Physical programming for preference driven evolutionary multi-objective optimization

Preference articulation in multi-objective optimization could be used to improve the pertinency of solutions in an approximated Pareto front. That is, computing the most interesting solutions from the designer's point of view in order to facilitate the Pareto front analysis and the selection of a design alternative. This articulation can be achieved in an a priori, progressive, or a posteriori manner. If it is used within an a priori frame, it could focus the optimization process toward the most promising areas of the Pareto front, saving computational resources and assuring a useful Pareto front approximation for the designer. In this work, a physical programming approach embedded in an evolutionary multi-objective optimization is presented as a tool for preference inclusion. The results presented and the algorithm developed validate the proposal as a potential tool for engineering design by means of evolutionary multi-objective optimization.     

Ensemble of multi-objective metaheuristic algorithms for multi-objective unconstrained binary quadratic programming problem

Metaheuristics have been widely utilized for solving NP-hard optimization problems. However, these algorithms usually perform differently from one problem to another, i.e., one may be effective on a problem but performs badly on another problem. Therefore, it is difficult to choose the best algorithm in advance for a given problem. In contrast to selecting the best algorithm for a problem, selection hyper-heuristics aim at performing well on a set of problems (instances). This paper proposes a selection hyper-heuristic based algorithm for multi-objective optimization problems. In the proposed algorithm, multiple metaheuristics exhibiting different search behaviors are managed and controlled as low-level metaheuristics in an algorithm pool, and the most appropriate metaheuristic is selected by means of a performance indicator at each search stage. To assess the performance of the proposed algorithm, an implementation of the algorithm containing four metaheuristics is proposed and tested for solving multi-objective unconstrained binary quadratic programming problem. Experimental results on 50 benchmark instances show that the proposed algorithm can provide better overall performance than single metaheuristics, which demonstrates the effectiveness of the proposed algorithm.     

求解多目标优化问题的一种多子群体进化算法

提出一种新的多目标粒子群优化（MOPSO）算法,根据多目标优化问题（MOP）的特点,将一个进化群体分成若干个子群体,利用非劣支配的概念构造全局最优区域,用以指导整个粒子群的进化．通过子群体间的信息交换．使整个群体分布更均匀,并且避免了局部最优,保证了解的多样性,通过很少的迭代次数便可得到分布均匀的Pareto有效解集．数值实验表明了该算法的有效性.     

A new boundary search scheme for topology optimization of continuum structures with design-dependent loads

The identification of the load surface is a key problem in solving topology optimization of continuum structures with design-dependent loads. In this paper, an element-based search scheme is introduced to identify the load surface. The load surfaces are formed by the connection of the real boundary of elements and the pressures are transferred directly to corresponding element nodes. The search scheme is very convenient to apply and is found to be efficient and effective in identifying the load surfaces. Only slight modifications to the load codes in the routine procedure are required and there is no need to calculate the sensitivities of the load with respect to the material density changes. Numerical examples are presented to demonstrate the efficiency of the boundary search scheme.     

Reliability analysis of spacecraft structures under static and dynamic loading

The aim of the present paper is to demonstrate that, thanks to recently proposed simulation-based methods, it is now possible to efficiently analyse the reliability of large-scale structures modelled with very large FE systems. This capability is of paramount importance for industrial applications, because the related FE models steadily grow in size and so does the number of model parameters associated with uncertainty. The analysis methods applied in this study belong to the class of advanced Monte-Carlo simulation methods, with which the computational costs induced by direct simulation can be drastically reduced. Based on the theoretical foundations of the methods, which are specifically geared towards problems featuring thousands of parameters affected by uncertainty, the present paper provides the first demonstration that these methods can be used to assess the reliability of complex structural assemblies, even for extremely high levels of reliability.The reliability analysis is performed using a refined finite element model (120,000 DOF) of a satellite, both under static and dynamic loading. For the static load case the reliability can be estimated with great efficiency, whereas for the dynamic load case the performance depends on the considered frequency range. The obtained results are very significant in that they show the feasibility of a full scale analysis of the structural reliability in a design context for large-scale structures.     

