Constrained multi-objective optimization algorithms: Review and comparison with application in reinforced concrete structures

Engineering design problems are often multi-objective in nature, which means trade-offs are required between conflicting objectives. In this study, we examine the multi-objective algorithms for the optimal design of reinforced concrete structures. We begin with a review of multi-objective optimization approaches in general and then present a more focused review on multi-objective optimization of reinforced concrete structures. We note that the existing literature uses metaheuristic algorithms as the most common approaches to solve the multi-objective optimization problems. Other efficient approaches, such as derivative-free optimization and gradient-based methods, are often ignored in structural engineering discipline. This paper presents a multi-objective model for the optimal design of reinforced concrete beams where the optimal solution is interested in trade-off between cost and deflection. We then examine the efficiency of six established multi-objective optimization algorithms, including one method based on purely random point selection, on the design problem. Ranking and consistency of the result reveals a derivative-free optimization algorithm as the most efficient one.     

Population-based optimization in structural engineering: a review

Structural engineering is focused on the safe and efficient design of infrastructure. Projects can range in size and complexity, many requiring massive amounts of materials and expensive construction and operational costs. Therefore, one of the primary objectives for structural engineers is a cost-effective design. Incorporating optimality criteria into the design procedure introduces additional complexities that result in problems that are nonlinear, nonconvex, and have a discontinuous solution space. Population-based optimization algorithms (known as metaheuristics) have been found to be very efficient approaches to these problems. Many researchers have developed and applied state-of-art metaheuristics to automate and optimize the design of real-world civil engineering problems. While there is a large body of published papers in this area, there are few comprehensive reviews that list, summarize, and categorize metaheuristic optimization in structural engineering. This paper provides an extensive survey of a wide range of metaheuristic techniques to structural engineering optimization problems. Also, information is provided on available structural engineering benchmark problems, the formulation of different objective functions, and the handling of various types of constraints. The performance of different optimization techniques is compared for many benchmark problems.

     

Multi-objective optimization with artificial weed colonies

Invasive Weed Optimization (IWO) was recently proposed as a simple but powerful metaheuristic algorithm for real parameter optimization. IWO draws inspiration from the ecological process of weeds colonization and distribution and is capable of solving general multi-dimensional, linear and nonlinear optimization problems with appreciable efficiency. This article extends the basic IWO for tackling multi-objective optimization problems that aim at achieving two or more objectives (very often conflicting) simultaneously. The concept of fuzzy dominance has been used to sort the promising candidate solutions at each iteration. The new algorithm has been shown to be statistically significantly better than some state of the art existing evolutionary multi-objective algorithms, namely NSGAIILS, DECMOSA-SQP, MOEP, Clustering MOEA, GDE3, and MOEADGM on a 12-function test-suite (including both unconstrained and constrained problems) from the IEEE CEC (Congress on Evolutionary Computation) 2009 competition and special session on multi-objective optimization algorithms. The following performance metrics were considered: IGD, Spacing, and Minimum Spacing. Our experimental results suggest that IWO holds immense promise to appear as an efficient metaheuristic for multi-objective optimization.     

A hybrid approach for multi-objective combinatorial optimisation problems in ship design and shipping

Numerous real-world problems relating to ship design and shipping are characterised by combinatorially explosive alternatives as well as multiple conflicting objectives and are denoted as multi-objective combinatorial optimisation (MOCO) problems. The main problem is that the solution space is very large and therefore the set of feasible solutions cannot be enumerated one by one. Current approaches to solve these problems are multi-objective metaheuristics techniques, which fall in two categories: population-based search and trajectory-based search. This paper gives an overall view for the MOCO problems in ship design and shipping where considerable emphasis is put on evolutionary computation and the evaluation of trade-off solutions. A two-stage hybrid approach is proposed for solving a particular MOCO problem in ship design, subdivision arrangement of a ROPAX vessel. In the first stage, a multi-objective genetic algorithm method is employed to approximate the set of pareto-optimal solutions through an evolutionary optimisation process. In the subsequent stage, a higher-level decision-making approach is adopted to rank these solutions from best to worst and to determine the best solution in a deterministic environment with a single decision maker.     

