Creation of Dihedral Escher-like Tilings Based on As-Rigid-As-Possible Deformation


Escherization with Large Deformations Based on As-Rigid-As-Possible Shape Modeling


High-Order Entropy-based Population Diversity Measures in the Traveling Salesman Problem


An Efficient Exhaustive Search Algorithm for the Escherization Problem


A genetic algorithm for the picture maze generation problem, Computers & Operations research


Modeling of a Vehicle Routing Problem with Actual Constraints and Re-scheduling for Dynamic Requests

実制約付き車両配送問題に対する即時配送を考慮した動的配送計画システムの提案

Transactions of the Society of Instrument and Control Engineers


Parallelization of GA-EAX using Identical Population in all Processes

全プロセスによる同一集団を維持したGA-EAXの並列化

One of the most powerful approximation solution methods for the traveling salesman problem (TSP) is a genetic algorithm using edge assembly crossover (GA-EAX), which has found best-known tours to several 100 thousand points scale TSP instances. However, due to the nature of multi-point search, in many cases GAs take more computation time than local search-based algorithms, and it is difficult to fully exercise the capability of GA-EAX for very large TSP instances having more than 1 million points within a reasonable computation time. In this research, we introduce a MPI parallel implementation of GA-EAX. However, in a naive master slave method, the communication costs between the processes are too high to obtain the effect of parallelization sufficiently. So, we introduce a method to reduce the amount of communication between processes to avoid this problem. We also introduce a MPI/thread hybrid parallel implementation of GA-EAX where each MPI process is executed using multiple threads. Experimental results show that the hybrid parallel model achieved up to 29.4 times speedup using 16 PCs, each with 4 cores.

Transaction of the Japanese Society for Evolutionary Computation


同卓スケジューリング問題のモデル化とその動的スケジューリング

同卓スケジューリング問題のモデル化とその動的スケジューリング


A Guided Local Search with Iterative Ejections of Bottleneck Operations for the Job Shop Scheduling Problem


Random Partial Neighborhood Search for the Post-Enrollment Course Timetabling Problem


TSPのためのGA-EAXにおける探索ステージ切換条件とマルチスタート戦略の提案


A Novel Evolution Strategy for Noisy Function Optimization

ノイズを有する関数最適化のための進化戦略

This paper proposes a novel evolution strategy for noisy function optimization. We consider minimization of the expectation of a continuous domain function with stochastic parameters. The proposed method is an extended variant of distance-weighted exponential evolution strategy (DX-NES), which is a state-of-the-art algorithm for deterministic function optimization. We name it DX-NES for uncertain environments (DX-NES-UE). DX-NES-UE estimates the objective function by a quadratic surrogate function. In order to make a balance between speed and accuracy, DX-NES-UE uses surrogate function values when the noise is strong; otherwise it uses observed objective function values. We conduct numerical experiments on 20-dimensional benchmark problems to compare the performance of DX-NES-UE and that of uncertainty handling covariance matrix adaptation evolution strategy (UH-CMA-ES). UH-CMA-ES is one of the most promising methods for noisy function optimization. Benchmark problems include a multimodal function, ill-scaled functions and a non-C2 function with additive noise and decision variable perturbation (sometime called actuator noise). The experiments show that DX-NES-UE requires about 1/100 times as many observations as UH-CMA-ES does on well-scaled functions. The performance difference is greater on ill-scaled functions.