An effective ant colony optimization algorithm for multi-objective job-shop scheduling with equal-size lot-splitting

This paper proposes several novel hybrid ant colony optimization (ACO)-based algorithms to resolve multi-objective job-shop scheduling problem with equal-size lot splitting. The main issue discussed in this paper is lot-splitting of jobs and tradeoff between lot-splitting costs and makespan. One of the disadvantages of ACO is its uncertainty on time of convergence. In order to enrich search patterns of ACO and improve its performance, five enhancements are made in the proposed algorithms including: A new type of pheromone and greedy heuristic function; Three new functions of state transition rules; A nimble local search algorithm for the improvements of solution quality; Mutation mechanism for divisive searching; A particle swarm optimization (PSO)-based algorithm for adaptive tuning of parameters. The objectives that are used to measure the quality of the generated schedules are weighted-sum of makespan, tardiness of jobs and lot-splitting cost. The developed algorithms are analyzed extensively on real-world data obtained from a printing company and simulated data. A mathematical programming model is developed and paired-samples t-tests are performed between obtained solutions of mathematical programming model and proposed algorithms in order to verify effectiveness of proposed algorithms.     

Compliant mechanism design using multi-objective topology optimization scheme of continuum structures

Topology optimization problems for compliant mechanisms using a density interpolation scheme, the rational approximation of material properties (RAMP) method, and a globally convergent version of the method of moving asymptotes (GCMMA) are primarily discussed. First, a new multi-objective formulation is proposed for topology optimization of compliant mechanisms, in which the maximization of mutual energy (flexibility) and the minimization of mean compliance (stiffness) are considered simultaneously. The formulation of one-node connected hinges, as well as checkerboards and mesh-dependency, is typically encountered in the design of compliant mechanisms. A new hybrid-filtering scheme is proposed to solve numerical instabilities, which can not only eliminate checkerboards and mesh-dependency efficiently, but also prevent one-node connected hinges from occurring in the resulting mechanisms to some extent. Several numerical applications are performed to demonstrate the validity of the methods presented in this paper.     

A new multi-objective programming scheme for topology optimization of compliant mechanisms

This paper presents an alternative method in implementing multi-objective optimization of compliant mechanisms in the field of continuum-type topology optimization. The method is designated as “SIMP-PP” and it achieves multi-objective topology optimization by merging what is already a mature topology optimization method—solid isotropic material with penalization (SIMP) with a variation of the robust multi-objective optimization method—physical programming (PP). By taking advantages of both sides, the combination causes minimal variation in computation algorithm and numerical scheme, yet yields improvements in the multi-objective handling capability of topology optimization. The SIMP-PP multi-objective scheme is introduced into the systematic design of compliant mechanisms. The final optimization problem is formulated mathematically using the aggregate objective function which is derived from the original individual design objectives with PP, subjected to the specified constraints. A sequential convex programming method, the method of moving asymptotes (MMA) is then utilized to process the optimization evolvement based on the design sensitivity analysis. The main findings in this study include distinct advantages of the SIMP-PP method in various aspects such as computation efficiency, adaptability in convex and non-convex multi-criteria environment, and flexibility in problem formulation. Observations are made regarding its performance and the effect of multi-objective optimization on the final topologies. In general, the proposed SIMP-PP method is an appealing multi-objective topology optimization scheme suitable for “real world” problems, and it bridges the gap between standard topological design and multi-criteria optimization. The feasibility of the proposed topology optimization method is exhibited by benchmark examples.     

A dynamic multi-colony artificial bee colony algorithm for multi-objective optimization

This paper suggests a dynamic multi-colony multi-objective artificial bee colony algorithm (DMCMOABC) by using the multi-deme model and a dynamic information exchange strategy. In the proposed algorithm, K colonies search independently most of the time and share information occasionally. In each colony, there are S bees containing equal number of employed bees and onlooker bees. For each food source, the employed or onlooker bee will explore a temporary position generated by using neighboring information, and the better one determined by a greedy selection strategy is kept for the next iterations. The external archive is employed to store non-dominated solutions found during the search process, and the diversity over the archived individuals is maintained by using crowding-distance strategy. If a randomly generated number is smaller than the migration rate R, then an elite, defined as the intermediate individual with the maximum crowding-distance value, is identified and used to replace the worst food source in a randomly selected colony. The proposed DMCMOABC is evaluated on a set of unconstrained/constrained test functions taken from the CEC2009 special session and competition in terms of four commonly used metrics EPSILON, HV, IGD and SPREAD, and it is compared with other state-of-the-art algorithms by applying Friedman test on the mean of IGD. The test results show that DMCMOABC is significantly better than or at least comparable to its competitors for both unconstrained and constrained problems.     

