Solving multiobjective optimization problems using quasi-separable MDO formulations and analytical target cascading

One approach to multiobjective optimization is to define a scalar substitute objective function that aggregates all objectives and solve the resulting aggregate optimization problem (AOP). In this paper, we discern that the objective function in quasi-separable multidisciplinary design optimization (MDO) problems can be viewed as an aggregate objective function (AOF). We consequently show that a method that can solve quasi-separable problems can also be used to obtain Pareto points of associated AOPs. This is useful when AOPs are too hard to solve or when the design engineer does not have access to the models necessary to evaluate all the terms of the AOF. In this case, decomposition-based design optimization methods can be useful to solve the AOP as a quasi-separable MDO problem. Specifically, we use the analytical target cascading methodology to formulate decomposed subproblems of quasi-separable MDO problems and coordinate their solution in order to obtain Pareto points of the associated AOPs. We first illustrate the approach using a well-known simple geometric programming example and then present a vehicle suspension design problem with three objectives related to ground vehicle ride and handling.     

A tutorial on multiobjective optimization: fundamentals and evolutionary methods

In almost no other field of computer science, the idea of using bio-inspired search paradigms has been so useful as in solving multiobjective optimization problems. The idea of using a population of search agents that collectively approximate the Pareto front resonates well with processes in natural evolution, immune systems, and swarm intelligence. Methods such as NSGA-II, SPEA2, SMS-EMOA, MOPSO, and MOEA/D became standard solvers when it comes to solving multiobjective optimization problems. This tutorial will review some of the most important fundamentals in multiobjective optimization and then introduce representative algorithms, illustrate their working principles, and discuss their application scope. In addition, the tutorial will discuss statistical performance assessment. Finally, it highlights recent important trends and closely related research fields. The tutorial is intended for readers, who want to acquire basic knowledge on the mathematical foundations of multiobjective optimization and state-of-the-art methods in evolutionary multiobjective optimization. The aim is to provide a starting point for researching in this active area, and it should also help the advanced reader to identify open research topics.     

The balance between proximity and diversity in multiobjective evolutionary algorithms

Over the last decade, a variety of evolutionary algorithms (EAs) have been proposed for solving multiobjective optimization problems. Especially more recent multiobjective evolutionary algorithms (MOEAs) have been shown to be efficient and superior to earlier approaches. An important question however is whether we can expect such improvements to converge onto a specific efficient MOEA that behaves best on a large variety of problems. In this paper, we argue that the development of new MOEAs cannot converge onto a single new most efficient MOEA because the performance of MOEAs shows characteristics of multiobjective problems. While we point out the most important aspects for designing competent MOEAs in this paper, we also indicate the inherent multiobjective tradeoff in multiobjective optimization between proximity and diversity preservation. We discuss the impact of this tradeoff on the concepts and design of exploration and exploitation operators. We also present a general framework for competent MOEAs and show how current state-of-the-art MOEAs can be obtained by making choices within this framework. Furthermore, we show an example of how we can separate nondomination selection pressure from diversity preservation selection pressure and discuss the impact of changing the ratio between these components.     

Comparing multiobjective swarm intelligence metaheuristics for DNA motif discovery

In recent years, a huge number of biological problems have been successfully addressed through computational techniques, among all these computational techniques we highlight metaheuristics. Also, most of these biological problems are directly related to genomic, studying the microorganisms, plants, and animals genomes. In this work, we solve a DNA sequence analysis problem called Motif Discovery Problem (MDP) by using two novel algorithms based on swarm intelligence: Artificial Bee Colony (ABC) and Gravitational Search Algorithm (GSA). To guide the pattern search to solutions that have a better biological relevance, we have redefined the problem formulation and incorporated several biological constraints that should be satisfied by each solution. One of the most important characteristics of the problem definition is the application of multiobjective optimization (MOO), maximizing three conflicting objectives: motif length, support, and similarity. So, we have adapted our algorithms to the multiobjective context. This paper presents an exhaustive comparison of both multiobjective proposals on instances of different nature: real instances, generic instances, and instances generated according to a Markov chain. To analyze their operations we have used several indicators and statistics, comparing their results with those obtained by standard algorithms in multiobjective computation, and by 14 well-known biological methods.     

