Opposition-based multi-objective whale optimization algorithm with global grid ranking

Multi-objective optimization problems (MOP) are frequently encountered in practice. In some cases, different computationally expensive analyses may be independently used for computing different objectives of the MOP. Additionally, the analyses may be executed to obtain estimates with different fidelity, typically higher fidelity requiring a longer run-time. For instance, in automotive design, the aerodynamic drag is computed using computational fluid dynamic (CFD) analysis and its crashworthiness/strength is assessed using finite element analysis (FEA). Both the objectives can be independently computed and the underlying fidelity of each analysis can also be controlled using different mesh sizes/thresholds on the residual errors. While there exist a number of generic MOP benchmark problems in the literature, there is scarce work on constructing MOPs with multi-fidelity (MF) analyses to support the development of multi-fidelity, multi-objective optimization algorithms. The existing MF benchmarks are limited to unconstrained, single-objective optimization problems only. Towards addressing this gap, in this paper, we introduce a test suite for multi-objective, multi-fidelity optimization (MOMF). The problems are derived by combining existing unconstrained, multi-objective design optimization problems with resolution/stochastic/instability errors that are common manifestations of MF simulations. The method allows for the construction of any number of low-fidelity functions with desired level of correlations for a given high-fidelity objective function. We hope that the test suite would motivate novel algorithmic developments to support optimization involving computationally expensive and independently evaluable objectives.

During recent decades, evolutionary algorithms have been widely studied in optimization problems. The multi-objective whale optimization algorithm based on multi-leader guiding is proposed in this paper, which attempts to offer a proper framework to apply whale optimization algorithm and other swarm intelligence algorithms to solving multi-objective optimization problems. The proposed algorithm adopts several improvements to enhance optimization performance. First, search agents are classified into leadership set and ordinary set by grid mechanism, and multiple leadership solutions guide the population to search the sparse spaces to achieve more homogeneous exploration in per iteration. Second, the differential evolution and whale optimization algorithm are employed to generate the offspring for the leadership and ordinary solutions, respectively. In addition, a novel opposition-based learning strategy is developed to improve the distribution of the initial population. The performance of the proposed algorithm is verified in contrast to 10 classic or state-of-the-arts algorithms on 20 bi-objective and tri-objective unconstrained problems, and experimental results demonstrate the competitive advantages in optimization quality and convergence speed. Moreover, it is tested on load distribution of hot rolling, and the result proves its good performance in real-world applications. Thus, all of the aforementioned experiments have indicated that the proposed algorithm is comparatively effective and efficient.

Battle Royale Optimizer (BRO) is a recently proposed optimization algorithm that has added a new category named game-based optimization algorithms to the existing categorization of optimization algorithms. Both continuous and binary versions of this algorithm have already been proposed. Generally, optimization problems can be divided into single-objective and multi-objective problems. Although BRO has successfully solved single-objective optimization problems, no multi-objective version has been proposed for it yet. This gap motivated us to design and implement the multi-objective version of BRO (MOBRO). Although there are some multi-objective optimization algorithms in the literature, according to the no-free-lunch theorem, no optimization algorithm can efficiently solve all optimization problems. We applied the proposed algorithm to four benchmark datasets: CEC 2009, CEC 2018, ZDT, and DTLZ. We measured the performance of MOBRO based on three aspects: convergence, spread, and distribution, using three performance criteria: inverted generational distance, maximum spread, and spacing. We also compared its obtained results with those of three state-of-the-art optimization algorithms: the multi-objective Gray Wolf optimization algorithm (MOGWO), the multi-objective particle swarm optimization algorithm (MOPSO), the multi-objective artificial vulture's optimization algorithm (MOAVAO), the optimization algorithm for multi-objective problems (MAOA), and the multi-objective non-dominated sorting genetic algorithm III (NSGA-III). The obtained results approve that MOBRO outperforms the existing optimization algorithms in most of the benchmark suites and operates competitively with them in the others.