BS-AWA: A More Scalable Adaptive Weighted Aggregation for Continuous Multiobjective Optimization

BS-AWA: Adaptive Weighted Aggregationの目的数に対するスケーラビリティの向上

This paper proposes a more scalable variant of Adaptive Weighted Aggregation (AWA) with respect to the number of objectives in continuous multiobjective optimization. AWA is a scalarization-based multi-start strategy for generating finite points that approximate the entire Pareto set and Pareto front, which is especially focused on many-objective problems (having four or more objectives). In our last study, we discussed a reasonable stopping criterion for AWA, the representing iteration, and analyzed the time and space complexity of AWA when the representing iteration is used as a stopping criterion. Theoretical and empirical results showed that the running time and memory consumption of AWA depends on the number of solutions found in the representing iteration, the representing number. Due to the factorial increase of the representing number for objectives, the applicability of AWA is limited to 16-objective problems. In this study, we therefore redesign two central operations in AWA, the subdivision and the relocation, in order to reduce the representing number. The new subdivision is based on the simplicial complex and its barycentric subdivision and the new relocation is based on the simplicial approximation of a mapping and its range, both of which are well-known notions in topology. We theoretically compare the new AWA, named the barycentric subdivision-based AWA (BS-AWA), with the old AWA in terms of their representing iteration, representing number and approximate memory consumption to illustrate the improvement of scalability; the result implies that BS-AWA is applicable to over 20-objective problems. Numerical experiments using 2- to 17-objective benchmark problems show that BS-AWA achieves a better coverage of obtained solutions than conventional multi-start descent methods in both the variable and objective spaces. The running time and the solution distribution of BS-AWA are also discussed.


Distance-weighted Exponential Natural Evolution Strategyの提案と性能評価


A Powerful Genetic Algorithm using Edge Assembling Crossover for the Traveling Salesman Problem


On the Stopping Criterion of Adaptive Weighted Aggregation for Multiobjective Continuous Optimization

This paper proposes a reasonable stopping criterion for Adaptive Weighted Aggregation (AWA), which is a scalarization-based multi-start framework developed in our previous study on continuous multiobjective optimization. Our previous study shows that AWA yields good solutions covering the entire Pareto set and front within a small consumption of running time and function evaluation on 2- to 6-objective benchmark problems. The experimental results also indicate, however, that the number of solutions generated by AWA is multiplied every iteration. The rapid increase of solutions requires a careful choice of the stopping criterion: even one iteration of shortage may deteriorate the coverage of solutions into an unsatisfactory level and one of excess gives rise to a significant waste of computational resources. We therefore discuss the minimum iteration that AWA yields an enough solution set to cover the Pareto set and front in the sense that the set contains at least one interior point of each of their non-empty "faces", that is, boundary submanifolds induced from the Pareto sets of subproblems with the same inclusion relation as faces of the simplex. Then, such an iteration, named the representing iteration, is proposed as a stopping criterion for AWA, and the number of solutions found by the representing iteration, named the representing number, is derived to analyze the space complexity of AWA. We also discuss the time complexity of AWA based on numerical experiments. The distribution of obtained solutions and its coverage measure show the usefulness of the proposed stopping criterion.


An Evolutionary Algorithm for Black-Box Chance-Constrained Function Optimization

Journal of Advanced Computational Intelligence and Intelligent Informatics


Big-valley Explorer: A Framework of Real-coded Genetic Algorithms for Multi-funnel Function Optimization

大域的多峰性関数最適化のための実数値GAの枠組みBig-valley Explorerの提案

This paper proposes a new framework of real-coded genetic algorithms (RCGAs) for the multi-funnel function optimization. The RCGA is one of the most powerful function optimization methods. Most conventional RCGAs work effectively on the single-funnel function that consists of a single big-valley. However, it is reported that they show poor performance or, sometimes, fail to find the optimum on the multi-funnel function that consists of multiple big-valleys. In order to remedy this deterioration, Innately Split Model (ISM) has been proposed as a framework of RCGAs. ISM initializes an RCGA in a small region and repeats a search with the RCGA as changing the position of the region randomly. ISM outperforms conventional RCGAs on the multi-funnel functions. However, ISM has two problems in terms of the search efficiency and the difficulty of setting parameters. Our proposed method, Big-valley Explorer (BE), is a framework of RCGAs like ISM and it has two novel mechanisms to overcome these problems, the big-valley estimation mechanism and the adaptive initialization mechanism. Once the RCGA finishes a search, the big-valley estimation mechanism estimates a big-valley that the RCGA already explored and removes the region from the search space to prevent the RCGA from searching the same big-valley many times. After that, the adaptive initialization mechanism initializes the RCGA in a wide unexplored region adaptively to find unexplored big-valleys. We evaluate BE through some numerical experiments with both single-funnel and multi-funnel benchmark functions.