Multi-objective two-sided mixed-model assembly line balancing using particle swarm optimisation with negative knowledge

Particle swarm optimisation (PSO) is an evolutionary metaheuristic inspired by the swarming behaviour observed in flocks of birds. The applications of PSO to solve multi-objective discrete optimisation problems are not widespread. This paper presents a PSO algorithm with negative knowledge (PSONK) to solve multi-objective two-sided mixed-model assembly line balancing problems. Instead of modelling the positions of particles in an absolute manner as in traditional PSO, PSONK employs the knowledge of the relative positions of different particles in generating new solutions. The knowledge of the poor solutions is also utilised to avoid the pairs of adjacent tasks appearing in the poor solutions from being selected as part of new solution strings in the next generation. Much of the effective concept of Pareto optimality is exercised to allow the conflicting objectives to be optimised simultaneously. Experimental results clearly show that PSONK is a competitive and promising algorithm. In addition, when a local search scheme (2-Opt) is embedded into PSONK (called M-PSONK), improved Pareto frontiers (compared to those of PSONK) are attained, but longer computation times are required.     

Multi-directional local search

This paper introduces multi-directional local search, a metaheuristic for multi-objective optimization. We first motivate the method and present an algorithmic framework for it. We then apply it to several known multi-objective problems such as the multi-objective multi-dimensional knapsack problem, the bi-objective set packing problem and the bi-objective orienteering problem. Experimental results show that our method systematically provides solution sets of comparable quality with state-of-the-art methods applied to benchmark instances of these problems, within reasonable CPU effort. We conclude that the proposed algorithmic framework is a viable option when solving multi-objective optimization problems.     

An objective reduction algorithm using representative Pareto solution search for many-objective optimization problems

In recent years, many-objective optimization problems (i.e. more than three objectives) have attracted the interests of many researchers. The main difficulties of many-objective optimization problems lie in high computational cost, stagnation in search process, etc. It is almost impossible to design an algorithm effective for all problems. However, for some problems, especially for problems with redundant objectives, it is possible to design effective algorithms by removing the redundant objectives and keeping the non-redundant objectives so that the original problem becomes the one with much fewer objectives. To do so, first, a multi-objective evolutionary algorithm-based decomposition is adopted to generate a smaller number of representative non-dominated solutions widely distributed on the Pareto front. Then the conflicting objective pairs are identified through these non-dominated solutions, and the redundant objectives are determined by these pairs and then removed. Based on these, a fast non-redundant objectives generation algorithm is proposed in this paper. Finally, the experiments are conducted on a set of benchmark test problems and the results indicate the effectiveness and efficiency of the proposed algorithm.     

Multi-objective nonlinear predictive control of process systems: A dual-mode tracking control approach

There typically exist different and often conflicting control objectives, e.g., reference tracking, robustness and economic performance, in many chemical processes. The current work considers the multi-objective control problems of continuous-time nonlinear systems subject to state and input constraints and multiple conflicting objectives. We propose a new multi-objective nonlinear model predictive control (NMPC) design within the dual-mode paradigm, which guarantees stability and constraint satisfaction. The notions of utopia point and compromise solution are used to reconcile the confliction of the multiple objectives. The designed controller minimizes the distance of its cost vector to a vector of independently minimized objectives, i.e., the steady-state utopia point. Recursive feasibility is established via a particular terminal region formulation while stabilizing the closed-loop system to the compromise solution via the dual-mode control principle. In order to derive the terminal region as large as possible, a terminal control law with free-parameters is constructed by using the control Lyapunov functions (CLFs) technique. Two examples of multi-objective control of a CSTR and a free-radical polymerization process are used to illustrate the effectiveness of the new multi-objective NMPC and to compare their performance.     

A multi objective volleyball premier league algorithm for green scheduling identical parallel machines with splitting jobs

Parallel machine scheduling is one of the most common studied problems in recent years, however, this classic optimization problem has to achieve two conflicting objectives, i.e. minimizing the total tardiness and minimizing the total wastes, if the scheduling is done in the context of plastic injection industry where jobs are splitting and molds are important constraints. This paper proposes a mathematical model for scheduling parallel machines with splitting jobs and resource constraints. Two minimization objectives - the total tardiness and the number of waste - are considered, simultaneously. The obtained model is a bi-objective integer linear programming model that is shown to be of NP-hard class optimization problems. In this paper, a novel Multi-Objective Volleyball Premier League (MOVPL) algorithm is presented for solving the aforementioned problem. This algorithm uses the crowding distance concept used in NSGA-II as an extension of the Volleyball Premier League (VPL) that we recently introduced. Furthermore, the results are compared with six multi-objective metaheuristic algorithms of MOPSO, NSGA-II, MOGWO, MOALO, MOEA/D, and SPEA2. Using five standard metrics and ten test problems, the performance of the Pareto-based algorithms was investigated. The results demonstrate that in general, the proposed algorithm has supremacy than the other four algorithms.