This paper deals with the multi-objective optimization of tire reinforcement structures such as the tread belt and the carcass path. The multi-objective functions are defined in terms of the discrete-type design variables and approximated by artificial neutral network, and the sensitivity analyses of these functions are replaced with the iterative genetic evolution. The multi-objective optimization algorithm introduced in this paper is not only highly CPU-time-efficient but it can also be applicable to other multi-objective optimization problems in which the objective function, the design variables and the constraints are not continuous but discrete. Through the illustrative numerical experiments, the fiber-reinforced tire belt structure is optimally tailored. The proposed multi-objective optimization algorithm is not limited to the tire reinforcement structure, but it can be applicable to the generalized multi-objective structural optimization problems in various engineering applications.

In order to solve the problem of the multi-objective spectrum allocation on the joint optimization of maximal network utility and fairness of users in cognitive radio network, based on quantum bee colony theory and membrane computing, a novel multi-objective discrete combinatorial optimization algorithm, named membrane-inspired quantum bee optimization, is proposed. The global optimal solution of single objective can be searched in the elementary membranes, and Pareto front solutions which take account of network utility and fairness, can be obtained from skin membrane with the proposed method. The multi-objective optimization algorithm, which can solve both single objective and multi-objective optimization problems at the same time, is designed by the communication rules between membranes, the cooperative evolution of foraging behavior based on quantum state, and non-dominated sorting. Compared with classical color-sensitive graph coloring algorithm, genetic algorithm, quantum genetic algorithm, and particle swarm optimization under different objective functions, the proposed spectrum allocation method can search the global optimal solution of single objective as shown by the simulation results, and it is superior to classical spectrum allocation algorithms and existing intelligence spectrum allocation methods. The optimal Pareto front solutions of multi-objective spectrum allocation are also obtained.

In this paper, we propose a Multi-objective Five-element Cycle Optimization algorithm based on Multi-strategy fusion (MOFECO-MS) to address the Bi-objective Traveling Thief Problem (BITTP), an extension of the Traveling Thief Problem that incorporates two conflicting objectives. The novelty of our approach lies in a unique individual selection strategy coupled with an innovative element update mechanism rooted in the Five-element Cycle Model. To balance global exploration and local exploitation, the algorithm categorizes the population into distinct groups and applies crossover operations both within and between these groups, while also employing a mutation operator for local searches on the best individuals. This coordinated approach optimizes parameter settings and enhances the search capabilities of the algorithm. Extensive experiments were conducted on nine BITTP instances, comparing MOFECO-MS against eight state-of-the-art multi-objective optimization algorithms. The results show that MOFECO-MS excels in both Hypervolume (HV) and Spread (SP) indicators, while also maintaining a high level of Pure Diversity (PD). Overall, MOFECO-MS outperformed the other algorithms in most instances, demonstrating its superiority and robustness in solving complex multi-objective optimization problems.

Various real-world problems are essentially multiobjective optimization problems (MOPs), which involve several conflicting objectives. We propose a Quantum-inspired multiobjective Salp Swarm Algorithm based on the Decomposition technique to locate the multiple Pareto-optimal solutions (POS). The main objective while designing the algorithms for the multiobjective optimization problems is to attain a good convergence and uniform dissemination of the solutions, which remains a significant challenge for the algorithms. The proposed Decomposition-based Quantum-inspired Salp Swarm Algorithm for Multiobjective Optimization (DMQSSA) extends the primary form of SSA by using the quantum-inspired framework and a basic decomposition strategy to improve the balance between exploration and exploitation for MOPs. The Delta potential-well model (DPWM) from quantum mechanics is known for enhancing the convergence and diversity in the population, and the decomposition strategy is proved to be effective to generate evenly distributed solutions set on the Pareto front for simultaneous optimization of the subproblems. In this paper, the existing DPWM model is analysed and redesigned for MOPs with a modification in the contraction equation, and decomposition strategy is used along with an intelligent selection technique to ensure non-dominated solutions. The proposed hybrid approach is evaluated and compared with other techniques on a set of well-known benchmark problems. The results show that DMQSSA can handle the multiobjective optimization problems to find better and well-distributed Pareto optimal set. Also, success of the proposed algorithm is further illustrated on a real-world application.

