Yasuhiro Hitotsuyanagi

Effectiveness of scalability improvement attempts on the performance of NSGA-II for many-objective problems

Recently a number of approaches have been proposed to improve the scalability of evolutionary multiobjective optimization (EMO) algorithms to many-objective problems. In this paper, we examine the effectiveness of those approaches through computational experiments on multiobjective knapsack problems with two, four, six, and eight objectives. First we briefly review related studies on evolutionary many-objective optimization. Next we explain why Pareto dominance-based EMO algorithms do not work well on many-objective optimization problems. Then we explain various scalability improvement approaches. We examine their effects on the performance of NSGA-II through computational experiments. Experimental results clearly show that the diversity of solutions is decreased by most scalability improvement approaches while the convergence of solutions to the Pareto front is improved. Finally we conclude this paper by pointing out future research directions.

Many-objective test problems to visually examine the behavior of multiobjective evolution in a decision space

Many-objective optimization is a hot issue in the EMO (evolutionary multiobjective optimization) community. Since almost all solutions in the current population are non-dominated with each other in many-objective EMO algorithms, we may need a different fitness evaluation scheme from the case of two and three objectives. One difficulty in the design of many-objective EMO algorithms is that we cannot visually observe the behavior of multiobjective evolution in the objective space with four or more objectives. In this paper, we propose the use of many-objective test problems in a two- or three-dimensional decision space to visually examine the behavior of multiobjective evolution. Such a visual examination helps us to understand the characteristic features of EMO algorithms for many-objective optimization. Good understanding of existing EMO algorithms may facilitates their modification and the development of new EMO algorithms for many-objective optimization.

Effects of the existence of highly correlated objectives on the behavior of MOEA/D

Recently MOEA/D (multi-objective evolutionary algorithm based on decomposition) was proposed as a high-performance EMO (evolutionary multiobjective optimization) algorithm. MOEA/D has high search ability as well as high computational efficiency. Whereas other EMO algorithms usually do not work well on many-objective problems with four or more objectives, MOEA/D can properly handle them. This is because its scalarizing function-based fitness evaluation scheme can generate an appropriate selection pressure toward the Pareto front without severely increasing the computation load. MOEA/D can also search for well-distributed solutions along the Pareto front using a number of weight vectors with different directions in scalarizing functions. Currently MOEA/D seems to be one of the best choices for multi-objective optimization in various application fields. In this paper, we examine its performance on multi-objective problems with highly correlated objectives. Similar objectives to existing ones are added to two-objective test problems in computational experiments. Experimental results on multi-objective knapsack problems show that the inclusion of similar objectives severely degrades the performance of MOEA/D while it has almost no negative effects on NSGA-II and SPEA2. We also visually examine such an undesirable behavior of MOEA/D using manyobjective test problems with two decision variables.

Use of biased neighborhood structures in multiobjective memetic algorithms

In this paper, we examine the use of biased neighborhood structures for local search in multiobjective memetic algorithms. Under a biased neighborhood structure, each neighbor of the current solution has a different probability to be sampled in local search. In standard local search, all neighbors of the current solution usually have the same probability because they are randomly sampled. On the other hand, we assign larger probabilities to more promising neighbors in order to improve the search ability of multiobjective memetic algorithms. In this paper, we first explain our multiobjective memetic algorithm, which is a simple hybrid algorithm of NSGA-II and local search. Then we explain its variants with biased neighborhood structures for multiobjective 0/1 knapsack and flowshop scheduling problems. Finally we examine the performance of each variant through computational experiments. Experimental results show that the use of biased neighborhood structures clearly improves the performance of our multiobjective memetic algorithm.

How to choose solutions for local search in multiobjective combinatorial memetic algorithms

This paper demonstrates that the performance of multiobjective memetic algorithms (MOMAs) for combinatorial optimization strongly depends on the choice of solutions to which local search is applied. We first examine the effect of the tournament size to choose good solutions for local search on the performance of MOMAs. Next we examine the effectiveness of an idea of applying local search only to non-dominated solutions in the offspring population. We show that this idea has almost the same effect as the use of a large tournament size because both of them lead to high selection pressures. Then we examine different configurations of genetic operators and local search in MOMAs. For example, we examine the use of genetic operators after local search. In this case, improved solutions by local search are used as parents for recombination while local search is applied to the current population after generation update.

