Even Search in a Promising Region for Constrained Multi-Objective Optimization

In recent years, a large number of approaches to constrained multi-objective optimization problems(CMOPs) have been proposed, focusing on developing tweaked strategies and techniques for handling constraints. However, an overly finetuned strategy or technique might overfit some problem types,resulting in a lack of versatility. In this article, we propose a generic search strategy that performs an even search in a promising region. The promising region, determined by obtained feasible non-dominated solutions, possesses two general properties.First, the constrained Pareto front(CPF) is included in the promising region. Second, as the number of feasible solutions increases or the convergence performance(i.e., approximation to the CPF) of these solutions improves, the promising region shrinks. Then we develop a new strategy named even search,which utilizes the non-dominated solutions to accelerate convergence and escape from local optima, and the feasible solutions under a constraint relaxation condition to exploit and detect feasible regions. Finally, a diversity measure is adopted to make sure that the individuals in the population evenly cover the valuable areas in the promising region. Experimental results on 45 instances from four benchmark test suites and 14 real-world CMOPs have demonstrated that searching evenly in the promising region can achieve competitive performance and excellent versatility compared to 11 most state-of-the-art methods tailored for CMOPs.

An Immune-Inspired Approach with Interval Allocation in Solving Multimodal Multi-Objective Optimization Problems with Local Pareto Sets

In practical engineering,multi-objective optimization often encounters situations where multiple Pareto sets(PS)in the decision space correspond to the same Pareto front(PF)in the objective space,known as Multi-Modal Multi-Objective Optimization Problems(MMOP).Locating multiple equivalent global PSs poses a significant challenge in real-world applications,especially considering the existence of local PSs.Effectively identifying and locating both global and local PSs is a major challenge.To tackle this issue,we introduce an immune-inspired reproduction strategy designed to produce more offspring in less crowded,promising regions and regulate the number of offspring in areas that have been thoroughly explored.This approach achieves a balanced trade-off between exploration and exploitation.Furthermore,we present an interval allocation strategy that adaptively assigns fitness levels to each antibody.This strategy ensures a broader survival margin for solutions in their initial stages and progressively amplifies the differences in individual fitness values as the population matures,thus fostering better population convergence.Additionally,we incorporate a multi-population mechanism that precisely manages each subpopulation through the interval allocation strategy,ensuring the preservation of both global and local PSs.Experimental results on 21 test problems,encompassing both global and local PSs,are compared with eight state-of-the-art multimodal multi-objective optimization algorithms.The results demonstrate the effectiveness of our proposed algorithm in simultaneously identifying global Pareto sets and locally high-quality PSs.

GNN Representation Learning and Multi-Objective Variable Neighborhood Search Algorithm for Wind Farm Layout Optimization

With the increasing demand for electrical services,wind farm layout optimization has been one of the biggest challenges that we have to deal with.Despite the promising performance of the heuristic algorithm on the route network design problem,the expressive capability and search performance of the algorithm on multi-objective problems remain unexplored.In this paper,the wind farm layout optimization problem is defined.Then,a multi-objective algorithm based on Graph Neural Network(GNN)and Variable Neighborhood Search(VNS)algorithm is proposed.GNN provides the basis representations for the following search algorithm so that the expressiveness and search accuracy of the algorithm can be improved.The multi-objective VNS algorithm is put forward by combining it with the multi-objective optimization algorithm to solve the problem with multiple objectives.The proposed algorithm is applied to the 18-node simulation example to evaluate the feasibility and practicality of the developed optimization strategy.The experiment on the simulation example shows that the proposed algorithm yields a reduction of 6.1% in Point of Common Coupling(PCC)over the current state-of-the-art algorithm,which means that the proposed algorithm designs a layout that improves the quality of the power supply by 6.1%at the same cost.The ablation experiments show that the proposed algorithm improves the power quality by more than 8.6% and 7.8% compared to both the original VNS algorithm and the multi-objective VNS algorithm.

