Kengo Katayama

Performance of simulated annealing-based heuristic for the unconstrained binary quadratic programming problem

Abstract The unconstrained binary quadratic programming problem (BQP) is known to be NP-hard and has many practical applications. This paper presents a simulated annealing (SA)-based heuristic for the BQP. The new SA heuristic for the BQP is based on a simple (1- opt ) local search heuristic and designed with a simple cooling schedule, but the multiple annealing processes are adopted. To show practical performances of the SA, we test on publicly available benchmark instances of large size ranging from 500 to 2500 variables and compare them with other heuristics such as multi-start local search, the previous SA, tabu search, and genetic algorithm incorporating the 1- opt local search. Computational results indicate that our SA leads to high-quality solutions with short times and is more effective than the competitors particularly for the largest benchmark set. Furthermore, the values of new best-known solutions found by the SA for several large instances are also reported.

An effective local search for the maximum clique problem

We propose a variable depth search based algorithm, called k-opt local search (KLS), for the maximum clique problem. KLS efficiently explores the k-opt neighborhood defined as the set of neighbors that can be obtained by a sequence of several add and drop moves that are adaptively changed in the feasible search space. Computational results on DIMACS benchmark graphs indicate that KLS is capable of finding considerably satisfactory cliques with reasonable running times in comparison with those of state-of-the-art metaheuristics.

The efficiency of hybrid mutation genetic algorithm for the travelling salesman problem

In this paper, we present an efficient genetic algorithm (GA) for solving the travelling salesman problem (TSP) as a combinatorial optimization problem. In our computational model, we propose a complete subtour exchange crossover that does not break as some good subtours as possible, because the good subtours are worth preserving for descendants. Generally speaking, global search GA is considered to be better approaches than local searches. However, it is necessary to strengthen the ability of local search as well as global ones in order to increase a GA total efficiency. In this study, our GA applies a stochastic hill climbing procedure in the mutation process of the GA. Experimental results showed that the GA leads good convergence as high as 99 percent even for 500 cities TSP.

A new iterated local search algorithm using genetic crossover for the traveling salesman problem

This paper proposes a new iterared local search (ILS) algorit.hm ihar escapes from local optima usin, a geuet ic crossover. In usual IL9 for solving the rraveling salesman problem, a double-bridge 4change move is geuerally employed as a useful technique to escape from t.he local opt ima fouud by a local search procedure. Proposed ILS uses a technique of crossover developed in a field of the genetic algorit.hms in spite of the double-bridge move. In our algorithm, !ve emplo\the disrauce preserviug crossover (UPX) proposed by Freislebeu and Merz. Therefore rhis DPS is performed as a special k-change ulove according to srates of t.wo solutions Lbat ueed fol crossover process. Experimeutal results demoust.rate t.hat proposed ILS Buds much better quality solutions than usual ILS using the double-bridge move. (:ousequeut.ly. this paper will show au efrect to employ tbe genet.ic crossover as the escape t.echuique.

Solving the maximum clique problem by k-opt local search

This paper presents a local search algorithm based on variable depth search, called the k-opt local search, for the maximum clique problem. The k-opt local search performs add and drop moves, each of which can be interpreted as 1-opt move, to search a k-opt neighborhood solution at each iteration until no better k-opt neighborhood solution can be found. To evaluate our k-opt local search algorithm, we repeatedly apply the local search for each of DIMACS benchmark graphs and compare with the state-of-the-art metaheuristics such as the genetic local search and the iterated local search reported previously. The computational results show that in spite of the absence of major metaheuristic components, the k-opt local search is capable of finding better (at least the same) solutions on average than those obtained by these metaheuristics for all the graphs.

