Offspring Solutions Research Articles

An effective multi-level memetic search with neighborhood reduction for the clustered team orienteering problem

The Clustered Team Orienteering Problem (CluTOP) extends the classic Clustered Orienteering Problem by considering the use of multiple vehicles. The problem is known to be NP-hard and can be used to formulate many real-life applications. This work presents a highly effective multi-level memetic search for CluTOP that combines a backbone-based edge assembly crossover to generate promising offspring solutions with an effective bilevel synergistic local search procedure at both cluster and customer levels to improve offspring solutions. Other novel features of the proposed approach include a joint use of three specific hash functions to identify the tabu status of candidate solutions at the cluster level, a multi-neighborhood search with inter-route and intra-route optimization at the customer level, a pre-processing neighborhood reduction strategy to avoid examining non-promising candidate solutions, and a strategy for controlled exploration of infeasible solutions. Extensive experimental results on 1848 benchmark instances convincingly demonstrate high competitiveness of the approach in terms of both solution quality and computational time, compared to the state-of-the-art heuristics from the literature. In particular, the proposed algorithm improves upon the existing best-known solutions for 294 instances, while matching the previous best-known results for all but 3 of the remaining instances. To gain further insights into the algorithm’s performance, additional experiments are conducted to analyze its main components.

A discrete Jaya algorithm for vehicle routing problems with uncertain demands

Vehicle Routing Problem with Uncertain Demands (VRPUD) is one of the research hotspots in the field of logistics scheduling. In this paper, a Discrete Jaya (DJaya) algorithm is presented for the VRPUD to minimize the total cost. A novel dividing-point-based coding scheme is designed to represent solutions with higher robustness. In addition, an efficient repair strategy is embedded into the decoding process to avoid the failure of producing feasible solutions. The best and worst solutions are employed to generate offspring solutions in DJaya. Several efficient local search methods are also presented to enhance the exploitation ability and increase the diversity of solutions. Based on the benchmark data sets of the VRPUD, numerical simulations are carried out for the proposed DJaya algorithm with uncertain demands. Computational results and comparisons with the state-of-the-art algorithms demonstrate the superiority of the proposed algorithm in solving VRPUD.

A gene-inspired metaheuristic for scheduling workflow tasks in mobile edge computing-supported cyber–physical systems

This paper proposes a cost-minimization scheduling algorithm for the joint optimization of task offloading and resource allocation for workflow applications in a mobile edge computing (MEC)-supported cyber–physical system. We model this scheduling problem as an integer program that minimizes the total communication and computation cost under resources and deadline constraints upon workflow applications. To cope with this complicated optimization problem, we develop an efficient heuristic method to dispatch the workflow tasks onto MEC servers with sufficient resources. By using the task dispatching heuristic to evaluate the quality of each candidate solution, we construct a novel gene-inspired metaheuristic algorithm (GIMA) that incorporates an offspring-production operator and a conditional insertion scheme into the improvement strategy to explore high-quality solutions. Specifically, the offspring-production operator can enhance the scheduling quality by generating improved offspring solutions based on existing solutions. The conditional insertion scheme is further incorporated to reduce the computational overhead involved in solution exploration. We perform extensive simulations to justify the performance of the proposed GIMA in solving the scheduling problem studied in this work. Experimental results on real-world and synthetic workflow applications show that GIMA outperforms other metaheuristics in terms of cost reduction and computational efficiency.

A co-evolutionary algorithm based on sparsity clustering for sparse large-scale multi-objective optimization