Whale Optimization Algorithm (WOA) proposed by Seyedali Mirjalili and Andrew Lewis in 2016 is popular and powerful metaheuristic algorithm to search the global solution of optimization problems. WOA is nature-inspired, metaheuristic (randomization and deterministic) algorithm, which has been widely used to solve various single objective, multi objective and multidimensional optimization problems. WOA and its variant have been introduced in engineering applications, bioinformatics, multi-level image segmentation, clustering applications, design of low pass filter, Email classification, Diabetes classification, heterogeneous networks, machine learning etc. WOA is gradient free, easy to represent, capable to explore, exploit the search space and able to avoid local optima. This paper presents overview of WOA, its variants and applications. The performance of WOA is enhanced by introducing hybridization of other methods with WOA such as WOA-PSO, WOA-Levy, WOA-BAT, WOA-ANN, WOA-SVM etc. Objective of metaheuristic algorithm is tofind best position or leader position X* which is near to optimal solution for target prey over successive iteration. Objective function could be based on minimization or maximization approach.

A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems

In this paper, the problems of fuel cost and emission reduction based on multi-objective optimization are studied and solved. Various multi-objective optimization algorithms, such as the multi-objective ant lion optimization (MOALO), the multi-objective multiverse optimization (MOMVO), the multi-objective particle swarm optimization (MOPSO), the multi-objective thermal exchange optimization (MOTEO), and the multi-objective grasshopper optimization algorithm (MOGOA), are used to reduce the cost and emissions of generation fuel. With equality and inequality restrictions, the suggested work is carried out in an IEEE 30 bus system. To determine the lowest system-wide minimization of generating cost and emission, the results of several optimization strategies are compared. In terms of lowering fuel costs and emissions, the MOGOA performs better than any other multi-objective algorithms.

Multi-objective optimal control of bioconversion process considering system sensitivity and control variation

Real-world optimization problems in engineering, logistics, and resource allocation are often constrained and multi-modal, posing a challenge for traditional optimization algorithms. Metaheuristic algorithms inspired by natural and artificial phenomena have shown promise, but many fail to balance exploration and exploitation effectively, especially under stringent constraints. Existing algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE) face issues in convergence speed and constraint handling, particularly in high-dimensional spaces or when constraints are dynamic or complex. We propose an Adaptive Pattern-Driven Optimization (APDO) algorithm, a novel tailor-inspired metaheuristic that mimics the adaptive decision-making process of a tailor designing garments. APDO integrates three primary operators—Pattern Selection, Fabric Adjustment, and Stitch Reinforcement—to handle constraints adaptively. The algorithm combines pattern memory (historical bests), probabilistic pattern mutation, and a constraint-domination principle to ensure feasibility and diversity. The core idea is to iteratively “cut and stitch” solutions to adapt the search process, enabling dynamic constraint satisfaction and global optimization. We benchmarked APDO against five popular methods (GA, PSO, DE, Firefly Algorithm, and Whale Optimization Algorithm) on a suite of 10 real-world constrained problems, including mechanical component design and energy scheduling tasks. APDO outperformed all baselines in terms of convergence speed, constraint satisfaction rate, and solution quality. In particular, APDO achieved an average feasibility rate of 97.6% and an improvement of 4.2–11.8% in best fitness across problems.