An empirical study on the specification of the local search application probability in multiobjective memetic algorithms

This paper empirically examines the effect of the specification of the local search application probability on the performance of multiobjective memetic algorithms. In each generation of multiobjective memetic algorithms, local search is probabilistically applied to each solution. We handle the local search application probability as a controllable parameter. In computational experiments in this paper, we examine the effect of dynamically changing the probability using the five control strategies: constant, step-wise increase, step-wise decrease, linear increase, and linear decrease. Better results are obtained for almost all test problems by changing the local search application probability than specifying it as a constant value. An interesting observation is that the choice of an appropriate control strategy is problem-dependent. Gradually decreasing its value leads to good results for many problems. Such a control strategy, however, does not work on some test problems.

Implementation of Multiobjective Memetic Algorithms for Combinatorial Optimization Problems: A Knapsack Problem Case Study

In this chapter, we discuss various issues related to the implementation of multiobjective memetic algorithms (MOMAs) for combinatorial optimization problems. First we explain an outline of our MOMA, which is a hybrid algorithm of NSGA-II and local search. Our MOMA is a general framework where we can implement a number of variants. For example, we can use Pareto dominance as well as scalarizing functions such as a weighted sum in local search. Through computational experiments on multiobjective knapsack problems, we examine various issues in the implementation of our MOMA. More specifically, we examine the following issues: the frequency of local search, the choice of initial solutions for local search, the specification of an acceptance rule of local moves, the specification of a termination condition of local search, and the handling of infeasible solutions. We also examine the dynamic control of the balance between genetic operations (i.e., global search) and local search during the execution of our MOMA. Experimental results show that the hybridization with local search does not necessarily improve the performance of NSGA-II whereas local search with problem-specific knowledge leads to drastic performance improvement. Experimental results also show the importance of the balance between global search and local search. Finally we suggest some future research issues in the implementation of MOMAs.

Use of Heuristic Local Search for Single-Objective Optimization in Multiobjective Memetic Algorithms

This paper proposes an idea of using heuristic local search procedures specific for single-objective optimization in multiobjective genetic local search (MOGLS). A large number of local search techniques have been studied for various combinatorial optimization problems. Thus we may have a situation where a powerful local search procedure specific for a particular objective is available in multiobjective optimization. Such a local search procedure, however, can improve only a single objective. Moreover, it may have severe side-effects on the other objectives. For example, in a scheduling problem, an insertion move of a job with the maximum delay to an earlier position in a current schedule is likely to improve only the maximum tardiness. In this paper, we assume a situation where each objective has its own heuristic local search procedure. First we explain our MOGLS algorithm, which is the hybridization of NSGA-II and weighted sum-based local search. Next we propose an idea of using heuristic local search procedures specific for single-objective optimization in MOGLS. Then we implement the proposed idea as a number of variants of MOGLS. These variants are different from each other in the choice of a heuristic local search procedure. We examine three schemes: random, probabilistic and deterministic. Finally we examine the performance of each variant through computational experiments on multiobjective 0/1 knapsack problems with two, three and four objectives. It is shown that the use of heuristic local search procedures and their appropriate choice improve the performance of MOGLS.

Scalability of multiobjective genetic local search to many-objective problems: Knapsack problem case studies

It is well-known that Pareto dominance-based evolutionary multiobjective optimization (EMO) algorithms do not work well on many-objective problems. This is because almost all solutions in each population become non-dominated with each other when the number of objectives is large. That is, the convergence property of EMO algorithms toward the Pareto front is severely deteriorated by the increase in the number of objectives. Currently the design of scalable EMO algorithms is a hot issue in the EMO community. In this paper, we examine the scalability of multiobjective genetic local search (MOGLS) to many-objective problems using a hybrid algorithm of NSGA-lI and local search. Multiobjective knapsack problems with 2, 4, 6, 8, and 10 objectives are used in computational experiments. It is shown by experimental results that the performance of NSGA-lI is improved by the hybridization with local search independent of the number of objectives in the range of 2 to 10 objectives.

Multiobjectivization from two objectives to four objectives in evolutionary multi-objective optimization algorithms

Multiobjectivization is an interesting idea to solve a difficult single-objective optimization problem through its reformulation as a multiobjective problem. The reformulation is performed by introducing an additional objective function or decomposing the original objective function into multiple ones. Evolutionary multiobjective optimization (EMO) algorithms are often used to solve the reformulated problem. Such an optimization approach, which is called multiobjectivization, has been used to solve difficult single-objective problems in many studies. In this paper, we discuss the use of multiobjectivization to solve two-objective problems. That is, we discuss the idea of solving a two-objective optimization problem by reformulating it as a four-objective one. In general, the increase in the number of objectives usually makes the problem more difficult for EMO algorithms. Thus the handling of two-objective problems as four-objective ones may simply lead to the deterioration in the quality of obtained non-dominated solutions. However, in this paper, we demonstrate through computational experiments that better results are obtained for some two-objective test problems by increasing the number of objectives from two to four.