Sparse large-scale multi-objective optimization problems (LSMOPs), which are characterized by high dimensional search space and sparse Pareto optimal solutions, have a widespread existence in academic research and practical applications. While the high dimensional decision space poses challenges to multi-objective evolutionary algorithms (MOEAs), the difficulty of solving sparse LSMOPs can be alleviated by utilizing the prior knowledge that the optimal solutions are sparse. In this paper, a co-evolutionary algorithm based on sparsity clustering, namely SCEA, is proposed, where the prior knowledge of sparse optimal solutions is utilized explicitly. At each generation, SCEA first calculates the current optimal sparsity by sparsity clustering. Then, SCEA divides the population into a winner subpopulation and two loser subpopulations. While the winner subpopulation reproduces offspring solutions by conventional genetic operators, the loser subpopulations generate offspring solutions along two competitive directions under the guidance of current optimal sparsity and variable importance. In the experiments, four state-of-the-art MOEAs are selected as the comparative algorithms. Experimental results show that the proposed algorithm is superior to the four competitors on both benchmark problems and practical applications, which include the sparse signal reconstruction problem, the community detection problem, and the instance selection problem.

A Bi-Objective Evolutionary Algorithm for Multimodal Multiobjective Optimization

Multimodal multi-objective optimization problems (MMOPs) possess multiple Pareto optimal sets corresponding to the identical Pareto optimal front (PF). To handle MMOPs, we propose a bi-objective evolutionary algorithm (BOEA), which transforms an MMOP into a bi-objective optimization problem. This problem is constructed by the penalty boundary intersection technique and a diversity indicator to obtain multiple Pareto optimal sets. The first objective reflects the population convergence and factors in the population diversity in the objective space, while the other objective concentrates more on the population diversity in the decision space. Furthermore, an environmental selection strategy is designed to choose the offspring solutions, which consists of non-dominated sorting based on the transformed optimization problem and hierarchical clustering for selecting promising solutions. Experiments on 34 MMOPs demonstrate that BOEA performs better than selected state-of-the-art representatives, including 22 MMOPs from CEC2019 and 12 imbalanced MMOPs. In addition, the effectiveness of BOEA is further validated by six feature selection problemsin real-world applications.

A multi-neighborhood tabu search for solving multi-budget maximum coverage problem

Many practical decision-making problems involve selecting k distinct subsets of objects from a set of candidate objects such that the chosen objects optimize a given goal while satisfying some constraints. The multi-budget maximum coverage problem (MMCP) is a general model that facilitates formulating such decision-making problems. Given a budget of k, a set of elements with profits, and a set of items with costs where each item is composed of a subset of the elements, the MMCP aims to select k disjoint subsets of items that maximize the total profits of the elements covered by these subsets, while their costs do not exceed their respective budgets. In this work, we present a multi-neighborhood tabu search (MTS) for this NP-hard problem. MTS comprises three essential components that employ four efficient neighborhoods to collaboratively perform the neighborhood exploration to obtain high-quality local optima, select neighborhood solutions with added perturbations, and generate offspring solutions based on population information exchange. To evaluate the effectiveness of MTS, we performed computations on 30 benchmark instances of the extended BMCP. We compared the results with the approximation algorithm, genetic algorithm, particle swarm optimization algorithm, and CPLEX solver. We also provide experiments to highlight the beneficial effect of the essential components in the MTS algorithm. The experimental results demonstrate that MTS not only performs efficiently but also yields solutions of superior quality.

An evolutionary algorithm based on fully connected weight networks for mixed-variable multi-objective optimization

Multi-objective optimization research has mostly focused on continuous-variable problems. However, real-world optimization problems often involve multiple types of variables (continuous, integer, and discrete) and multiple conflicting optimization objectives, called mixed-variable multi-objective optimization problems (MVMOPs). Discrete variables make the decision space of the problem discrete. In contrast, while different types of variables need different treatments by the evolutionary algorithm, which poses a challenge to the efficient search of the evolutionary algorithm. Therefore, we propose an evolutionary algorithm based on a fully connected weight network (FCWNEA). The fully connected network structure characterizes the entire decision space, the node access count records the frequency of visits to the node, and the weights of connections and the activity of variables estimate the distribution of the decision space. This information assists in generating offspring solutions. To evaluate the performance of the proposed algorithm, we conduct empirical experiments on different types of problems. The results show that the proposed algorithm has a significant advantage in mixed-variable multi-objective problems. Moreover, the proposed algorithm is also quite competitive in continuous problems and can better handle the correlation between variables in optimization problems.

