An Improved Artificial Rabbits Optimization Algorithm with Chaotic Local Search and Opposition-Based Learning for Engineering Problems and Its Applications in Breast Cancer Problem

Artificial rabbits optimization(ARO)is a recently proposed biology-based optimization algorithm inspired by the detour foraging and random hiding behavior of rabbits in nature.However,for solving optimization problems,the ARO algorithm shows slow convergence speed and can fall into local minima.To overcome these drawbacks,this paper proposes chaotic opposition-based learning ARO(COARO),an improved version of the ARO algorithm that incorporates opposition-based learning(OBL)and chaotic local search(CLS)techniques.By adding OBL to ARO,the convergence speed of the algorithm increases and it explores the search space better.Chaotic maps in CLS provide rapid convergence by scanning the search space efficiently,since their ergodicity and non-repetitive properties.The proposed COARO algorithm has been tested using thirty-three distinct benchmark functions.The outcomes have been compared with the most recent optimization algorithms.Additionally,the COARO algorithm’s problem-solving capabilities have been evaluated using six different engineering design problems and compared with various other algorithms.This study also introduces a binary variant of the continuous COARO algorithm,named BCOARO.The performance of BCOARO was evaluated on the breast cancer dataset.The effectiveness of BCOARO has been compared with different feature selection algorithms.The proposed BCOARO outperforms alternative algorithms,according to the findings obtained for real applications in terms of accuracy performance,and fitness value.Extensive experiments show that the COARO and BCOARO algorithms achieve promising results compared to other metaheuristic algorithms.

A Comparative Study of Metaheuristic Optimization Algorithms for Solving Real-World Engineering Design Problems

Real-world engineering design problems with complex objective functions under some constraints are relatively difficult problems to solve.Such design problems are widely experienced in many engineering fields,such as industry,automotive,construction,machinery,and interdisciplinary research.However,there are established optimization techniques that have shown effectiveness in addressing these types of issues.This research paper gives a comparative study of the implementation of seventeen new metaheuristic methods in order to optimize twelve distinct engineering design issues.The algorithms used in the study are listed as:transient search optimization(TSO),equilibrium optimizer(EO),grey wolf optimizer(GWO),moth-flame optimization(MFO),whale optimization algorithm(WOA),slimemould algorithm(SMA),harris hawks optimization(HHO),chimp optimization algorithm(COA),coot optimization algorithm(COOT),multi-verse optimization(MVO),arithmetic optimization algorithm(AOA),aquila optimizer(AO),sine cosine algorithm(SCA),smell agent optimization(SAO),and seagull optimization algorithm(SOA),pelican optimization algorithm(POA),and coati optimization algorithm(CA).As far as we know,there is no comparative analysis of recent and popular methods against the concrete conditions of real-world engineering problems.Hence,a remarkable research guideline is presented in the study for researchersworking in the fields of engineering and artificial intelligence,especiallywhen applying the optimization methods that have emerged recently.Future research can rely on this work for a literature search on comparisons of metaheuristic optimization methods in real-world problems under similar conditions.

Dimension-down iterative algorithm for the mixed transportation network design problem

An optimal dimension-down iterative algorithm （DDIA） is proposed for solving a mixed （continuous/ discrete） transportation network design problem （MNDP）, which is generally expressed as a mathematical programming with equilibrium constraints （MPEC）. The upper level of the MNDP aims to optimize the network performance via both the expansion of existing links and the addition of new candidate links, whereas the lower level is a traditional Wardrop user equilibrium （UE） model. The idea of the proposed DDIA is to reduce the dimensions of the problem. A group of variables （discrete/continuous） are fixed to altemately optimize another group of variables （continuous/discrete）. Some continuous network design problems （CNDPs） and discrete network design problems （DNDPs） are solved repeatedly until the optimal solution is obtained. A numerical example is given to demonstrate the efficiency of the proposed algorithm.