An Evolutionary Approach for the Maximum Diversity Problem

The objective of the maximum diversity problem (MDP) is to select a set of m-elements from larger set of n-elements such that the selected elements maximize a given diversity measure. The paper presents an evolutionary algorithm incorporating local search — memetic algorithm (MA) — for the MDP which consists of a greedy method, simple evolutionary operators, a repair method, and a k-flip local search based on variable depth search. In the MA, the k-flip local search starts with a feasible solution and obtains a local optimum in the feasible search space. Since infeasible solutions may be created by the simple crossover and mutation operators even if they start with feasible ones found by the local search, the repair method is applied to such infeasible solutions after the crossover and the mutation in order to guarantee feasibility of solutions to the problem. To show the effectiveness of the MA with the k-flip local search, we compare with a MA with 2-flip local search for large-scale problem instances (of up to n=2500) which are larger than those investigated by other researchers. The results show that the k-flip local search based MA is effective particularly for larger instances. We report the best solution found by the MA as this is the first time such large instances are tackled.

On fundamental design of parthenogenetic algorithm for the binary quadratic programming problem

The aims of this paper are to develop a heuristic called Parthenogenetic Algorithm (PA) for the binary quadratic programming problem (BQP) and to show empirical performance of PA on large test instances of the BQP. The PA may be interpreted as iterated local search where a population consists of a single individual and a mutation operator rather than a crossover is fully used to generate new offspring, which is used as a starting solution for a local search process in each iteration. Due to the first attempt of PA approach to the BQP, we investigate several PA implementations to choose the best PA. Each of them incorporates each of four local search heuristics (deterministic 1-opt, randomized 1-opt, deterministic k-opt, and randomized k-opt) known for the BQP so far and has a random mutation controlled by a probability parameter. Computational results after extensive experiments show that search abilities of PAs with k-opt are not as sensitive in the parameter values as PAs with 1-opt. Moreover, it turns out that the PA incorporating the randomized k-opt local search and with the near-optimal parameter value of the mutation is superior or at least competitive to the other existing powerful heuristics.

Analysis of crossovers and selections in a coarse-grained parallel genetic algorithm

The parallel genetic algorithms (PGA) have been developed for combinatorial optimization problems, and its parallel efficiencies have been investigated on a specific problem. These investigations were concerned with how to design a topology and the determination of the optimum setting for parameters (for example, size of subpopulations, migration interval, and so on) rather than the effectiveness of genetic operators. This paper investigates a relation between the parallel efficiency of the coarse-grained PGA and genetic (crossover and selection) operators for the traveling salesman problem on an MIMD parallel computer. The following genetic operators are considered: improved edge recombination (IERX), distance preserving (DPX), and complete subtour exchange (CSEX) crossovers, and two selection operators, which have relatively high selection pressures. Computational results indicate that the parallel efficiency is significantly affected by the difference of crossovers rather than the selections, and the PGA with CSEX gives better properties.

Reinforcement learning agents with primary knowledge designed by analytic hierarchy process

This paper presents a novel model of reinforcement learning agents. A feature of our learning agent model is to integrate analytic hierarchy process (AHP) into a standard reinforcement learning agent model, which consists of three modules: state recognition, learning, and action selecting modules. In our model, AHP module is designed with primary knowledge that human intrinsically should have in order to attain a goal state. This aims at increasing promising actions of agent especially in the earlier stages of learning instead of completely random actions as in the standard reinforcement learning algorithms. We adopt profit-sharing as a reinforcement learning algorithm and demonstrate the potential of our approach on two learning problems of a pursuit problem and a Sokoban problem with deadlock in the grid-world domains, where results indicate that the learning time can be decreased considerably for the problems and our approach efficiently avoids the deadlock for the Sokoban problem. We also show that bad effect that can be usually observed by introducing a priori knowledge into reinforcement learning process can be restrained by a method that decreases a rate of using knowledge during learning.

Performance of a genetic algorithm for the graph partitioning problem

The performance of the genetic algorithm (GA) for the graph partitioning problem (GPP) is investigated by comparison with standard heuristics on well-known benchmark graphs. In general, there is a case where a practical performance of a conventional genetic approach, which performs only simple operations without a local search strategy, is not sufficient. However, it is known that a combination of GA and local search can produce better solutions. From this practice, we incorporate a simple local search algorithm into the GA. In particular, the search ability of the GA is compared with standard heuristics such as multistart local search and simulated annealing, which use the same neighborhood structure of the simple local search, for solving the GPP. Experimental results show that the GA performs better than its competitors.