Bi-Trajectory Hybrid Search to Solve Bottleneck-Minimized Colored Traveling Salesman Problems

A bottleneck-minimized colored traveling salesman problem is an important variant of colored traveling salesman problems. It is useful in handling the planning problems with partially overlapped workspace such as the scheduling transportation resources for timely delivery of goods. In this work, we propose an efficient bi-trajectory hybrid search method for it. The proposed method integrates a route-based crossover operator to generate promising offspring solutions, a multi-neighborhood simulated annealing to perform local optimization, and a stagnation-detect-escape mechanism to help the search escape from local optima. We also propose a bidirectional adjacency solution representation method to encode a solution, which extends the traditional adjacency representation method by additionally employing an array to represent its reverse counterpart. Extensive evaluations on two sets of 58 widely used benchmark instances demonstrate that the proposed method significantly outperforms state-of-the-art algorithms. Investigations on key algorithm modules are performed to confirm the novelty and effectiveness of the proposed ideas and strategies. Finally, we verify the generalization of the proposed method via its use to solve a colored traveling salesman problem with its aim to balance workload among salesmen. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work is motivated by the problems of scheduling transportation resources for timely delivery of goods. It proposes an effective bi-trajectory hybrid search to tackle bottleneck-minimized colored traveling salesman problem. The proposed approach performs bi-trajectory hybrid evolutionary search by maintaining only two individuals during the whole search process. Extensive numerical experiments and comparisons show that our proposed algorithm significantly outperforms state-of-the-art algorithms and can help decision-makers in designing best-routing solutions.

Dual-Fuzzy-Classifier-Based Evolutionary Algorithm for Expensive Multiobjective Optimization

Multiobjective evolutionary algorithms (MOEAs) have been widely used to solve multiobjective optimization problems (MOPs). Conventional MOEAs usually require a large number of function evaluations (FEs) for evaluating the quality of solutions. However, only a limited number of FEs are affordable in many real-world optimization problems where the FEs are computationally or economically expensive. The use of a large number of FEs decreases the effectiveness of MOEAs in solving these problems. This article proposes a dual fuzzy classifier-based surrogate model (DFC) and a DFC-based multiobjective evolutionary algorithm framework (DFC-MOEA) for expensive optimization problems. The DFC model is used for offspring pre-selection to choose high-quality offspring solutions and for categorization to divide unevaluated solutions into three categories. In the proposed framework, two fuzzy classifiers are built to predict the quality of each unevaluated solution. To strike a balance between convergence and diversity, one classifier is designed for predicting the dominance relation of unevaluated solutions (i.e., convergence), and another classifier is designed for predicting the crowdedness of unevaluated solutions (i.e., diversity). The integration of the proposed framework in three different types of MOEAs (i.e., a dominance-based MOEA, an indicator-based MOEA, and a decomposition-based MOEA) demonstrates its usefulness in handling expensive optimization problems. Comprehensive experiments on four well-known test suites and several real-world optimization problems demonstrate that the proposed framework is able to improve the performance of MOEAs under a limited number of FEs.

Incorporating gradient information into dimension perturbation mutation for high-dimensional expensive optimization

Surrogate-assisted evolutionary algorithms (SAEAs) have recently shown excellent abilities in solving computationally expensive optimization problems (EOPs), but most of them are not designed for high-dimensional EOPs (HEOPs). A new algorithm where the gradient information is well-incorporated into dimension perturbation mutation called as GIDPM for HEOPs, is proposed and fully investigated in this paper. Specifically, for each solution, a local candidate offspring pool is obtained by combining the gradient descent information and dimension perturbation mutation, and the DE/current-to-rand/2/bin is employed to generate a global candidate offspring pool. Then an offspring selection strategy is used to identify the exact offspring solutions, in which the overall qualities of two pools, the directions of near gradient descent of candidate solutions, and the distributions and RBF predictions of candidate solutions are considered in turn, to achieve appropriate local exploitation or global exploration. In addition, an Autoencoder-embedded search strategy is used to quickly jump out of the local optima caused by some small ripples or oscillations of the landscape after each several iterations to achieve leapfrog search. The GIDPM maintains a good balance between exploration and exploitation. Experimental studies on benchmark problems demonstrate that the GIDPM achieves better convergence performance when the problem dimension is larger than or equal to 30, and the better performance of GIDPM can be achieved with the increase of dimension. The GIDPM is also used for the design of the sandwich panel with truss cores. Compared with gradient-based algorithm, the GIDPM obtains the design with better structural performance.

