On improving multiobjective genetic algorithms for design optimization

This paper presents some improvements to Multi-Objective Genetic Algorithms (MOGAs). MOGA modifies certain operators within the GA itself to produce a multiobjective optimization technique. The improvements are made to overcome some of the shortcomings in niche formation, stopping criteria and interaction with a design decision-maker. The technique involves filtering, mating restrictions, the idea of objective constraints, and detecting Pareto solutions in the non-convex region of the Pareto set. A step-by-step procedure for an improved MOGA has been developed and demonstrated via two multiobjective engineering design examples: (i) two-bar truss design, and (ii) vibrating platform design. The two-bar truss example has continuous variables while the vibrating platform example has mixed-discrete (combinatorial) variables. Both examples are solved by MOGA with and without the improvements. It is shown that MOGA with the improvements performs better for both examples in terms of the number of function evaluations.     

Evolutionary multiobjective optimization for base station transmitter placement with frequency assignment

We propose a new solution to the problem of positioning base station transmitters of a mobile phone network and assigning frequencies to the transmitters, both in an optimal way. Since an exact solution cannot be expected to run in polynomial time for all interesting versions of this problem (they are all NP-hard), our algorithm follows a heuristic approach based on the evolutionary paradigm. For this evolution to be efficient, i.e., goal-oriented and sufficiently random at the same time, problem-specific knowledge is embedded in the operators. The problem requires both the minimization of the cost and of the channel interference. We examine and compare two standard multiobjective techniques and a new algorithm - the steady-state evolutionary algorithm with Pareto tournaments. One major finding of the empirical investigation is a strong influence of the choice of the multiobjective selection method on the utility of the problem-specific recombination leading to a significant difference in the solution quality.     

Evolutionary algorithms and dynamic programming

Recently, it has been proven that evolutionary algorithms produce good results for a wide range of combinatorial optimization problems. Some of the considered problems are tackled by evolutionary algorithms that use a representation which enables them to construct solutions in a dynamic programming fashion. We take a general approach and relate the construction of such algorithms to the development of algorithms using dynamic programming techniques. Thereby, we give general guidelines on how to develop evolutionary algorithms that have the additional ability of carrying out dynamic programming steps. Finally, we show that for a wide class of the so-called DP-benevolent problems (which are known to admit FPTAS) there exists a fully polynomial-time randomized approximation scheme based on an evolutionary algorithm.     

Performance evaluation of evolutionary multiobjective optimization algorithms for multiobjective fuzzy genetics-based machine learning

Recently, evolutionary multiobjective optimization (EMO) algorithms have been utilized for the design of accurate and interpretable fuzzy rule-based systems. This research area is often referred to as multiobjective genetic fuzzy systems (MoGFS), where EMO algorithms are used to search for non-dominated fuzzy rule-based systems with respect to their accuracy and interpretability. In this paper, we examine the ability of EMO algorithms to efficiently search for Pareto optimal or near Pareto optimal fuzzy rule-based systems for classification problems. We use NSGA-II (elitist non-dominated sorting genetic algorithm), its variants, and MOEA/D (multiobjective evolutionary algorithm based on decomposition) in our multiobjective fuzzy genetics-based machine learning (MoFGBML) algorithm. Classification performance of obtained fuzzy rule-based systems by each EMO algorithm is evaluated for training data and test data under various settings of the available computation load and the granularity of fuzzy partitions. Experimental results in this paper suggest that reported classification performance of MoGFS in the literature can be further improved using more computation load, more efficient EMO algorithms, and/or more antecedent fuzzy sets from finer fuzzy partitions.     

Evolutionary algorithms for optimization problems with uncertainties and hybrid indices

Many optimization problems in real-world applications contain both explicit (quantitative) and implicit (qualitative) indices that usually contain uncertain information. How to effectively incorporate uncertain information in evolutionary algorithms is one of the most important topics in information science. In this paper, we study optimization problems with both interval parameters in explicit indices and interval uncertainties in implicit indices. To incorporate uncertainty in evolutionary algorithms, we construct a mathematical uncertain model of the optimization problem considering the uncertainties of interval objectives; and then we transform the model into a precise one by employing the method of interval analysis; finally, we develop an effective and novel evolutionary optimization algorithm to solve the converted problem by combining traditional genetic algorithms and interactive genetic algorithms. The proposed algorithm consists of clustering of a large population according to the distribution of the individuals and estimation of the implicit indices of an individual based on the similarity among individuals. In our experiments, we apply the proposed algorithm to an interior layout problem, a typical optimization problem with both interval parameters in the explicit index and interval uncertainty in the implicit index. Our experimental results confirm the feasibility and efficiency of the proposed algorithm.     