Evolutionary Multitasking With Global and Local Auxiliary Tasks for Constrained Multi-Objective Optimization

Constrained multi-objective optimization problems(CMOPs) include the optimization of objective functions and the satisfaction of constraint conditions, which challenge the solvers.To solve CMOPs, constrained multi-objective evolutionary algorithms(CMOEAs) have been developed. However, most of them tend to converge into local areas due to the loss of diversity. Evolutionary multitasking(EMT) is new model of solving complex optimization problems, through the knowledge transfer between the source task and other related tasks. Inspired by EMT, this paper develops a new EMT-based CMOEA to solve CMOPs, in which the main task, a global auxiliary task, and a local auxiliary task are created and optimized by one specific population respectively. The main task focuses on finding the feasible Pareto front(PF), and global and local auxiliary tasks are used to respectively enhance global and local diversity. Moreover, the global auxiliary task is used to implement the global search by ignoring constraints, so as to help the population of the main task pass through infeasible obstacles. The local auxiliary task is used to provide local diversity around the population of the main task, so as to exploit promising regions. Through the knowledge transfer among the three tasks, the search ability of the population of the main task will be significantly improved. Compared with other state-of-the-art CMOEAs, the experimental results on three benchmark test suites demonstrate the superior or competitive performance of the proposed CMOEA.

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.

Quantum walk search algorithm for multi-objective searching with iteration auto-controlling on hypercube

Shenvi et al.have proposed a quantum algorithm based on quantum walking called Shenvi-Kempe-Whaley(SKW)algorithm,but this search algorithm can only search one target state and use a specific search target state vector.Therefore,when there are more than two target nodes in the search space,the algorithm has certain limitations.Even though a multiobjective SKW search algorithm was proposed later,when the number of target nodes is more than two,the SKW search algorithm cannot be mapped to the same quotient graph.In addition,the calculation of the optimal target state depends on the number of target states m.In previous studies,quantum computing and testing algorithms were used to solve this problem.But these solutions require more Oracle calls and cannot get a high accuracy rate.Therefore,to solve the above problems,we improve the multi-target quantum walk search algorithm,and construct a controllable quantum walk search algorithm under the condition of unknown number of target states.By dividing the Hilbert space into multiple subspaces,the accuracy of the search algorithm is improved from p_(c)=(1/2)-O(1/n)to p_(c)=1-O(1/n).And by adding detection gate phase,the algorithm can stop when the amplitude of the target state becomes the maximum for the first time,and the algorithm can always maintain the optimal number of iterations,so as to reduce the number of unnecessary iterations in the algorithm process and make the number of iterations reach t_(f)=(π/2)(?).

Do Search and Selection Operators Play Important Roles in Multi-Objective Evolutionary Algorithms:A Case Study

Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.

Deep Neural Network Architecture Search via Decomposition-Based Multi-Objective Stochastic Fractal Search

Deep neural networks often outperform classical machine learning algorithms in solving real-world problems.However,designing better networks usually requires domain expertise and consumes significant time and com-puting resources.Moreover,when the task changes,the original network architecture becomes outdated and requires redesigning.Thus,Neural Architecture Search(NAS)has gained attention as an effective approach to automatically generate optimal network architectures.Most NAS methods mainly focus on achieving high performance while ignoring architectural complexity.A myriad of research has revealed that network performance and structural complexity are often positively correlated.Nevertheless,complex network structures will bring enormous computing resources.To cope with this,we formulate the neural architecture search task as a multi-objective optimization problem,where an optimal architecture is learned by minimizing the classification error rate and the number of network parameters simultaneously.And then a decomposition-based multi-objective stochastic fractal search method is proposed to solve it.In view of the discrete property of the NAS problem,we discretize the stochastic fractal search step size so that the network architecture can be optimized more effectively.Additionally,two distinct update methods are employed in step size update stage to enhance the global and local search abilities adaptively.Furthermore,an information exchange mechanism between architectures is raised to accelerate the convergence process and improve the efficiency of the algorithm.Experimental studies show that the proposed algorithm has competitive performance comparable to many existing manual and automatic deep neural network generation approaches,which achieved a parameter-less and high-precision architecture with low-cost on each of the six benchmark datasets.