Hybridizing artificial bee colony with biogeography-based optimization for constrained mechanical design problems

A novel hybrid algorithm named ABC-BBO, which integrates artificial bee colony(ABC) algorithm with biogeography-based optimization(BBO) algorithm, is proposed to solve constrained mechanical design problems. ABC-BBO combined the exploration of ABC algorithm with the exploitation of BBO algorithm effectively, and hence it can generate the promising candidate individuals. The proposed hybrid algorithm speeds up the convergence and improves the algorithm's performance. Several benchmark test functions and mechanical design problems are applied to verifying the effects of these improvements and it is demonstrated that the performance of this proposed ABC-BBO is superior to or at least highly competitive with other population-based optimization approaches.

Designing Physics Problems with Mathematica

We envision utilizing the versatility of a Computer Algebra System, specifically Mathematica to explore designing physics problems. As a focused project, we consider for instance a thermo-mechanical-physics problem showing its development from the ground up. Following the objectives of this investigation first by applying the fundamentals of physics principles we solve the problem symbolically. Applying the solution we investigate the sensitivities of the quantities of interest for various scenarios generating feasible numeric parameters. Although a physics problem is investigated, the proposed methodology may as well be applied to other scientific fields. The codes needed for this particular project are included enabling the interested reader to duplicate the results, extend and modify them as needed to explore various extended scenarios.

A Water Line Network Failure Application of Network Design Problems

This study investigated a water supply recovery problem involving municipal water service piping. The problem consisted in recovering full service after network failure, in order to rapidly satisfy all urgent citywide demands. The optimal recovery solution was achieved through the application of so-called network design problems （NDPs）, which are a form of combinatorial optimization problem. However, a conventional NDP is not suitable for addressing urgent situations because （1） it does not utilize the non-failure arcs in the network, and （2） it is solely concerned with stable costs such as flow costs. Therefore, to adapt the technique to such urgent situations, the conventional NDP is here modified to deal with the specified water supply problem. In addition, a numerical illustration using the Sendai water network is presented.

A Multi-strategy Improved Snake Optimizer Assisted with Population Crowding Analysis for Engineering Design Problems

Snake Optimizer(SO)is a novel Meta-heuristic Algorithm(MA)inspired by the mating behaviour of snakes,which has achieved success in global numerical optimization problems and practical engineering applications.However,it also has certain drawbacks for the exploration stage and the egg hatch process,resulting in slow convergence speed and inferior solution quality.To address the above issues,a novel multi-strategy improved SO(MISO)with the assistance of population crowding analysis is proposed in this article.In the algorithm,a novel multi-strategy operator is designed for the exploration stage,which not only focuses on using the information of better performing individuals to improve the quality of solution,but also focuses on maintaining population diversity.To boost the efficiency of the egg hatch process,the multi-strategy egg hatch process is proposed to regenerate individuals according to the results of the population crowding analysis.In addition,a local search method is employed to further enhance the convergence speed and the local search capability.MISO is first compared with three sets of algorithms in the CEC2020 benchmark functions,including SO with its two recently discussed variants,ten advanced MAs,and six powerful CEC competition algorithms.The performance of MISO is then verified on five practical engineering design problems.The experimental results show that MISO provides a promising performance for the above optimization cases in terms of convergence speed and solution quality.

