizer (PSO) capable of handling constrained multi-objective optimization problems. The latter occur frequently in engineering design, especially when cost and performance are simultaneously optimized. The proposed algorithm combines the swarm intelligence fundamentals with elements from bio-inspired algorithms. A distinctive feature of the algorithm is the utilization of an arithmetic recombination operator, which allows interaction between non-dominated particles. Furthermore, there is no utilization of an external archive to store optimal solutions. The PSO algorithm is applied to multi-objective optimization benchmark problems and also to constrained multi-objective engineering design problems. The algorithmic effectiveness is demonstrated through comparisons of the PSO results with those obtained from other evolutionary optimization algorithms. The proposed particle swarm optimizer was able to perform in a very satisfactory manner in problems with multiple constraints and/or high dimensionality. Promising results were also obtained for a multi-objective engineering design problem with mixed variables.

Multiobjective extremal optimization with applications to engineering design

In this paper, we extend a novel unconstrained multiobjective optimization algorithm, so-called multiobjective extremal optimization (MOEO), to solve the constrained multiobjective optimization problems (MOPs). The proposed approach is validated by three constrained benchmark problems and successfully applied to handling three multiobjective engineering design problems reported in literature. Simulation results indicate that the proposed approach is highly competitive with three state-of-the-art multiobjective evolutionary algorithms, i.e., NSGA-II, SPEA2 and PAES. Thus MOEO can be considered a good alternative to solve constrained multiobjective optimization problems.