     

Bio-inspired optimization for the molecular docking problem: State of the art,recent results and perspectives

Molecular docking is a Bioinformatics method based on predicting the position and orientation of a small molecule or ligand when it is bound to a target macromolecule. This method can be modeled as an optimization problem where one or more objectives can be defined, typically around an energy scoring function. This paper reviews developments in the field of single- and multi-objective meta-heuristics for efficiently addressing molecular docking optimization problems. We comprehensively analyze both problem formulations and applied techniques from Evolutionary Computation and Swarm Intelligence, jointly referred to as Bio-inspired Optimization. Our prospective analysis is supported by an experimental study dealing with a molecular docking problem driven by three conflicting objectives, which is tackled by using different multi-objective heuristics. We conclude that genetic algorithms are the most widely used techniques by far, with a noted increasing prevalence of particle swarm optimization in the last years, being these last techniques particularly adequate when dealing with multi-objective formulations of molecular docking problems. We end this experimental survey by outlining future research paths that should be under target in this vibrant area.     

多目标优化在特征选择子集评价中的应用

特征选择是处理高维大数据常用的降维手段,但其中牵涉到的多个彼此冲突的特征子集评价目标难以平衡。为综合考虑特征选择中多种子集评价方式间的折中,优化子集性能,提出一种基于子集评价多目标优化的特征选择框架,并重点对多目标粒子群优化（MOPSO）在特征子集评价中的应用进行了研究。该框架分别根据子集的稀疏度、分类能力和信息损失度设计多目标优化函数,继而基于多目标优化算法进行特征权值向量寻优,并通过权值向量Pareto解集膝点选取确定最优向量,最终实现基于权值向量排序的特征选择。设计实验对比了基于多目标粒子群优化算法的特征选择（FS_MOPSO）与四种经典方法的性能,多个数据集上的结果表明,FS_MOPSO在低维空间表现出更高的分类精度,并保证了更少的信息损失。     

An exploratory study of mono and multi-objective metaheuristics to ensemble of classifiers

This paper performs an exploratory study of the use of metaheuristic optimization techniques to select important parameters (features and members) in the design of ensemble of classifiers. In order to do this, an empirical investigation, using 10 different optimization techniques applied to 23 classification problems, will be performed. Furthermore, we will analyze the performance of both mono and multi-objective versions of these techniques, using all different combinations of three objectives, classification error as well as two important diversity measures to ensembles, which are good and bad diversity measures. Additionally, the optimization techniques will also have to select members for heterogeneous ensembles, using k-NN, Decision Tree and Naive Bayes as individual classifiers and they are all combined using the majority vote technique. The main aim of this study is to define which optimization techniques obtained the best results in the context of mono and multi-objective as well as to provide a comparison with classical ensemble techniques, such as bagging, boosting and random forest. Our findings indicated that three optimization techniques, Memetic, SA and PSO, provided better performance than the other optimization techniques as well as traditional ensemble generator (bagging, boosting and random forest).     

A multi-objective GRASP for partial classification

Metaheuristic algorithms have been used successfully in a number of data mining contexts and specifically in the production of classification rules. Classification rules describe a class of interest or a subset of this class, and as such may also be used as an aid in prediction. The production and selection of classification rules for a particular class of the database is often referred to as partial classification. Since partial classification rules are often evaluated according to a number of conflicting objectives, the generation of such rules is a task that is well suited to a multi-objective (MO) metaheuristic approach. In this paper we discuss how to adapt well known MO algorithms for the task of partial classification. Additionally, we introduce a new MO algorithm for this task based on a greedy randomized adaptive search procedure (GRASP). GRASP has been applied to a number of problems in combinatorial optimization, but it has very seldom been used in a MO setting, and generally only through repeated optimization of single objective problems, using either linear combinations of the objectives or additional constraints. The approach presented takes advantage of some specific characteristics of the data mining problem being solved, allowing for the very effective construction of a set of solutions that form the starting point for the local search phase of the GRASP. The resulting algorithm is guided solely by the concepts of dominance and Pareto-optimality. We present experimental results for our partial classification GRASP and other MO metaheuristics. These show that such algorithms are generally very well suited to this data mining task and furthermore, the GRASP brings additional efficiency to the search for partial classification rules.     