分层多目标最优化进化算法

文章用进化算法给出了求解二层字典分层多目标最优化的方法,该算法把求解问题转化为多目标最优化,并研究了这两个问题的解集之间的联系。对多目标最优化定义了一个新的选择算子和适应值函数,这样定义的选择算子和适应值函数结合均匀设计能有效地引导搜索,直接求出问题的解而不用逐层求解。数值模拟表明该方法十分有效。     

Multiobjective cuckoo search for design optimization

Many design problems in engineering are typically multiobjective, under complex nonlinear constraints. The algorithms needed to solve multiobjective problems can be significantly different from the methods for single objective optimization. Computing effort and the number of function evaluations may often increase significantly for multiobjective problems. Metaheuristic algorithms start to show their advantages in dealing with multiobjective optimization. In this paper, we formulate a new cuckoo search for multiobjective optimization. We validate it against a set of multiobjective test functions, and then apply it to solve structural design problems such as beam design and disc brake design. In addition, we also analyze the main characteristics of the algorithm and their implications.     

Multiobjective optimization using population-based extremal optimization

In recent years, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied in some NP-hard combinatorial optimization problems. In this paper, we present a novel Pareto-based algorithm, which can be regarded as an extension of EO, to solve multiobjective optimization problems. The proposed method, called Multiobjective Population-based Extremal Optimization (MOPEO), is validated by using five benchmark functions and metrics taken from the standard literature on multiobjective evolutionary optimization. The experimental results demonstrate that MOPEO is competitive with the state-of-the-art multiobjective evolutionary algorithms. Thus MOPEO can be considered as a viable alternative to solve multiobjective optimization problems.     

A solution process for simulation-based multiobjective design optimization with an application in the paper industry

In this paper, we address some computational challenges arising in complex simulation-based design optimization problems. High computational cost, black-box formulation and stochasticity are some of the challenges related to optimization of design problems involving the simulation of complex mathematical models. Solving becomes even more challenging in case of multiple conflicting objectives that must be optimized simultaneously. In such cases, application of multiobjective optimization methods is necessary in order to gain an understanding of which design offers the best possible trade-off. We apply a three-stage solution process to meet the challenges mentioned above. As our case study, we consider the integrated design and control problem in paper mill design where the aim is to decrease the investment cost and enhance the quality of paper on the design level and, at the same time, guarantee the smooth performance of the production system on the operational level. In the first stage of the three-stage solution process, a set of solutions involving different trade-offs is generated with a method suited for computationally expensive multiobjective optimization problems using parallel computing. Then, based on the generated solutions an approximation method is applied to create a computationally inexpensive surrogate problem for the design problem and the surrogate problem is solved in the second stage with an interactive multiobjective optimization method. This stage involves a decision maker and her/his preferences to find the most preferred solution to the surrogate problem. In the third stage, the solution best corresponding that of stage two is found for the original problem.     

Dynamic multiobjective optimization problems: test cases, approximations, and applications

After demonstrating adequately the usefulness of evolutionary multiobjective optimization (EMO) algorithms in finding multiple Pareto-optimal solutions for static multiobjective optimization problems, there is now a growing need for solving dynamic multiobjective optimization problems in a similar manner. In this paper, we focus on addressing this issue by developing a number of test problems and by suggesting a baseline algorithm. Since in a dynamic multiobjective optimization problem, the resulting Pareto-optimal set is expected to change with time (or, iteration of the optimization process), a suite of five test problems offering different patterns of such changes and different difficulties in tracking the dynamic Pareto-optimal front by a multiobjective optimization algorithm is presented. Moreover, a simple example of a dynamic multiobjective optimization problem arising from a dynamic control loop is presented. An extension to a previously proposed direction-based search method is proposed for solving such problems and tested on the proposed test problems. The test problems introduced in this paper should encourage researchers interested in multiobjective optimization and dynamic optimization problems to develop more efficient algorithms in the near future.     

Coupling dynamic simulation and interactive multiobjective optimization for complex problems: An APROS-NIMBUS case study

Dynamic process simulators for plant-wide process simulation and multiobjective optimization tools can be used by industries as a means to cut costs and enhance profitability. Specifically, dynamic process simulators are useful in the process plant design phase, as they provide several benefits such as savings in time and costs. On the other hand, multiobjective optimization tools are useful in obtaining the best possible process designs when multiple conflicting objectives are to be optimized simultaneously. Here we concentrate on interactive multiobjective optimization. When multiobjective optimization methods are used in process design, they need an access to dynamic process simulators, hence it is desirable for them to coexist on the same software platform. However, such a co-existence is not common. Hence, users need to couple multiobjective optimization software and simulators, which may not be trivial. In this paper, we consider APROS, a dynamic process simulator and couple it with IND-NIMBUS, an interactive multiobjective optimization software. Specifically, we: (a) study the coupling of interactive multiobjective optimization with a dynamic process simulator; (b) bring out the importance of utilizing interactive multiobjective optimization; (c) propose an augmented interactive multiobjective optimization algorithm; and (d) apply an APROS-NIMBUS coupling for solving a dynamic optimization problem in a two-stage separation process.     