Improved Dwarf Mongoose Optimization for Constrained Engineering Design Problems

This paper proposes a modified version of the Dwarf Mongoose Optimization Algorithm (IDMO) for constrained engineering design problems. This optimization technique modifies the base algorithm (DMO) in three simple but effective ways. First, the alpha selection in IDMO differs from the DMO, where evaluating the probability value of each fitness is just a computational overhead and contributes nothing to the quality of the alpha or other group members. The fittest dwarf mongoose is selected as the alpha, and a new operator ω is introduced, which controls the alpha movement, thereby enhancing the exploration ability and exploitability of the IDMO. Second, the scout group movements are modified by randomization to introduce diversity in the search process and explore unvisited areas. Finally, the babysitter's exchange criterium is modified such that once the criterium is met, the babysitters that are exchanged interact with the dwarf mongoose exchanging them to gain information about food sources and sleeping mounds, which could result in better-fitted mongooses instead of initializing them afresh as done in DMO, then the counter is reset to zero. The proposed IDMO was used to solve the classical and CEC 2020 benchmark functions and 12 continuous/discrete engineering optimization problems. The performance of the IDMO, using different performance metrics and statistical analysis, is compared with the DMO and eight other existing algorithms. In most cases, the results show that solutions achieved by the IDMO are better than those obtained by the existing algorithms.

New Classes of Interconnection Topology Structures and Their Properties

In the first part of this- paper, three generalizations of arrangement graph A.,k of [1], namely Bn,k, Cn,k and Dn,k , are introduced. We prove that all the three classes of graphs are vertex symmetric, two of them are edge symmetric. They have great faulty tolerance and high connectivity. We give the diameters of B..k and Cn,k, the Hamiltonian cycle of Cn,k and Hamiltonian path of B.,k. We list several open problems, one of them related to the complexity of sorting algorithm on the arrangement graphs. All these graphs can be thought as generalizations of star graph but are more flexible so that they can be considered as new interconnection network topologies. In the second part of this paper, we provide other four classes of combinatorial graphes, Chn , Cyn, Zhn and Zyn. Many good properties of them, such as high node--connectivity, node symmetry, edge symmetry, diameter, ets., are shown in this paper.

Chaotic Social Group Optimization for Structural Engineering Design Problems

Till now,several novel metaheuristic algorithms are proposed for global search.But only specific algorithms have become popular or attracted researchers,who are efficient in solving global optimization problems as well as real-world application problems.The Social Group Optimization(SGO)algorithm is a new metaheuristic bioinspired algorithm inspired by human social behavior that attracted researchers due to its simplicity and problem-solving capability.In this study,to deal with the problems of low accuracy and local convergence in SGO,the chaos theory is introduced into the evolutionary process of SGO.Since chaotic mapping has certainty,ergodicity,and stochastic property,by replacing the constant value of the self-introspection parameter with chaotic maps,the proposed chaotic social group optimization algorithm increases its convergence rate and resulting precision.The proposal chaotic SGO is validated through 13 benchmark functions and after that 9 structural engineering design problems have been solved.The simulated results have been noticed as competent with that of state-of-art algorithms regarding convergence quality and accuracy,which certifies that improved SGO with chaos is valid and feasible.

Multi-trial Vector-based Whale Optimization Algorithm

The Whale Optimization Algorithm(WOA)is a swarm intelligence metaheuristic inspired by the bubble-net hunting tactic of humpback whales.In spite of its popularity due to simplicity,ease of implementation,and a limited number of parameters,WOA’s search strategy can adversely affect the convergence and equilibrium between exploration and exploitation in complex problems.To address this limitation,we propose a new algorithm called Multi-trial Vector-based Whale Optimization Algorithm(MTV-WOA)that incorporates a Balancing Strategy-based Trial-vector Producer(BS_TVP),a Local Strategy-based Trial-vector Producer(LS_TVP),and a Global Strategy-based Trial-vector Producer(GS_TVP)to address real-world optimization problems of varied degrees of difficulty.MTV-WOA has the potential to enhance exploitation and exploration,reduce the probability of being stranded in local optima,and preserve the equilibrium between exploration and exploitation.For the purpose of evaluating the proposed algorithm's performance,it is compared to eight metaheuristic algorithms utilizing CEC 2018 test functions.Moreover,MTV-WOA is compared with well-stablished,recent,and WOA variant algorithms.The experimental results demonstrate that MTV-WOA surpasses comparative algorithms in terms of the accuracy of the solutions and convergence rate.Additionally,we conducted the Friedman test to assess the gained results statistically and observed that MTV-WOA significantly outperforms comparative algorithms.Finally,we solved five engineering design problems to demonstrate the practicality of MTV-WOA.The results indicate that the proposed MTV-WOA can efficiently address the complexities of engineering challenges and provide superior solutions that are superior to those of other algorithms.

