Multi-objective Design Problem Research Articles

A multi-objective meta-heuristic approach for transit network design and frequency setting problem in a bus transit system

This paper studies a multi-objective transit network design and frequency setting (TNDFS) problem with the aim of determining a set of routes and frequency on each route for public buses. The TNDFS problem is solved in two stages. First, the transit network design problem is solved to generate a set of routes using an initial route set generation (IRSG) procedure combined with genetic algorithm. Second, the frequency setting problem is formulated as a multi-objective model to assign the frequency on each route with the objectives of minimizing the passenger time and the operating cost simultaneously. This problem is solved using the multi-objective particle swarm optimization with multiple search strategies (MMOPSO) to generate a Pareto-Front between the passenger time and the operating cost. An extensive computational experiment is performed on the benchmark Mandl’s Swiss network (Mandl, 1980) considering different scenarios and instances. The results obtained using the proposed approach to solve the transit network design problem are compared with that of the state-of-the-art methodologies available in the literature (Arbex & Cunha, 2015; Kechagiopoulos & Beligiannis, 2014; Nikolić & Teodorović, 2013), which outperforms in terms of trip directness and average travel time of passengers. For the frequency setting problem, the solutions obtained using MMOPSO are justified over the NSGA-II.

A node-depth phylogenetic-based artificial immune system for multi-objective Network Design Problems

Abstract Network Design Problems (NDP) constitute a traditional class of combinatorial optimization problems. They usually rely on finding an optimal tree on a graph that respects the particular constraints of the problem at hand. When using evolutionary algorithms to solve NDP, one can use specific encodings to represent a tree. A newly proposed tree encoding in the literature is the Node-depth Phylogenetic-based encoding (NPE), which possess small time and space complexity, among other desirable characteristics. In this work, we propose the first metaheuristic on the literature that implements the NPE, the Node-depth Phylogenetic-based Non-dominated Sorting Artificial Immune System (NPE-NSAIS). We assess the quality of the proposed algorithm by solving a bi-objective NDP, the Minimum-Cost Bounded-Error Calibration Tree problem (MBCT). Our results reveal that the NPE-NSAIS outperforms the state-of-the-art algorithm for the MBCT. Moreover, we show that the NPE-NSAIS outperforms three other NSAIS algorithms that employ different encodings, the NSGA-II, and the SPEA2.

A New Model for the Multi-Objective Multiple Allocation Hub Network Design and Routing Problem

In this paper, we propose a new model for the multi-objective multiple allocation hub network design and routing problem which contains determining the location of hubs, the design of hub network, and the routing of commodities between source-destination pairs in the given network. The selected hubs are not assumed to be fully connected, and each node and arc in the network has capacity constraints. The multiple objectives of the problem are the minimization of total fixed and transportation costs and the minimization of the maximum travel time required for routing. We propose a mathematical formulation for the multi-objective problem and present a meta-heuristic solution based on a well-known multi-objective evolutionary algorithm. Using the proposed formulation, we are able to find the optimal solution for small networks of five nodes and seven nodes. To evaluate the performance of our heuristic approach on real data, the computational experiments are conducted on Turkish postal system data set. The results demonstrate that our heuristic approach can find feasible solutions to the problem in reasonable execution time, which is less than 10 min.

A Goal Programming Embedded Genetic Algorithm for Multi-objective Manufacturing Cell Design

In this paper, a multi-objective manufacturing cell design problem is studied. A goal programming (GP) embedded real-coded genetic algorithm (GA) is designed for solving this problem. Initially, the GA is used to obtain the individual minimum of each objective. Thereafter, utilising the concepts of GP, an equivalent problem is derived, and the sum of deviation variables associated with the objectives are minimised. The GA is used further to obtain the optimal cell design. A software toolkit is developed based on the proposed technique using C Sharp.net to ensure its use in a larger scale. The effectiveness of the technique is judged based on a set of test problems of different sizes. The proposed technique is found to be better in terms of the performance measure over the existing ones.

Design and Experimental Validation of a Robust Output Feedback Control for the Coupled Dynamics of a Micro Air Vehicle

This paper addresses the design and experimental validation of a linear robust static output feedback controller for a 150 mm span fixed wing micro air vehicle (MAV). Severe coupling between longitudinal and lateral dynamics of the MAV lead to the design of a multivariable controller for the combined dynamics. The control design problem is posed in the framework of static output feedback (SOF) due to the inexpensive computational requirements for implementation. The multiobjective control design problem including stability requirements, closed loop damping ratio requirements and H∞ norm minimization is solved using the hybrid technique of linear matrix inequalities (LMI) and genetic algorithm (GA). The design is carried out in the discrete time domain, facilitating in direct implementation of the multivariable controller in the onboard autopilot hardware. The robustness of the resulting closed loop system under parametric uncertainties is evaluated using structured singular value analysis. The effectiveness of the proposed controller is demonstrated through outdoor flight trial of the micro air vehicle with a customized lightweight autopilot hardware.