A hybrid genetic algorithm for the Hamiltonian p‐median problem

AbstractThe Hamiltonian p‐median problem consists of finding p( is given) non‐intersecting Hamiltonian cycles in a complete edge‐weighted graph such that each cycle visits at least three vertices and each vertex belongs to exactly one cycle, while minimizing the total cost of pcycles. In this work, we present an effective and scalable hybrid genetic algorithm to solve this computationally challenging problem. The algorithm combines an edge‐assembly crossover to generate promising offspring solutions from high‐quality parents, and a multiple neighborhood local search to improve each offspring solution. To promote population diversity, the algorithm applies a mutation operator to the offspring solutions and a quality‐and‐distance update strategy to manage the population. We compare the method to the best reference algorithms in the literature based on three sets of 145 popular benchmark instances (with up to 318 vertices), and report improved best upper bounds for eight instances. To evaluate the scalability of the method, we perform experiments on a new set of 70 large instances (with up to 1060 vertices). We examine the contributions of key components of the algorithm.

An effective hybrid evolutionary algorithm for the set orienteering problem

The Set Orienteering Problem (SOP) is a variant of the popular Orienteering Problem (OP) arising from a number of real-life applications. The aim is to find a tour across a subset of customers, while maximizing the collected profit within a given travel time limit. In SOP, vertices (customers) are partitioned into clusters, where a profit is associated to each cluster. The profit of a cluster is collected only if at least one vertex belonging to the cluster is contained in the tour. For this NP-hard problem, we present a highly effective hybrid evolutionary algorithm that integrates a cluster-based crossover operator, a randomized mutation operator to generate multiple distinct promising offspring solutions, and a two-phase local refinement procedure that explores both feasible and infeasible solutions in search of high-quality local optima. Extensive experiments on 192 large benchmark instances show that the proposed algorithm significantly outperforms all the existing approaches from the SOP literature. In particular, it reports improved best-known solutions (new lower bounds) for 54 instances, while matching the existing best-known result for 133 instances. We further investigate the contribution of the key algorithmic elements to the success of the proposed approach.

Code and Data Repository for Detecting Critical Nodes in Sparse Graphs via “Reduce-Solve-Combine” Memetic Search

This study considers a well-known critical node detection problem that aims to minimize a pairwise connectivity measure of an undirected graph via the removal of a subset of nodes (referred to as critical nodes) subject to a cardinality constraint. Potential applications include epidemic control, emergency response, vulnerability assessment, carbon emission monitoring, network security and drug design. To solve the problem, we present a "reduce-solve-combine" memetic search approach that integrates a problem reduction mechanism into the popular population-based memetic algorithm framework. At each generation, a common pattern mined from two parent solutions is first used to reduce the given problem instance, then the reduced instance is solved by a component-based hybrid neighborhood search that effectively combines an articulation point impact strategy and a node weighting strategy, and finally an offspring solution is produced by combining the mined common pattern and the solution of the reduced instance. Extensive evaluations on 42 real-world and synthetic benchmark instances show the efficacy of the proposed method, which discovers 9 new upper bounds and significantly outperforms the current state-of-the-art algorithms. Investigation of key algorithmic modules additionally discloses the importance of the proposed ideas and strategies. Finally, we demonstrate the generality of the proposed method via its adaptation to solve the node-weighted critical node problem.