An introduction to goal programming with applications in urban systems

Decisions involving large-scale, complex systems, particularly those in which “society” serves as an ultimate judge of their outcome and effectiveness, also involve multiple, conflicting and noncommensurable goals. Traditional models for the representation and solution of such problems have generally been forced to ignore the multiobjective nature of such problems. As a result, we obtain “optimal” solutions to the simplified models but, since the models do not reflect the actual situation, these solutions can sometimes cause more harm than good. Since large-scale, complex and multiobjective systems are so predominate in urban systems, it is vital that any improved methodology for modeling and solution be at least considered.In this paper we direct our attention to just one of the several new approaches to multiobjective decision analysis; the tool known as goal programming. Considerable interest seems to have been generated in this area recently but the perceptions of goal programming are varied and conflicting and, all too often, erroneous.In this paper an attempt is made to present the reader with a logical structuring of multiobjective optimization and, in particular, to identify goal programming's place and role within this framework. In doing this we hope to dispel a number of myths and misconceptions that have arisen while, at the same time, present an accurate view of the scope and limitations of the methodology. While the paper is primarily tutorial, we will however, also consider the actual and potential implementation of goal programming in problems encountered in the study of urban systems.     

Interactive multiobjective decision making in environmental systems using sequential proxy optimization techniques (SPOT)

In this paper, a new interactive multiobjective decision-making technique for solving multiobjective optimization problems: the sequential proxy optimization technique (SPOT), is presented. Using this technique, the preferred solution for the decision maker can be derived efficiently from among a pareto optimal solution set by assessing his marginal rates of substitution and maximizing the local proxy preference functions sequentially. Based on the algorithm of SPOT, a time-sharing computer program is also written to implement man-machine interactive procedures. The industrial pollution control problem in Osaka City in Japan is formulated and the interaction processes are demonstrated together with the computer outputs.     

The Challenges of Multidisciplinary Education in Computer Science

Some of the most important problems facing the United States and China, indeed facing our entire planet, require approaches that are fundamentally multidisciplinary in nature. Many of those require skills in computer science (CS), basic understanding of another discipline, and the ability to apply the skills in one discipline to the problems of another. Modern training in computer science needs to prepare students to work in other disciplines or to work on multidisciplinary problems. What do we do to prepare them for a multidisciplinary world when there are already too many things we want to teach them about computer science? This paper describes successful examples of multidisciplinary education at the interface between CS and the biological sciences, as well as other examples involving CS and security, CS and sustainability, and CS and the social and economic sciences. It then discusses general principles for multidisciplinary education of computer scientists.     

Metamodels for Computer-based Engineering Design: Survey and recommendations

The use of statistical techniques to build approximations of expensive computer analysis codes pervades much of today’s engineering design. These statistical approximations, or metamodels, are used to replace the actual expensive computer analyses, facilitating multidisciplinary, multiobjective optimization and concept exploration. In this paper, we review several of these techniques, including design of experiments, response surface methodology, Taguchi methods, neural networks, inductive learning and kriging. We survey their existing application in engineering design, and then address the dangers of applying traditional statistical techniques to approximate deterministic computer analysis codes. We conclude with recommendations for the appropriate use of statistical approximation techniques in given situations, and how common pitfalls can be avoided.     

Post-optimal procedures for structural optimization

Structural optimization is a very well established design tool in several engineering fields when the problem is formulated with a single objective function and the feasible design region turns out to be convex. Nevertheless, many real problems lead to more complex formulations, sometimes because more than one local minima exist, or because more than one objective function must be included in the formulation. For such cases two procedures intended to enhance the capabilities of design optimization, namely, one approach to global optimization and a recent procedure to obtain sensitivity analysis in multiobjective optimization, are presented in the paper.     