A Parallel Search System for Dynamic Multi-Objective Traveling Salesman Problem

This paper introduces a parallel search system for dynamic multi-objective traveling salesman problem. We design a multi-objective TSP in a stochastic dynamic environment. This dynamic setting of the problem is very useful for routing in ad-hoc networks. The proposed search system first uses parallel processors to identify the extreme solutions of the search space for each ofk objectives individually at the same time. These solutions are merged into the so-called hit-frequency matrix E. The solutions in E are then searched by parallel processors and evaluated for dominance relationship. The search system is implemented in two different ways master-worker architecture and pipeline architecture.

MULTI OBJECTIVE OPTIMIZATION USING GENETIC ALGORITHM WITH LOCAL SEARCH

In this paper,we propose a hybrid algorithm for finding a set of non dominated solutions of a multi objective optimization problem.In the proposed algorithm,a local search procedure is applied to each solution generated by genetic operations.The aim of the proposed algorithm is not to determine a single final solution but to try to find all the non dominated solutions of a multi objective optimization problem.The choice of the final solution is left to the decision makers preference.High search ability of the proposed algorithm is demonstrated by computer simulation.

Solving material distribution routing problem in mixed manufacturing systems with a hybrid multi-objective evolutionary algorithm

The material distribution routing problem in the manufacturing system is a complex combinatorial optimization problem and its main task is to deliver materials to the working stations with low cost and high efficiency. A multi-objective model was presented for the material distribution routing problem in mixed manufacturing systems, and it was solved by a hybrid multi-objective evolutionary algorithm (HMOEA). The characteristics of the HMOEA are as follows: 1) A route pool is employed to preserve the best routes for the population initiation; 2) A specialized best?worst route crossover (BWRC) mode is designed to perform the crossover operators for selecting the best route from Chromosomes 1 to exchange with the worst one in Chromosomes 2, so that the better genes are inherited to the offspring; 3) A route swap mode is used to perform the mutation for improving the convergence speed and preserving the better gene; 4) Local heuristics search methods are applied in this algorithm. Computational study of a practical case shows that the proposed algorithm can decrease the total travel distance by 51.66%, enhance the average vehicle load rate by 37.85%, cut down 15 routes and reduce a deliver vehicle. The convergence speed of HMOEA is faster than that of famous NSGA-II.

Emergency Local Searching Approach for Job Shop Scheduling

Existing methods of local search mostly focus on how to reach optimal solution.However,in some emergency situations,search time is the hard constraint for job shop scheduling problem while optimal solution is not necessary.In this situation,the existing method of local search is not fast enough.This paper presents an emergency local search(ELS) approach which can reach feasible and nearly optimal solution in limited search time.The ELS approach is desirable for the aforementioned emergency situations where search time is limited and a nearly optimal solution is sufficient,which consists of three phases.Firstly,in order to reach a feasible and nearly optimal solution,infeasible solutions are repaired and a repair technique named group repair is proposed.Secondly,in order to save time,the amount of local search moves need to be reduced and this is achieved by a quickly search method named critical path search(CPS).Finally,CPS sometimes stops at a solution far from the optimal one.In order to jump out the search dilemma of CPS,a jump technique based on critical part is used to improve CPS.Furthermore,the schedule system based on ELS has been developed and experiments based on this system completed on the computer of Intel Pentium(R) 2.93 GHz.The experimental result shows that the optimal solutions of small scale instances are reached in 2 s,and the nearly optimal solutions of large scale instances are reached in 4 s.The proposed ELS approach can stably reach nearly optimal solutions with manageable search time,and can be applied on some emergency situations.