Immune-based algorithms for dynamic optimization

The main problem with biologically inspired algorithms (like evolutionary algorithms or particle swarm optimization) when applied to dynamic optimization is to force their readiness for continuous search for new optima occurring in changing locations. Immune-based algorithm, being an instance of an algorithm that adapt by innovation seem to be a perfect candidate for continuous exploration of a search space. In this paper we describe various implementations of the immune principles and we compare these instantiations on complex environments.     

Immune clonal coevolutionary algorithm for dynamic multiobjective optimization

In this paper, a new evolutionary algorithm, called immune clonal coevolutionary algorithm (ICCoA) for dynamic multiobjective optimization (DMO) is proposed. On the basis of the basic principles of artificial immune system, the proposed algorithm adopts the immune clonal selection to solve DMO problems. In addition, the theory of coevolution is incorporated in ICCoA in global operation to preserve the diversity of Pareto-fronts. Moreover, coevolutionary competitive and cooperative operation is designed to enhance the uniformity and the diversity of the solutions. In comparison with NSGA-II, immune clonal algorithm for DMO and direction-based method, the simulation results obtained on 5 difficult test problems and on related performance metrics suggest that ICCoA can achieve better distributed solutions and be very effective in maintaining the uniformity of Pareto-fronts.     

Mean-semivariance portfolio optimization with multiobjective evolutionary algorithms and technical analysis rules

Recent work has been devoted to study the use of multiobjective evolutionary algorithms (MOEAs) in stock portfolio optimization, within a common mean-variance framework. This article proposes the use of a more appropriate framework, mean-semivariance framework, which takes into account only adverse return variations instead of overall variations. It also proposes the use and comparison of established technical analysis (TA) indicators in pursuing better outcomes within the risk-return relation. Results show there is some difference in the performance of the two selected MOEAs – non-dominated sorting genetic algorithm II (NSGA II) and strength pareto evolutionary algorithm 2 (SPEA 2) – within portfolio optimization. In addition, when used with four TA based strategies – relative strength index (RSI), moving average convergence/divergence (MACD), contrarian bollinger bands (CBB) and bollinger bands (BB), the two selected MOEAs achieve solutions with interesting in-sample and out-of-sample outcomes for the BB strategy.     

Evolutionary multiobjective optimization using an outranking-based dominance generalization

One aspect that is often disregarded in the current research on evolutionary multiobjective optimization is the fact that the solution of a multiobjective optimization problem involves not only the search itself, but also a decision making process. Most current approaches concentrate on adapting an evolutionary algorithm to generate the Pareto frontier. In this work, we present a new idea to incorporate preferences into a multi-objective evolutionary algorithm (MOEA). We introduce a binary fuzzy preference relation that expresses the degree of truth of the predicate “x is at least as good as y”. On this basis, a strict preference relation with a reasonably high degree of credibility can be established on any population. An alternative x is not strictly outranked if and only if there does not exist an alternative y which is strictly preferred to x. It is easy to prove that the best solution is not strictly outranked. For validating our proposed approach, we used the non-dominated sorting genetic algorithm II (NSGA-II), but replacing Pareto dominance by the above non-outranked concept. So, we search for the non-strictly outranked frontier that is a subset of the Pareto frontier. In several instances of a nine-objective knapsack problem our proposal clearly outperforms the standard NSGA-II, achieving non-outranked solutions which are in an obviously privileged zone of the Pareto frontier.     

Evolutionary structural optimization for dynamic problems

This paper presents a simple method for structural optimization with frequency constraints. The structure is modelled by a fine mesh of finite elements. At the end of each eigenvalue analysis, part of the material is removed from the structure so that the frequencies of the resulting structure will be shifted towards a desired direction. A sensitivity number indicating the optimum locations for such material elimination is derived. This sensitivity number can be easily calculated for each element using the information of the eigenvalue solution. The significance of such an evolutionary structural optimization (ESO) method lies in its simplicity in achieving shape and topology optimization for both static and dynamic problems. In this paper, the ESO method is applied to a wide range of frequency optimization problems, which include maximizing or minimizing a chosen frequency of a structure, keeping a chosen frequency constant, maximizing the gap of arbitrarily given two frequencies, as well as considerations of multiple frequency constraints. The proposed ESO method is verified through several examples whose solutions may be obtained by other methods.     

Target-matching test problem for multiobjective topology optimization using genetic algorithms

This paper describes the multiobjective topology optimization of continuum structures solved as a discrete optimization problem using a multiobjective genetic algorithm (GA) with proficient constraint handling. Crucial to the effectiveness of the methodology is the use of a morphological geometry representation that defines valid structural geometries that are inherently free from checkerboard patterns, disconnected segments, or poor connectivity. A graph- theoretic chromosome encoding, together with compatible reproduction operators, helps facilitate the transmission of topological/shape characteristics across generations in the evolutionary process. A multicriterion target-matching problem developed here is a novel test problem, where a predefined target geometry is the known optimum solution, and the good results obtained in solving this problem provide a convincing demonstration and a quantitative measure of how close to the true optimum the solutions achieved by GA methods can be. The methodology is then used to successfully design a path-generating compliant mechanism by solving a multicriterion structural topology optimization problem.     