Distributed energy resources (DERs) can improve the performance of radial distribution systems. The nonlinear power flow constraints, multi-objective trade-offs, and network reconfiguration scenarios for DER placement and sizing call for the formulation of optimization problems. Most of the times optimization algorithms suffer from premature convergence and poor exploration-exploitation balance. These problems exhibit an inherent internal structural symmetry. In order to overcome the above problem, this study uses the Multi-Objective Archimedes Optimization Algorithm (MAOA) to optimally allocate DERs in the Radial Distribution Networks (RDNs), moreover the performance of the proposed MAOA is compared with the other well established algorithms including Particel Swarm Optimization (PSO), Whale Optimization Algorithm (WOA), Shuffled Frog Leaping Algorithm (SFLA), Atom Search Optimization (ASO), and Butterfly Optimization Algorithm (BOA) on the IEEE-33 RDN. The comparison is made for the four cases (S1: DER Only), (S2—Network Reconfiguration Only), (S3—DER Followed by Reconfiguration), and (S4—Reconfiguration Followed by DER) considering factors like voltage profile, network reconfiguration, active and reactive power loss reduction, carbon emission DER utilization and Cost reduction. The MAOA is observed to provide better results among all the other benchmark algorithms. In S3, the active power loss is reduced by 68.41%, whereas the reactive power loss is reduced by 57.44% and the MAOA algorithm improves the voltage by 3.98%. The minimum voltage of the network is also improved by 6.28%. The algorithm improves convergence with a percentage of 18.50% enhancing the system’s operational symmetry and stability, while satisfying all constraints. At Bus 3 and Bus 6 of IEEE-33 bus radial distribution network (Baran–Wu test system), DG capacity is allocated to be 3.8 MW and 2.1 MW, respectively.

In the context of Internet of Things (IoT), optimizing quality of service (QoS) parameters is a critical challenge due to its heterogeneous and resource-constrained nature. This paper proposes a novel quantum-inspired multi-objective optimization algorithm for IoT service management. Traditional multi-objective optimization algorithms often face limitations such as slow convergence and susceptibility to local optima, reducing their effectiveness in complex IoT environments. To address these issues, we introduce a quantum-inspired hybrid algorithm that combines the strengths of Multi-Objective Grey Wolf Optimization Algorithm (MOGWOA) and Multi-Objective Whale Optimization Algorithm (MOWOA), enhanced with quantum principles. This novel integration overcomes the limitations of traditional algorithms by improving convergence speed and avoiding local optima. The hybrid algorithm enhances QoS in IoT applications by achieving superior optimization in terms of energy efficiency, latency reduction, convergence, and coverage cost. The incorporation of quantum-inspired mechanisms, such as quantum position and behavior, strengthens the exploration and exploitation capabilities of the algorithm, enabling faster and more accurate optimization. Extensive simulations and testing demonstrate the proposed method’s superior performance compared to existing algorithms, validating its effectiveness in addressing key IoT challenges.

Although various optimization methods for solving single-objective problems have been developed in the last few decades, these methods have lost their eligibility due to the fact that today’s engineering problems are toward multiple objective optimization problems, in real applications. For single-objective optimization problems, for example, in case of a minimization problem, this value is the decision vector giving the smallest objective that can be achieved within the specified constraints. Hence the minimum decision vector within all possible (feasible) solution vectors is the so-called optimal solution and/or optimal design. However, in multi-objective optimization problems, since a different objective value is generated against each decision vector, the superiority of the solutions over each other is determined by considering the trade-off among the objective values. Therefore, the solution of multi-objective optimization problems, unlike single-objective problems, is a set of vectors rather than a single decision vector. In multi-objective optimization problems, especially if there are intricate objectives, the computational cost of the problem increases. In other words, while synchronously trying to maximize one of the objectives and to minimize another one makes it difficult to find the global optimum design. One of the important techniques used in multi-objective optimization problems is Pareto optimality which enables to select the global optimum solution taking into account the trade-off among all objectives. In this context, using of derivative-based methods has decreased, but the use of metaheuristic methods has increased due to the rapid availability of global optimum solution. This is because the improvements in the field of optimization are progressing in proportion to technology and varying according to the needs. In this chapter, one of the recent metaheuristic optimization methods based on swarm intelligence that is so-called a Pareto-based bat algorithm inspired by the behavior of determining the direction and distance of an object using the echo of the sound called the echolocation of bats is used in order to obtain optimum solutions for multi-objective engineering design problems. In this regard, a four-bar planar truss, a real-sized welded steel beam as well as a multi-layer radar absorber are selected as multi-objective engineering design optimization problems. In case the obtained results (optimal designs) are examined, the potency and the reliability of the proposed multi-objective Pareto-based bat algorithm are demonstrated.