TWO-WAY ROAD NETWORK DESIGN PROBLEM WITH VARIABLE LANES

This paper studies a new form of transportation network design problem. In urban transportation network, unreasonable phenomenon can occur in certain traffic period （e.g. on/off duty period）, which demonstrates that the flows of opposite directions on a two-way road are seriously asymmetric; one traffic link of a two-way road congest heavily but the other is hardly used. In order to reduce transportation congestion and make full use of the existing road resources, we propose a lane reallocating approach in peak period, and establish a discrete hi-level programming model for the decision-making. Then, based on particle swarm optimization （PSO） technique, a heuristic solution algorithm for the hi-level model is designed. Finally, the lane reallocating approach is demonstrated through a simple transportation network.

A surrogate-based optimization algorithm for network design problems

Network design problems （NDPs） have long been regarded as one of the most challenging problems in the field of transportation planning due to the intrinsic non-convexity of their bi-level programming form. Furthermore, a mixture of continuous/discrete decision variables makes the mixed network design problem （MNDP） more complicated and difficult to solve. We adopt a surrogate-based optimization （SBO） framework to solve three featured categories of NDPs （continuous, discrete, and mixed-integer）. We prove that the method is asymptotically completely convergent when solving continuous NDPs, guaranteeing a global optimum with probability one through an indefinitely long run. To demonstrate the practical performance of the proposed framework, numerical examples are provided to compare SBO with some existing solving algorithms and other heuristics in the literature for NDP. The results show that SBO is one of the best algorithms in terms of both accuracy and efficiency, and it is efficient for solving large-scale problems with more than 20 decision variables. The SBO approach presented in this paper is a general algorithm of solving other optimization problems in the transportation field.

Comparative Performance Analysis of Differential Evolution Variants on Engineering Design Problems

Because of their superior problem-solving ability,nature-inspired optimization algorithms are being regularly used in solving complex real-world optimization problems.Engineering academics have recently focused on meta-heuristic algorithms to solve various optimization challenges.Among the state-of-the-art algorithms,Differential Evolution(DE)is one of the most successful algorithms and is frequently used to solve various industrial problems.Over the previous 2 decades,DE has been heavily modified to improve its capabilities.Several DE variations secured positions in IEEE CEC competitions,establishing their efficacy.However,to our knowledge,there has never been a comparison of performance across various CEC-winning DE versions,which could aid in determining which is the most successful.In this study,the performance of DE and its eight other IEEE CEC competition-winning variants are compared.First,the algorithms have evaluated IEEE CEC 2019 and 2020 bound-constrained functions,and the performances have been compared.One unconstrained problem from IEEE CEC 2011 problem suite and five other constrained mechanical engineering design problems,out of which four issues have been taken from IEEE CEC 2020 non-convex constrained optimization suite,have been solved to compare the performances.Statistical analyses like Friedman's test and Wilcoxon's test are executed to verify the algorithm’s ability statistically.Performance analysis exposes that none of the DE variants can solve all the problems efficiently.Performance of SHADE and ELSHADE-SPACMA are considerable among the methods used for comparison to solve such mechanical design problems.

Hybrid Meta-Model Based Design Space Differentiation Method for Expensive Problems

In this work,a hybrid meta-model based design space differentiation（HMDSD）method is proposed for practical problems.In the proposed method,an iteratively reduced promising region is constructed using the expensive points,with two different search strategies respectively applied inside and outside the promising region.Besides,the hybrid meta-model strategy applied in the search process makes it possible to solve the complex practical problems.Tested upon a serial of benchmark math functions,the HMDSD method shows great efficiency and search accuracy.On top of that,a practical lightweight design demonstrates its superior performance.