A multiobjective approach for optimal placement and sizing of distributed generators and capacitors in distribution network

Both active and reactive power play important roles in power system transmission and distribution networks. While active power does the useful work, reactive power supports the voltage that necessitates control from system reliability aspect as deviation of voltage from nominal range may lead to inadvertent operation and premature failure of system components. Reactive power flow must also be controlled in the system to maximize the amount of real power that can be transferred across the power transmitting media. This paper proposes an approach to simultaneously minimize the real power loss and the net reactive power flow in the system when reinforced with distributed generators (DGs) and shunt capacitors (SCs). With the suggested method, the system performance, reliability and loading capacity can be increased by reduction of losses. A multiobjective evolutionary algorithm based on decomposition (MOEA/D) is adopted to select optimal sizes and locations of DGs and SCs in large scale distribution networks with objectives being minimizing system real and reactive power losses. MOEA/D is the process of decomposition of a multiobjective optimization problem into a number of scalar optimization subproblems and optimizing those concurrently. Case studies with standard IEEE 33-bus, 69-bus, 119-bus distribution networks and a practical 83-bus distribution network are performed. Output results of MOEA/D method are compared with similar past studies and notable improvement is observed.     

Approximated set-valued mapping approach for handling multiobjective bilevel problems

A significant amount of research has been done on bilevel optimization problems both in the realm of classical and evolutionary optimization. However, the multiobjective extensions of bilevel programming have received relatively little attention from researchers in both the domains. The existing algorithms are mostly brute-force nested strategies, and therefore computationally demanding. In this paper, we develop insights into multiobjective bilevel optimization through theoretical progress made in the direction of parametric multiobjective programming. We introduce an approximated set-valued mapping procedure that would be helpful in the development of efficient evolutionary approaches for solving these problems. The utility of the procedure has been emphasized by incorporating it in a hierarchical evolutionary framework and assessing the improvements. Test problems with varying levels of complexity have been used in the experiments.     

嵌入式Linux中调度算法的实现及优化

本文论述实时嵌入式Linux的多任务调度算法实现机制。结合嵌入式操作系统的特点，重点介绍基于优先级驱动嵌入式系统的一种实时调度优化算法的实现机制，讨论如何在GPL下充分利用现有的实时调度算法开发适合嵌入式Linux的优化调度方法，并提出了具体的实现思路。     

Bicriteria network design using a spanning tree-based genetic algorithm

The optimization problems in communication networks have received the attention of many researchers in such related fields as network designer, network analysis, and network administration. The use of computer communication networks has been increasing rapidly in order to share expensive hardware/software resources and provide access to main systems from distant locations. These network problems have many applications in telecommunications, computer networking, and related domains in electric, gas, and sewer networks. In computer networking, LANs (local area networks) are commonly used as the communication infrastructure that meets the demands of users in the local environment. These networks typically consist of several LAN segments connected together via bridges. The use of these transparent bridges requires.loop-free paths between LAN segments. Therefore, only spanning tree topologies can be used as active LAN configurations. Recently, genetic algorithms have greatly advanced in related research fields such as network optimization problems, combinatorial optimization, multiobjective optimization, and so on. Genetic algorithms have also received a great deal of attention because of their ability as optimization techniques for many real-world problems. In this paper, we attempt to solve the LAN topology design problem with bicriteria which minimize the cost and average message delay using genetic algorithms, and propose a method of searching the Pareto solutions. We also employ the Prüfer number in order to represent the chromosomes, because the interconnection between the network service centers must yield spanning tree configurations. Finally, we conduct experiments to certify the quality of the networks designs obtained by using genetic algorithms. This work was presented, in part, at the Third International Symposium on Artificial Life and Robotics, Oita, Japan, January 19–21, 1998     

Recent Advances in Optimal Reliability Allocation

Reliability has become a greater concern in recent years, because high-tech industrial processes with ever increasing levels of sophistication comprise most engineering systems today. To keep pace with this rapidly developing field, this paper provides a broad overview of recent research on reliability optimization problems and their solution methodologies. In particular, we address issues related to: 1) universal generating-function-based optimal multistate system design; 2) percentile life employed as a system performance measure; 3) multiobjective optimization of reliability systems, especially with uncertain component-reliability estimations; and 4) innovation and improvement in traditional reliability optimization problems, such as fault-tolerance mechanism and cold-standby redundancy-involved system design. New developments in optimization techniques are also emphasized in this paper, especially the methods of ant colony optimization and hybrid optimization. We believe that the interesting problems that are reviewed here are deserving of more attention in the literature. To that end, this paper concludes with a discussion of future challenges related to reliability optimization