Integrating a multi-objective optimization framework into a structural design software

In this paper, we present a tool combining two software applications aimed at optimizing structural design problems of the civil engineering domain. Our approach lies in integrating an application for designing 2D and 3D bar structures, called Ebes, with the jMetal multi-objective optimization framework. The result is a software package that helps civil engineers to create bar structures which can be optimized further with multi-objective metaheuristics according to different goals, such as minimizing the structure weight and minimizing the deformation. The main features of both Ebes and jMetal are described and how they are combined together in one single tool is explained. Finally a case study to illustrate how the application works is presented.     

Multi-objective optimization of water distribution systems based on a real options approach

This paper describes a multi-objective optimization model including Real Options concepts for the design and operation of water distribution networks. This approach is explained through a case study with some possible expansion areas defined to fit different future scenarios. A multi-objective decision model with conflicting objectives is detailed. Also, environmental impacts are considered that take into account not only the life cycle carbon emissions of the different materials used during the construction of the networks but also the emissions related to energy consumption during operation. These impacts are translated by giving a cost to each tonne of carbon dioxide emitted. This work presents a new multi-objective simulated annealing algorithm linked to a hydraulic simulator to verify the hydraulic constraints, and the results are represented as points on the Pareto front. The results show that the approach can deal explicitly with conflicting objectives, with environmental impacts and with future uncertainty.     

Self-adaptive differential evolution algorithm with α-constrained-domination principle for constrained multi-objective optimization

Real-world problems are inherently constrained optimization problems often with multiple conflicting objectives. To solve such constrained multi-objective problems effectively, in this paper, we put forward a new approach which integrates self-adaptive differential evolution algorithm with α-constrained-domination principle, named SADE-αCD. In SADE-αCD, the trial vector generation strategies and the DE parameters are gradually self-adjusted adaptively based on the knowledge learnt from the previous searches in generating improved solutions. Furthermore, by incorporating domination principle into α-constrained method, α-constrained-domination principle is proposed to handle constraints in multi-objective problems. The advantageous performance of SADE-αCD is validated by comparisons with non-dominated sorting genetic algorithm-II, a representative of state-of-the-art in multi-objective evolutionary algorithms, and constrained multi-objective differential evolution, over fourteen test problems and four well-known constrained multi-objective engineering design problems. The performance indicators show that SADE-αCD is an effective approach to solving constrained multi-objective problems, which is basically enabled by the integration of self-adaptive strategies and α-constrained-domination principle.     

A decision support system for cyclic master surgery scheduling with multiple objectives

This paper presents a decision support system for cyclic master surgery scheduling and describes the results of an extensive case study applied in a medium-sized Belgian hospital. Three objectives are taken into account when building the master surgery schedule. First of all, the resulting bed occupancy at the hospitalization units should be leveled as much as possible. Second, a particular operating room is best allocated exclusively to one group of surgeons having the same speciality; i.e., operating rooms should be shared as little as possible between different surgeon groups. Third, the master surgery schedule is preferred to be as simple and repetitive as possible, with few changes from week to week. The system relies on mixed integer programming techniques involving the solution of multi-objective linear and quadratic optimization problems, and on a simulated annealing metaheuristic.     

Multi-objective colonial competitive algorithm for hybrid flowshop problem

This study analyses the multi-objective optimization in hybrid flowshop problem, in which two conflicting objectives, makespan and total weighted tardiness, are considered to be minimized simultaneously. The multi-objective version of Colonial Competitive Algorithm (CCA) for real world optimization problem is introduced and investigated. In contrast to multi-objective problems solved by CCA, presented in the literature, which used the combination of the objectives as single objective, the proposed algorithm is established on Pareto solutions concepts. Another novelty of this paper is estimating the power of each imperialist by a probabilistic criterion for this multi objective algorithm. Besides that, the variable neighborhood search is implemented as an assimilation strategy. Performance of the algorithm is finally compared with a famous algorithm for scheduling problem, NSGA-II, and the multi-objective form of CCA [28].     

基于多目标进化算法的手机概念设计优化

针对手机设计领域应用计算机辅助设计存在的一些问题,以及如何处理相互冲突的多目标间的优化问题,深入地分析了概念设计过程中的创新思维和多目标优化的基本理论.在手机概念设计阶段同时考虑了用户要求.构件设计属性.设计成本和综合评价值等多种因素,将分布估计算法应该于求解手机集成的多目标优化问题,给出了具体的方法和步骤.实验结果表明,该方法可以提高设计的创新性,给设计人员提供有益的借鉴.