Enhancing the synchronizability of networks by rewiring based on tabu search and a local greedy algorithm

By considering the eigenratio of the Laplacian matrix as the synchronizability measure, this paper presents an efficient method to enhance the synchronizability of undirected and unweighted networks via rewiring. The rewiring method combines the use of tabu search and a local greedy algorithm so that an effective search of solutions can be achieved. As demonstrated in the simulation results, the performance of the proposed approach outperforms the existing methods for a large variety of initial networks, both in terms of speed and quality of solutions.

Hybrid particle swarm optimization with differential evolution and chaotic local search to solve reliability-redundancy allocation problems

In order to solve reliability-redundancy allocation problems more effectively, a new hybrid algorithm named CDEPSO is proposed in this work, which combines particle swarm optimization （PSO） with differential evolution （DE） and a new chaotic local search. In the CDEPSO algorithm, DE provides its best solution to PSO if the best solution obtained by DE is better than that by PSO, while the best solution in the PSO is performed by chaotic local search. To investigate the performance of CDEPSO, four typical reliability-redundancy allocation problems were solved and the results indicate that the convergence speed and robustness of CDEPSO is better than those of PSO and CPSO （a hybrid algorithm which only combines PSO with chaotic local search）. And, compared with the other six improved meta-heuristics, CDEPSO also exhibits more robust performance. In addition, a new performance was proposed to more fairly compare CDEPSO with the same six improved recta-heuristics, and CDEPSO algorithm is the best in solving these problems.

A Hybrid Multi-Objective Evolutionary Algorithm for Optimal Groundwater Management under Variable Density Conditions

In this paper, a new hybrid multi-objective evolutionary algorithm （MOEA）, the niched Pareto tabu search combined with a genetic algorithm （NPTSGA）, is proposed for the management of groundwater resources under variable density conditions. Relatively few MOEAs can possess global search ability contenting with intensified search in a local area. Moreover, the overall searching ability of tabu search （TS） based MOEAs is very sensitive to the neighborhood step size. The NPTSGA is developed on the thought of integrating the genetic algorithm （GA） with a TS based MOEA, the niched Pareto tabu search （NPTS）, which helps to alleviate both of the above difficulties. Here, the global search ability of the NPTS is improved by the diversification of candidate solutions arising from the evolving genetic algorithm population. Furthermore, the proposed methodology coupled with a density-dependent groundwater flow and solute transport simulator, SEAWAT, is developed and its performance is evaluated through a synthetic seawater intrusion management problem. Optimization results indicate that the NPTSGA offers a tradeoff between the two conflicting objectives. A key conclusion of this study is that the NPTSGA keeps the balance between the intensification of nondomination and the diversification of near Pareto-optimal solutions along the tradeoff curves and is a stable and robust method for implementing the multi-objective design of variable-density groundwater resources.

Coevolutionary Framework for Generalized Multimodal Multi-Objective Optimization

Most multimodal multi-objective evolutionary algorithms(MMEAs)aim to find all global Pareto optimal sets(PSs)for a multimodal multi-objective optimization problem(MMOP).However,in real-world problems,decision makers(DMs)may be also interested in local PSs.Also,searching for both global and local PSs is more general in view of dealing with MMOPs,which can be seen as generalized MMOPs.Moreover,most state-of-theart MMEAs exhibit poor convergence on high-dimension MMOPs and are unable to deal with constrained MMOPs.To address the above issues,we present a novel multimodal multiobjective coevolutionary algorithm(Co MMEA)to better produce both global and local PSs,and simultaneously,to improve the convergence performance in dealing with high-dimension MMOPs.Specifically,the Co MMEA introduces two archives to the search process,and coevolves them simultaneously through effective knowledge transfer.The convergence archive assists the Co MMEA to quickly approach the Pareto optimal front.The knowledge of the converged solutions is then transferred to the diversity archive which utilizes the local convergence indicator and the-dominance-based method to obtain global and local PSs effectively.Experimental results show that Co MMEA is competitive compared to seven state-of-the-art MMEAs on fifty-four complex MMOPs.