Quantum immune clonal coevolutionary algorithm for dynamic multiobjective optimization

The existing algorithms to solve dynamic multiobjective optimization (DMO) problems generally have difficulties in non-uniformity, local optimality and non-convergence. Based on artificial immune system, quantum evolutionary computing and the strategy of co-evolution, a quantum immune clonal coevolutionary algorithm (QICCA) is proposed to solve DMO problems. The algorithm adopts entire cloning and evolves the theory of quantum to design a quantum updating operation, which improves the searching ability of the algorithm. Moreover, coevolutionary strategy is incorporated in global operation and coevolutionary competitive operation and coevolutionary cooperative operation are designed to improve the uniformity, the diversity and the convergence performance of the solutions. The results on test problems and performance metrics compared with ICADMO and DBM suggest that QICCA has obvious effectiveness and advantages which shows great capability of evolving convergent, diverse and uniformly distributed Pareto fronts.     

Multi-objective dynamic optimization with genetic algorithms for automatic parking

This paper addresses the problem of automatic parking by a back-wheel drive vehicle, using a biomimetic model based on direct coupling between vehicle perceptions and actions. This problem is solved by means of a bio-inspired approach in which the vehicle controller does not need to know the car kinematics and dynamic, neither does it call for a priori knowledge of the environment map. The key point in the proposed approach is the definition of performance indices that for automatic parking happen to be functions of the strategic orientations to be injected, in real time, to the car-like robot controller. This solution leads to a dynamic multi-objective optimization problem, which is extremely hard to be dealt analytically. A genetic algorithm is therefore applied, thanks to which we obtain a very simple and efficient solution.     

Divergent exploration in design with a dynamic multiobjective optimization formulation

Formulation space exploration is a new strategy for multiobjective optimization that facilitates both divergent exploration and convergent optimization during the early stages of design. The formulation space is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into the formulation space, the solution to an optimization problem is no longer predefined by any single problem formulation, as it is with traditional optimization methods. Instead, a designer is free to change, modify, and update design objectives, variables, and constraints and explore design alternatives without requiring a concrete understanding of the design problem a priori. To facilitate this process, we introduce a new vector/matrix-based definition for multiobjective optimization problems, which is dynamic in nature and easily modified. Additionally, we provide a set of exploration metrics to help guide designers while exploring the formulation space. Finally, we provide an example to illustrate the use of this new, dynamic approach to multiobjective optimization.     

Integrated multiobjective optimization and a priori preferences using genetic algorithms

One of the tasks of decision-making support systems is to develop methods that help the designer select a solution among a set of actions, e.g. by constructing a function expressing his/her preferences over a set of potential solutions. In this paper, a new method to solve multiobjective optimization (MOO) problems is developed in which the user’s information about his/her preferences is taken into account within the search process. Preference functions are built that reflect the decision-maker’s (DM) interests and use meaningful parameters for each objective. The preference functions convert these objective preferences into numbers. Next, a single objective is automatically built and no weight selection is performed. Problems found due to the multimodality nature of a generated single cost index are managed with Genetic Algorithms (GAs). Three examples are given to illustrate the effectiveness of the method.     

MIJ2K Optimization using evolutionary multiobjective optimization algorithms

This paper deals with the multiobjective definition of video compression and its optimization. The optimization will be done using NSGA-II, a well-tested and highly accurate algorithm with a high convergence speed developed for solving multiobjective problems. Video compression is defined as a problem including two competing objectives. We try to find a set of optimal, so-called Pareto-optimal solutions, instead of a single optimal solution. The two competing objectives are quality and compression ratio maximization. The optimization will be achieved using a new patent pending codec, called MIJ2K, also outlined in this paper. Video will be compressed with the MIJ2K codec applied to some classical videos used for performance measurement, selected from the Xiph.org Foundation repository. The result of the optimization will be a set of near-optimal encoder parameters. We also present the convergence of NSGA-II with different encoder parameters and discuss the suitability of MOEAs as opposed to classical search-based techniques in this field.     

Evolutionary pattern search algorithms for unconstrained andlinearly constrained optimization

We describe a convergence theory for evolutionary pattern search algorithms (EPSA) on a broad class of unconstrained and linearly constrained problems. EPSA adaptively modify the step size of the mutation operator in response to the success of previous optimization steps. The design of EPSA is inspired by recent analyzes of pattern search methods. Our analysis significantly extends the previous convergence theory for EPSA. Our analysis applies to a broader class of EPSA and it applies to problems that are nonsmooth, have unbounded objective functions, and are linearly constrained. Further, we describe a modest change to the algorithmic framework of EPSA for which a nonprobabilistic convergence theory applies. These analyses are also noteworthy because they are considerably simpler than previous analyses of EPSA