Mixed-Integer Distributed Ant Colony Multi-Objective Optimization of Single-Tuned Passive Harmonic Filter Parameters

The extended ant colony known as the Mixed Integer Distributed Ant Colony Optimization (MIDACO) is presented in this paper as a new application of solving multi-objective single-tuned passive filters design problems. This paper presents a new non-dominated solution for the optimization of four independent objective functions which are maximized power factor, minimized total harmonic voltage distortion, minimized total demand distortion, and minimized investment cost of the filter. The global solution is achieved by maintaining the quality factor of the filter in a specified range, avoiding the harmonic resonance and maintaining the capacitor's capability limits within the standard limits. The attained parameters of the filter are used to weigh the performance of the system, and the robustness of the proposed algorithm is verified by comparing the results with three different highly competitive evolutionary techniques. Also, the proposed algorithm attains the Pareto front of the problem and tolerates the selection of its parameters to the most effective solution. The numerical results specify the comprehensive passive filter design through possible multi-objective approaches, and the improvements of multi-objective over single-objective optimization are also presented in this paper.

Surrogate-based optimization for multi-objective toll design problems

Abstract The toll design problem (TDP) provides a quantitative approach to the design of road pricing schemes. Its practical use, however, can be computationally challenging if the formulated TDP requires time-consuming computer models to evaluate candidate designs, especially if such designs must account for multiple objectives. For TDPs to be of practical relevance to the real-world planning of sustainable transportation networks, efficient TDP solution heuristics must be developed. To this end, two surrogate-based solution heuristics for multi-objective TDPs are proposed in this paper. Surrogate-based optimization uses simple approximations to computationally expensive models in order to accelerate the discovery of good solutions. The general search strategy of the proposed heuristics is as follows. In each iteration of the heuristics, a pool of candidate pricing schemes with unique sets of tolling locations and associated tolling levels is generated. From this pool of designs, the heuristics use the surrogate models to screen for solutions that are expected to be nondominated and that meet a specified selection criterion. Then, these promising designs are evaluated by the computationally expensive models, and the outputs obtained from these evaluations are used to update the surrogate models. Both heuristics repeat this general process until a maximum number of iterations are completed, at which point the best TDP solutions are returned. In addition to the solution heuristics, this paper presents a transportation network paradox that highlights how transportation network interventions intended to reduce traffic emissions could have unintended effects on a population’s exposure to pollutants. The paradox also is used to illustrate the practical complexity of accounting for environmental inequality objectives, as well as the relevance of multi-objective analysis approaches to transportation planning. Formulations of multi-objective TDPs that consider both travel and pollutant exposure-related objectives are also presented, including the objectives of reducing human intake of vehicle-generated air pollutants and of minimizing environmental inequality. The Sioux Falls and Chicago Sketch networks were used in tests that examined the relative performance of the heuristics, as well as the characteristics of pricing configurations obtained under different budget constraints. Among other results, the tests show that a pricing configuration could decrease total pollutant intake and environmental inequality, while at the same time producing an increase in pollutant concentrations in a significant number of pollutant receptor points.

Discrete Sine-Cosine Algorithm (DSCA) with Local Search for Solving Traveling Salesman Problem

One of the new population-based optimization algorithms, named sine-cosine algorithm (SCA), is introduced to solve continuous optimization problems. SCA utilizes the sine and cosine functions to recast a set of potential solutions to balance between exploration and exploitation in the search space. Many researchers have developed and introduced a modified version of SCA to solve engineering problems, multi-objective version of SCA to solve multi-objective engineering design problems, and a binary version of SCA to deal with datasets. Our goal from this work to propose discrete SCA (DSCA) to solve the traveling salesman problem (TSP). The TSP is one of the typical NP-hard problems. DSCA works on the basic concepts of exploration and exploitation. To balance the exploration and exploitation in DSCA, it uses two different mathematical expressions to update the solutions in each generation. DSCA is combined with 2-opt local search method to improve exploitation. To enhance the exploration heuristic crossover, it is united with the proposed DSCA. A benchmarks problem selected from TSPLIB is used to test the algorithm, and the results show that the DSCA algorithm proposed in this article is comparable with the other state-of-the-art algorithms over a wide range of TSP.

Measuring surplus capacity for multiobjective optimal design of foul sewer systems

ABSTRACTThis paper proposes a new performance index of foul sewer systems, i.e. sewer conveyance capacity (SCC) index, to quantify the surplus capacity for multi-objective optimization design problems. The use of the new SCC index is demonstrated using a hypothetical network and a real-world foul sewer network. Results obtained show clear trade-offs between SCC and the other two objectives considered, i.e., capital and operational costs and greenhouse gas emissions. The results show that the upstream sewers in the system often have a relatively large surplus capacity, while the sewer mains operate close to the design capacity. Moreover, SCC is compared with three common indicators at both individual sewer and system-wide levels. Strong correlations between SCC and other indicators are revealed, implying that SCC is a good representation of system performance and can provide a more comprehensive picture of the foul sewer system performance.