Feature Selection with a Local Search Strategy Based on the Forest Optimization Algorithm

Feature selection has been widely used in data mining and machine learning.Its objective is to select a minimal subset of features according to some reasonable criteria so as to solve the original task more quickly.In this article,a feature selection algorithm with local search strategy based on the forest optimization algorithm,namely FSLSFOA,is proposed.The novel local search strategy in local seeding process guarantees the quality of the feature subset in the forest.Next,the fitness function is improved,which not only considers the classification accuracy,but also considers the size of the feature subset.To avoid falling into local optimum,a novel global seeding method is attempted,which selects trees on the bottom of candidate set and gives the algorithm more diversities.Finally,FSLSFOA is compared with four feature selection methods to verify its effectiveness.Most of the results are superior to these comparative methods.

Bi-level hybrid local search approach for three-dimensional loading problem with balancing constraints

This paper presents a bi-level hybrid local search(BHLS)algorithm for the three-dimensional loading problem with balancing constraints(3DLP-B),where several rectangular boxes with even densities but different sizes are loaded into a single cubic bin to meet the requirements of the space or capacity utilization and the balance of the center of gravity.The proposed algorithm hybridizes a novel framed-layout procedure in which the concept of the core block and its generation strategy are introduced.Once the block-loading sequence has been determined,we can load one block at a time by the designed construction heuristic.Then,the double-search is introduced;its external search procedure generates a list of compact packing patterns while its internal search procedure is used to search the core-block frames and their best distribution locations.The approach is extensively tested on weakly to strongly heterogeneous benchmark data.The results show that it has better performance in improving space utilization rate and balanced condition of the placement than existed techniques:the overall averages from 79.85%to 86.45%were obtained for the balanced cases and relatively high space-usage rate of 89.44%was achieved for the unbalanced ones.

Combined Timetabling Procedure and Complete Local Search for No-Wait Job Shop Scheduling with Total Tardiness

The strong non-deterministic polynomial-hard( NP-hard)character of job shop scheduling problem( JSSP) has been acknowledged widely and it becomes stronger when attaches the nowait constraint,which widely exists in many production processes,such as chemistry process, metallurgical process. However,compared with the massive research on traditional job shop problem,little attention has been paid on the no-wait constraint.Therefore,in this paper, we have dealt with this problem by decomposing it into two sub-problems, the timetabling and sequencing problems,in traditional frame work. A new efficient combined non-order timetabling method,coordinated with objective of total tardiness,is proposed for the timetabling problems. As for the sequencing one,we have presented a modified complete local search with memory combined by crossover operator and distance counting. The entire algorithm was tested on well-known benchmark problems and compared with several existing algorithms.Computational experiments showed that our proposed algorithm performed both effectively and efficiently.

Enhanced Particle Swarm Optimization Based Local Search for Reactive Power Compensation Problem

This paper presents an enhanced Particle Swarm Optimization (PSO) algorithm applied to the reactive power compensation (RPC) problem. It is based on the combination of Genetic Algorithm (GA) and PSO. Our approach integrates the merits of both genetic algorithms (GAs) and particle swarm optimization (PSO) and it has two characteristic features. Firstly, the algorithm is initialized by a set of a random particle which traveling through the search space, during this travel an evolution of these particles is performed by a hybrid PSO with GA to get approximate no dominated solution. Secondly, to improve the solution quality, dynamic version of pattern search technique is implemented as neighborhood search engine where it intends to explore the less-crowded area in the current archive to possibly obtain more nondominated solutions. The proposed approach is carried out on the standard IEEE 30-bus 6-generator test system. The results demonstrate the capabilities of the proposed approach to generate true and well-distributed Pareto optimal nondominated solutions of the multiobjective RPC.