Theoretical Foundation for CMA-ES from Information Geometry Perspective


被覆度を考慮したマルチスタート法による多目的連続最適化

被覆度を考慮したマルチスタート法による多目的連続最適化

Transaction of the Japanese Society for Evolutionary Computation


A new genetic algorithm for the asymmetric traveling salesman problem


A new weather-routing system that accounts for ship stability based on a real-coded genetic algorithm

Journal of Marine Science and Technology


The mixed capacitated general routing problem with turn penalties


光学的情報τを用いた移動ロボットの設計と評価

光学的情報τを用いた移動ロボットの設計と評価

Journal of the Robotics Society of Japan


A Penalty-based Edge Assembly Memetic Algorithm for the Vehicle Routing Problem with Time Windows


Efficient Local Search Limitation Strategies in Memetic Algorithm

効果的な局所探索制限によるMemetic Algorithmの高速化

Applications of memetic algorithms (MAs) are usually computationally expensive. In this paper we suggest efficient search limiting strategies for local search used in MAs because local search is the most time consuming part of MAs. The suggested strategies are applied to a recently proposed powerful MA for the capacitated vehicle routing problem (CVRP). Experimental results on the well-known benchmarks show a significant speed-up of 80% in running time without worsening the solution quality. Moreover, the MA dominates state-of-the-art heuristics for the CVRP with respect to both the computation time and the solution quality.

Transactions of the Japanese Society for Artificial Intelligence


A New Real-coded Genetic Algorithm with an Adaptive Mating Selection for UV-landscapes

UV構造を考慮した適応的複製選択による実数値GAの提案

The purpose of this paper is to propose a new real-coded genetic algorithm (RCGA) named Networked Genetic Algorithm (NGA) that intends to find multiple optima simultaneously in deceptive globally multimodal landscapes. Most current techniques such as niching for finding multiple optima take into account big valley landscapes or non-deceptive globally multimodal landscapes but not deceptive ones called UV-landscapes. Adaptive Neighboring Search (ANS) is a promising approach for finding multiple optima in UV-landscapes. ANS utilizes a restricted mating scheme with a crossover-like mutation in order to find optima in deceptive globally multimodal landscapes. However, ANS has a fundamental problem that it does not find all the optima simultaneously in many cases. NGA overcomes the problem by an adaptive parent-selection scheme and an improved crossover-like mutation. We show the effectiveness of NGA over ANS in terms of the number of detected optima in a single run on Fletcher and Powell functions as benchmark problems that are known to have multiple optima, ill-scaledness, and UV-landscapes.


Analysis of The Behavior of MGG and JGG As A Selection Model for Real-coded Genetic Algorithms

実数値GAにおける生存選択モデルとしてのMGGとJGGの挙動解析

In this paper, we focus on analyzing the behavior of the selection models for real-coded genetic algorithms. Recent studies show that Just Generation Gap (JGG) selection model outperforms Minimal Generation Gap (MGG) model when a multi-parental crossover operator based on the hypothesis of the preservation of the statistics of parents is used. However, the validation of JGG selection model is not done yet. To validate the selection method of JGG, we analyze the differences of the behavior of JGG selection model and that of MGG selection model.