Detecting Critical Nodes in Sparse Graphs via “Reduce-Solve-Combine” Memetic Search

This study considers a well-known critical node detection problem that aims to minimize a pairwise connectivity measure of an undirected graph via the removal of a subset of nodes (referred to as critical nodes) subject to a cardinality constraint. Potential applications include epidemic control, emergency response, vulnerability assessment, carbon emission monitoring, network security, and drug design. To solve the problem, we present a “reduce-solve-combine” memetic search approach that integrates a problem reduction mechanism into the popular population-based memetic algorithm framework. At each generation, a common pattern mined from two parent solutions is first used to reduce the given problem instance, then the reduced instance is solved by a component-based hybrid neighborhood search that effectively combines an articulation point impact strategy and a node weighting strategy, and finally an offspring solution is produced by combining the mined common pattern and the solution of the reduced instance. Extensive evaluations on 42 real-world and synthetic benchmark instances show the efficacy of the proposed method, which discovers nine new upper bounds and significantly outperforms the current state-of-the-art algorithms. Investigation of key algorithmic modules additionally discloses the importance of the proposed ideas and strategies. Finally, we demonstrate the generality of the proposed method via its adaptation to solve the node-weighted critical node problem. History: Accepted by Erwin Pesch, Area Editor for Heuristic Search &amp; Approximation Algorithms. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72371157, 61903144, 72031007]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2022.0130 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2022.0130 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Frequent Itemset-Driven Search for Finding Minimal Node Separators and its Application to Air Transportation Network Analysis

The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -separator problem ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -SP) consists of finding the minimum set of vertices whose removal separates the network into multiple different connected components with fewer than a limited number of vertices in each component, which belongs to the family of critical node detection problems. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -SP problem is an important NP-hard problem with various real-world applications. In this paper, we propose a frequent itemset-driven search (FIS) algorithm to solve <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$</tex-math> </inline-formula> -SP, which integrates the concept of frequent itemset into the well-known memetic search framework. Starting from a high-quality population built by population construction and population repair, FIS then iteratively employs a frequent itemset recombination operator (to generate promising offspring solution), a tabu-based simulated annealing (to find local optima), a population repair procedure, and a population management strategy (to guarantee healthy/diverse population). Extensive evaluations on 50 benchmark instances show that FIS significantly outperforms the state-of-the-art algorithms. In particular, it discovers 29 new upper bounds and matches 18 previous best-known bounds. Finally, we experimentally analyze the importance of each key algorithmic component, and perform a case study on an air transportation network for understanding its network structure and identifying its influential airports.

A direction vector-guided multi-objective evolutionary algorithm for variable linkages problems

Recombination is a key component for the evolutionary algorithm to provide promising offspring solutions. However, conventional recombination operators cannot generate high-quality solutions for variable linkages problems due to the particularity of the Pareto optimal set (PS). To tackle this problem, a two-stage multi-objective evolutionary algorithm based on direction vector guidance (DSMOEA) is proposed in this paper. Firstly, a portion of the population is transformed by the eigenmatrix of the covariance matrix to increase the probability of generating high-quality offspring. Then the representative solutions are selected in the transformed population to create the direction vectors. Under the guidance of the direction vectors, the population rapidly approaches PS and generates promising offspring solutions. Finally, Differential Evolution (DE) is performed for searching globally to increase the diversity of the population. The proposed algorithm is tested on three classes of variable linkages problems with 30, 50, and 100 dimensions to verify its performance. The results show that the algorithm is promising for variable linkages problems.

Hybrid genetic algorithm for undirected traveling salesman problems with profits

AbstractThe orienteering problem (OP) and prize‐collecting traveling salesman problem (PCTSP) are two typical TSPs with profits, in which each vertex has a profit and the goal is to visit several vertices to optimize the collected profit and travel costs. The OP aims to collect the maximum profit without exceeding the given travel cost. The PCTSP seeks to minimize the travel costs while ensuring a minimum profit threshold. This study introduces a hybrid genetic algorithm that addresses both the OP and PCTSP under a unified framework. The algorithm combines an extended edge‐assembly crossover operator to produce promising offspring solutions, and an effective local search to ameliorate each offspring solution. The algorithm is further enforced by diversification‐oriented mutation and population‐diversity management. Extensive experiments demonstrate that the method competes favorably with the best existing methods in terms of both the solution quality and computational efficiency. Additional experiments provide insights into the roles of the key components of the proposed method.