An approximation algorithm for the k-median warehouse-retailer network design problem

We study the generalizedk-median version of the warehouse-retailer network design problem(kWRND).We formulate the k-WRND as a binary integer program and propose a 6-approximation randomized algorithm based on Lagrangian relaxation.

Chase,Pounce,and Escape Optimization Algorithm

While many metaheuristic optimization algorithms strive to address optimization challenges,they often grapple with the delicate balance between exploration and exploitation,leading to issues such as premature convergence,sensitivity to parameter settings,and difficulty in maintaining population diversity.In response to these challenges,this study introduces the Chase,Pounce,and Escape(CPE)algorithm,drawing inspiration from predator-prey dynamics.Unlike traditional optimization approaches,the CPE algorithm divides the population into two groups,each independently exploring the search space to efficiently navigate complex problem domains and avoid local optima.By incorporating a unique search mechanism that integrates both the average of the best solution and the current solution,the CPE algorithm demonstrates superior convergence properties.Additionally,the inclusion of a pouncing process facilitates rapid movement towards optimal solutions.Through comprehensive evaluations across various optimization scenarios,including standard test functions,Congress on Evolutionary Computation(CEC)-2017 benchmarks,and real-world engineering challenges,the effectiveness of the CPE algorithm is demonstrated.Results consistently highlight the algorithm’s performance,surpassing that of other well-known optimization techniques,and achieving remarkable outcomes in terms of mean,best,and standard deviation values across different problem domains,underscoring its robustness and versatility.

PARTIAL REGULARITY FOR OPTIMAL DESIGN PROBLEMS INVOLVING BOTH BULK AND SURFACE ENERGIES

This paper studies a class of variational problems which involving both bulk and surfaceenergies. The bulk energy is of Dirichlet type though it can be in very general forms allowingunknowns to be scalar or vectors.The surface energy is an arbitrary elliptic parametric integralwhich is defined on a free interface. One also allows other constraints such as volumes of partitioning sets. One establishes the existence and regularity theory, in particular, the regularityof the free interface of such problems.

A Chaotic Approach for the Bi-level Discrete Equilibrium Network Design Problem

A chaotic algorithm for providing a solution to the bi-level Discrete Equilibrium Network Design Problem （NDP） is discussed following an introduction of the Discrete Network Design Problem （DNDP） model and Chaos Optimization Algorithms （COA）. A description of the chaotic approach for the DNDP model is described in details. Then a numerical example for the DNDP is carried out to investigate the chaotic approach. The results have been encouraging, indicating that the chaotic approach has great potential ability in finding the optimal solution of DNDP models.

mLBOA:A Modified Butterfly Optimization Algorithm with Lagrange Interpolation for Global Optimization

Though the Butterfly Bptimization Algorithm(BOA)has already proved its effectiveness as a robust optimization algorithm,it has certain disadvantages.So,a new variant of BOA,namely mLBOA,is proposed here to improve its performance.The proposed algorithm employs a self-adaptive parameter setting,Lagrange interpolation formula,and a new local search strategy embedded with Levy flight search to enhance its searching ability to make a better trade-off between exploration and exploitation.Also,the fragrance generation scheme of BOA is modified,which leads for exploring the domain effectively for better searching.To evaluate the performance,it has been applied to solve the IEEE CEC 2017 benchmark suite.The results have been compared to that of six state-of-the-art algorithms and five BOA variants.Moreover,various statistical tests,such as the Friedman rank test,Wilcoxon rank test,convergence analysis,and complexity analysis,have been conducted to justify the rank,significance,and complexity of the proposed mLBOA.Finally,the mLBOA has been applied to solve three real-world engineering design problems.From all the analyses,it has been found that the proposed mLBOA is a competitive algorithm compared to other popular state-of-the-art algorithms and BOA variants.