A generalized evolutionary method for numerical topology optimization of structures under static loading conditions

Generalized evolutionary methods, which successively construct and solve static equilibrium problems with progressive mesh adaptation, are useful tools for defining structures that utilize their construction material to greatest effect in the finite element sense. By basing the successive element erosion upon (i) the contribution of an element to the strain energy of a structure and (ii) a certain material efficiency indicator of a structure, several weaknesses associated with previous methods have been overcome. Under static loading conditions, the strain energy contribution of an element is determined solely by the related stiffness and displacement vector. Consequently, the method is effective, and efficient when applied to problems involving such loading conditions. The efficacy of the method is demonstrated through numerical applications to the problem of optimizing the topologies of two structures, a cantilever structure and a Michell structure     

Robust and fuzzy goal programming optimization approaches for a novel multi-objective hub location-allocation problem: A supply chain overview

In this paper, a novel multi-objective mathematical model is developed to solve a capacitated single-allocation hub location problem with a supply chain overview. Three mathematical models with various objective functions are developed. The objective functions are to minimize: (a) total transportation and installation costs, (b) weighted sum of service times in the hubs to produce and transfer commodities and the tardiness and earliness times of the flows including raw materials and finished goods, and (c) total greenhouse gas emitted by transportation modes and plants located in the hubs. To come closer to reality, some of the parameters of the proposed mathematical model are regarded as uncertain parameters, and a robust approach is used to solve the given problem. Furthermore, two methods, namely fuzzy multi-objective goal programming (FMOGP) and the Torabi and Hassini's (TH) method are used to solve the multi-objective mathematical model. Finally, the concluding part presents the comparison of the obtained results.     

A bilevel integer programming method for blended composite structures

This paper proposes a new approach for the design of a composite structure. This approach is formulated as an optimization problem where the weight of the structure is minimized such that a reserve factor is higher than a threshold. The thickness of each region of the structure is optimized together with its stacking sequence and the ply drop-offs. The novelty of this approach is that, unlike in common practice, the optimization problem is not simplified and split into two steps, one for finding the thicknesses and one for the stacking sequence. The optimization problem is solved without any simplification assumption. It is formulated as a bilevel integer programming and it uses the backtracking procedure to satisfy the blending and the manufacturing rules. Some numerical experiments are performed to show the efficiency of the proposed optimization method over complex cases which cannot be solved with the existing methods.     

An effective hybrid particle swarm optimization algorithm for multi-objective flexible job-shop scheduling problem

Flexible job-shop scheduling problem (FJSP) is an extension of the classical job-shop scheduling problem. Although the traditional optimization algorithms could obtain preferable results in solving the mono-objective FJSP. However, they are very difficult to solve multi-objective FJSP very well. In this paper, a particle swarm optimization (PSO) algorithm and a tabu search (TS) algorithm are combined to solve the multi-objective FJSP with several conflicting and incommensurable objectives. PSO which integrates local search and global search scheme possesses high search efficiency. And, TS is a meta-heuristic which is designed for finding a near optimal solution of combinatorial optimization problems. Through reasonably hybridizing the two optimization algorithms, an effective hybrid approach for the multi-objective FJSP has been proposed. The computational results have proved that the proposed hybrid algorithm is an efficient and effective approach to solve the multi-objective FJSP, especially for the problems on a large scale.     

A topological derivative method for topology optimization

We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric resource constraint. A smooth and consistent projection of the region bounded by the level set onto the fictitious analysis domain simplifies the response analysis and enhances the convergence of the optimization algorithm. Moreover, the projection supports the reintroduction of solid material in void regions, a critical requirement for robust topology optimization. We present several numerical examples that demonstrate compliance minimization of fixed-volume, linearly elastic structures.     

基于拥挤度与变异的动态微粒群多目标优化算法

提出一种动态微粒群多目标优化算法(DCMOPSO),算法中的惯性权重和加速因子动态变化以增强算法的全局搜索能力,并采用拥挤度的方法对外部档案进行维护以增加非劣解的多样性.在维护过程中,从外部档案中按拥挤度为每个微粒选择全局最好位置,同时使用变异操作避免算法早熟.通过几个典型的多目标测试函数对DCMOPSO算法的性能进行了测试,并与多目标优化算法MOPSO和NSGA-Ⅱ进行对比.结果表明,DCMOPSO算法具有良好的搜索性能.     

A single front genetic algorithm for parallel multi-objective optimization in dynamic environments

This paper proposes a new parallel evolutionary procedure to solve multi-objective dynamic optimization problems along with some measures to evaluate multi-objective optimization in dynamic environments. These dynamic optimization problems appear in quite different real-world applications with actual socio-economic relevance. In these applications, the objective functions, the constraints, and hence, also the solutions, can change over time and usually demand to be solved online whilst the size of the changes is unknown. Although parallel processing could be very useful in these problems to meet the solution quality requirements and constraints, to date, not many parallel approaches have been reported in the literature. Taking this into account, we introduce a multi-objective optimization procedure for dynamic problems that are based on PSFGA, a parallel evolutionary algorithm previously proposed by us for multi-objective optimization. It uses an island model where a process divides the population among the remaining processes and allows the communication and coordination among the subpopulations in the different islands. The proposed algorithm makes an exclusive use of non-dominating individuals for the selection and variation operator and applies a crowding mechanism to maintain the diversity and the distribution of the solutions in the Pareto front. We also propose a model to understand the benefits of parallel processing in multi-objective problems and the speedup figures obtained in our experiments.     