An effective hybrid search method for the quadratic knapsack problem with conflict graphs

The quadratic knapsack problem (QKP) is a variant of the well-known knapsack problem and arises in a variety of real life applications. The quadratic knapsack problem with conflict graphs (QKPCG) further extends QKP by considering the conflicts of items. In this work, we propose an effective hybrid search method based on the framework of memetic algorithm to tackle QKPCG. The method integrates a randomized uniform-based crossover operator to generate promising offspring solutions, a multi-neighborhood tabu search to perform local optimization, and a streamline technique to speed up the evaluation of candidate solutions. The method shows a competitive performance compared to the state-of-the-art approaches in the literature. It finds 3 improved best-known solutions and matches the best-known solutions for all the remaining cases out of the 45 benchmark instances. We investigate the effects of the key ingredients of the algorithm.

Combined knowledge transfer and adaptive coordinate systems approach for evolutionary bilevel optimization

Reducing the number of lower-level function evaluations (LFEs) is crucial to designing a bilevel evolutionary algorithm (BLEA) for bilevel optimization. Direct neighbor solution transfer (DST) is regularly used in BLEA because it can improve the lower-level search efficiency and reduce the number of LFEs. But this method still faces the challenge of misleading searches to make the algorithm converge to the wrong optimum. This paper proposes a bilevel improved multi-operator differential evolution algorithm (BL-IMODE) for bilevel optimization, which uses the knowledge transfer and adaptive coordinate systems approach. Specifically, this paper proposes a lower-level search knowledge transfer (LLS-KT) and a lower-level (LL) optimal solution distribution information transfer (LLO-DIT) mechanism to implement knowledge transfer. In LLS-KT, transferring LL solutions to the LL optimizer is similar to DST, but the LLS-KT transfers multiple solutions and thus has less possibility of misleading searches than DST. Moreover, the LLO-DIT transfers the LL optimal solution distribution information to the LL optimizer for generating promising offspring solutions. Since this method does not directly transfer LL solutions, it avoids misleading searches. Additionally, the adaptive coordinate systems (ACS) approach is used in two-level optimizers to suit different fitness landscapes and further reduce the number of LFEs. In ACS, three differential evolution mutation operators are produced in two coordinate systems. An adaptive strategy is used to select the suitable differential evolution mutation operator to generate promising offspring solutions in the Eigen coordinate or original coordinate system. Experimental studies on three test suites benchmark problems for comparison with seven state-of-the-art algorithms are conducted. The results show BL-IMODE has a significant advantage over the comparative algorithms. Finally, BL-IMODE is applied to tackle the inverse optimal control problem.

Reinforcement-Learning-Based Multi-Objective Differential Evolution Algorithm for Large-Scale Combined Heat and Power Economic Emission Dispatch

As social and environmental issues become increasingly serious, both fuel costs and environmental impacts should be considered in the cogeneration process. In recent years, combined heat and power economic emission dispatch (CHPEED) has become a crucial optimization problem in power system management. In this paper, a novel reinforcement-learning-based multi-objective differential evolution (RLMODE) algorithm is suggested to deal with the CHPEED problem considering large-scale systems. In RLMODE, a Q-learning-based technique is adopted to automatically adjust the control parameters of the multi-objective algorithm. Specifically, the Pareto domination relationship between the offspring solution and the parent solution is used to determine the action reward, and the most-suitable algorithm parameter values for the environment model are adjusted through the Q-learning process. The proposed RLMODE was applied to solve four CHPEED problems: 5, 7, 100, and 140 generating units. The simulation results showed that, compared with four well-established multi-objective algorithms, the RLMODE algorithm achieved the smallest cost and smallest emission values for all four CHPEED problems. In addition, the RLMODE algorithm acquired better Pareto-optimal frontiers in terms of convergence and diversity. The superiority of RLMODE was particularly significant for two large-scale CHPEED problems.