Edge Assembly based Memetic Algorithm for the Capacitated Vehicle Routing Problem


Proposal and Evaluation of Adaptive Real-coded Crossover AREX

適応的実数値交叉 AREX の提案と評価

Since once premature convergence happens evolutionary algorithms for function optimization can no longer explore areas of the search space and fail to find the optimum, it is required to handle the notorious drawback. This paper proposes two novel approaches to overcome premature convergence of real-coded genetic algorithms (RCGAs). The first idea is to control the sampling region of crossover by adaptation of expansion rate. The second idea is to cause the acceleration of the movement of population by descending the mean of crossover. Finally, we propose a crossover that combines the adaptation of expansion rate technique and the crossover mean descent technique, called AREX (adaptive real-coded ensemble crossover). The performance of the real-coded GA using AREX is evaluated on several benchmark functions including functions whose landscape forms ridge structure or multi-peak structure, both of which are likely to lead to the miserable convergence phenomenon. The experimental results show not only that the proposed method can locate the global optima of functions on which it is difficult for the existing GAs to discover it but also that our approach outperforms the existing one in number of function evaluations on all functions. Our approach enlarges the classes of functions that real-coded GAs can solve.


A Powerful Route Minimization heuristic for the Vehicle Routing Problem with Time Windows


An Adaptive Niching Genetic Algorithm using a niche size equalization mechanism

均等に個体を分散化する適応的ニッチングGAの提案

Niching GAs have been widely investigated to apply genetic algorithms (GAs) to multimodal function optimization problems. In this paper, we suggest a new niching GA that attempts to form niches, each consisting of an equal number of individuals. The proposed GA can be applied also to combinatorial optimization problems by defining a distance metric in the search space. We apply the proposed GA to the job-shop scheduling problem (JSP) and demonstrate that the proposed niching method enhances the ability to maintain niches and improve the performance of GAs.


Fast Implementation of Genetic Algorithm by Localized EAX Crossover for the Traveling Salesman Problem

局所的な交叉EAXを用いたGAの高速化とTSPへの適用

We propose an genetic algorithm (GA) that applies to the traveling salesman problem (TSP). The GA uses edge assembly crossover (EAX), which is known to be effective for solving the TSP. We first propose a fast implementation of a localized EAX where localized edge exchanges are used in the EAX procedure. We also propose a selection model with an effective combination of the localized EAX that can maintain population diversity at negligible computational costs. Edge entropy measure is used to evaluate population diversity. We demonstrate that the proposed GA is comparable to state-of-the-art heuristics for the TSP. Especially, the GA is superior to them on large instances more than 10,000 cities. For example, the GA found an optimal solution of brd14051 (14,051 cities instance) with a reasonable computational cost. The results are quite impressive because the GA does not use Lin-Kernighan local search (LKLS) even though almost all existing state-of-the-art heuristics for the TSP based on LKLS and its variants.


New Approach of a Genetic Algorithm for TSP Using the Evaluation Function Considering Local Diversity Loss

局所的多様性の損失を考慮した評価関数を用いたGAのTSPへの適用,

The edge assembly crossover (EAX) is considered the best available crossover for traveling salesman problems (TSPs). In this paper, a modified EAX algorithm is proposed. The key idea is to maintain population diversity by eliminating any exchanges of edges by the crossover that does not contribute to an improved evaluation value. For this, a new evaluation function is designed considering local diversity loss of the population. The proposed method is applied to several benchmark instances with up to 4461 cities. Experimental results show that the proposed method works better than other genetic algorithms using other improvements of the EAX. The proposed method can reach optimal solutions for most benchmark instances with up to 2392 cities with probabilities higher than 90%. For an instance called fnl4461, this method can reach an optimal solution with probability 60% when the population size is set to 300 -- an extremely small population compared to that needed in previous studies.


巡回セールスマン問題に対する交叉:枝組み立て交叉の提案と評価

巡回セールスマン問題に対する交叉:枝組み立て交叉の提案と評価

Journal of Japanese Society for Artificial Intelligence

人工知能学会誌(-2013)


A classification and improvement method of metaheuristic algorithms based on complex networks

Bulletin of Advanced Institute of Industrial Technology