A new hybrid approach for dynamic continuous optimization problems

A new hybrid approach for dynamic optimization problems with continuous search spaces is presented. The proposed approach hybridizes efficient features of the particle swarm optimization in tracking dynamic changes with a new evolutionary procedure. In the proposed dynamic hybrid PSO (DHPSO) algorithm, the swarm size is varied in a self-regulatory manner. Inspired from the microbial life, the particles can reproduce infants and the old ones die. The infants are especially reproduced by high potential particles and located near the local optimum points, using the quadratic interpolation method. The algorithm is adapted to perform in continuous search spaces, utilizing continuous movement of the particles and using Euclidian norm to define the neighborhood in the reproduction procedure. The performance of the new proposed approach is tested against various benchmark problems and compared with those of some other heuristic optimization algorithms. In this regard, different types of dynamic environments including periodic, linear and random changes are taken with different performance metrics such as real-time error, offline performance and offline error. The results indicate a desirable better efficiency of the new algorithm over the existing ones.     

An efficient decomposition and dual-stage multi-objective optimization method for water distribution systems with multiple supply sources

This paper proposes an efficient decomposition and dual-stage multi-objective optimization (DDMO) method for designing water distribution systems with multiple supply sources (WDS-MSSs). Three phases are involved in the proposed DDMO approach. In Phase 1, an optimal source partitioning cut-set is identified for a WDS-MSS, allowing the entire WDS-MSS to be decomposed into sub-networks. Then in Phase 2 a non-dominated sorting genetic algorithm (NSGA-II) is employed to optimize the sub-networks separately, thereby producing an optimal front for each sub-network. Finally in Phase 3, another NSGA-II implementation is used to drive the combined sub-network front (an approximate optimal front) towards the Pareto front for the original complete WDS-MSS. Four WDS-MSSs are used to demonstrate the effectiveness of the proposed approach. Results obtained show that the proposed DDMO significantly outperforms the NSGA-II that optimizes the entire network as a whole in terms of efficiently finding good quality optimal fronts.     

A multi-objective programming model for scheduling emergency medicine residents

Scheduling emergency medicine residents (EMRs) is a complex task, which considers a large number of rules (often conflicting) related to various aspects such as limits on the number of consecutive work hours, number of day and night shifts that should be worked by each resident, resident staffing requirements according to seniority levels for the day and night shifts, restrictions on the number of consecutive day and night shifts assigned, vacation periods, weekend off requests, and fair distribution of responsibilities among the residents. Emergency rooms (ERs) are stressful workplaces, and in addition shift work is well-known to be more demanding than regular daytime work. For this reason, preparing schedules that suit the working rules for EMRs is especially important for reducing the negative impact on shift workers physiologically, psychologically, and socially. In this paper, we present a goal programming (GP) model that accommodates both hard and soft constraints for a monthly planning horizon. The hard constraints should be adhered to strictly, whereas the soft constraints can be violated when necessary. The relative importance values of the soft constraints have been computed by the analytical hierarchy process (AHP), which are used as coefficients of the deviations from the soft constraints in the objective function. The model has been tested in the ER of a major local university hospital. The main conclusions of the study are that problems of realistic size can be solved quickly and the generated schedules have very high qualities compared to the manually prepared schedules, which require a lot of effort and time from the chief resident who is responsible for this duty.     

Multi-objective optimization of the stack of a thermoacoustic engine using GAMS

This work illustrates the use of a multi-objective optimization approach to model and optimize the performance of a simple thermoacoustic engine. System parameters and constraints that capture the underlying thermoacoustic dynamics have been used to define the model. Work output, viscous loss, conductive heat loss, convective heat loss and radiative heat loss have been used to measure the performance of the engine. The optimization task is formulated as a five-criterion mixed-integer non-linear programming problem. Since we optimize multiple objectives simultaneously, each objective component has been given a weighting factor to provide appropriate user-defined emphasis. A practical example is given to illustrate the approach. We have determined a design statement of a stack describing how the design would change if emphasis is given to one objective in particular. We also considered optimization of multiple objectives components simultaneously and identify global optimal solutions describing the stack geometry using the augmented ɛ-constraint method. This approach has been implemented in GAMS (General Algebraic Modelling System).