A sequential LMI approach to design a BMI-based multi-objective nonlinear observer

An observer for a nonlinear system may be required to satisfy multiple performance criteria such as minimum convergence rate and disturbance rejection, in addition to asymptotic stability. In such cases, the observer can no longer be designed using a linear matrix inequality. A bilinear matrix inequality (BMI) is needed instead and involves a non-separable product of the observer gain matrices and the Lyapunov positive definite matrix. This paper develops a technique to solve a BMI for such a multi-objective observer design problem. The BMI design condition is transformed into an eigenvalue problem and a convex-concave based sequential linear matrix inequality (LMI) optimization method is used to find a feasible solution to the BMI. The developed observer design method is applied to a robust automotive slip angle estimation problem, where the L2 gain from the disturbance to the observer error is restricted be lower than 0.2 and the estimated states converges to the neighborhood of the real states within 0.3 s in the presence of uncertain vehicle dynamics.

A multiple lifecycle-based approach to sustainable product configuration design

Research on end-of-life (EoL) product recovery has focused on adopting reuse, remanufacturing, and/or recycling after product use. These product EoL strategies need to be considered early during product design in order to reduce the total lifecycle cost, minimize environmental impact, and enhance overall product sustainability. Considering the implementation of such EoL strategies across multiple lifecycles of a product will enable maximum recovery of the materials and embedded energy from previous lifecycle products for use in subsequent lifecycle products. Such practices can help companies increase global manufacturing competitiveness and promote corporate social responsibility for more sustainable economic growth. However, a multi-lifecycle based approach to product configuration design optimization, simultaneously considering conflicting objectives, has not been well addressed in previous studies. In this study, a multi-lifecycle based methodology is proposed to solve multi-objective product configuration design problems considering conflicting economic and environmental objectives. The methodology addresses issues across all the lifecycle stages, from extracting raw materials to product EoL recovery (i.e., pre-manufacturing, manufacturing, use, and post-use), and the entire demand cycle. The multi-objective optimization problem can be solved by introducing a non-dominated sorting genetic algorithm II using which various product design solutions can be generated by considering the tradeoff between several objectives. The proposed methodology is implemented on an industrial case study for the configuration design of toner cartridges. The Pareto optimal solutions yield better economic and environmental performances compared to the performance of the base toner cartridge. The results show that following the multi-lifecycle based approach to implement EoL strategies (i.e., reuse, remanufacturing, and recycling) could provide over 20% savings in total lifecycle cost, total global warming potential, and total water use in comparison to the same product configuration made up with entirely new components.

An enhanced genetic algorithm–based multi-objective design optimization strategy

In this study, an enhanced genetic algorithm is proposed to solve multi-objective design and optimization problems in practical engineering. In the given approach, designers choose available design results from the given samples first. These samples are re-ordered according to their mutual relationships. After that, designers choose an exact ratio of conformity as available field. Furthermore, more weight information can be obtained through finding the minimum value of the norm of unconformity and satisfactory samples. These samples can be used to reflect the preference chosen for Pareto design solutions. A structure design problem of speed increaser used in wind turbine generator systems is solved to show the application of the given design strategy.

Vibration Suppression of a Single-Cylinder Engine by Means of Multi-objective Evolutionary Optimisation

This paper presents a new design strategy for the passive vibration suppression of a single-cylindrical engine (SCE) through multi-objective evolutionary optimisation. The vibration causes machine damages and human pain, which are unsustainable problemsthat need to be alleviated. Mathematical forced vibration analyses of a single-cylinder engine, including dynamic pressure force due to ignition combustion, are presented. A multi-objective design problem is set to find the shape and size variables of the crank and connecting rod of the engine. The objective functions consist of the minimisation of the crank and connecting rod mass, and the minimisation of vibration response while the SCE is subject to inertial force and pressure force. Moreover, design constraints include crank and rod safety. The design problem is tackled by using an adaptation of a hybrid of multi-objective population-based incremental learning and differential evolution (RPBIL-DE). The optimum results found that the proposed design strategy is a powerful tool for the vibration suppression of SCE.

Optimal multiobjective design of a vehicle restraint system using pre-acting control

Purpose The purpose of this paper is to perform the limiting performance analysis of a vehicle restraint system (seat belt) in order to find the optimal control force, and its pre-acting time that minimizes the risk of injury. Design/methodology/approach A discrete model of the human thorax is used. A multiobjective optimum design problem is formulated in order to minimize the risk of injuries in case of impact. Several injury criteria are minimized and are required to remain below a safety threshold value. Findings The authors found which of the objectives are contradictory and which are not. Several of the optimal sets of design variables are analyzed and their performance compared to one another. The results are also compared to the case of not taking in account the pre-acting time. As expected, the results in this case are worse. Research limitations/implications As with all limiting performance analysis, the technological implementation restraints of the control force are not taken into account. As such, the solutions must be considered a benchmark to which the actual solution can be compared to. Practical implications The limiting performance analysis concept allows us to have a theoretical benchmark to which the real control performance can be compared to. Originality/value As far as the authors know, the pre-acting time, and its implications on the improvement of the performance of the control system, is an original contribution to the problem the authors tried to solve.

An efficient evolutionary algorithm for engineering design problems

This study introduces a multi-objective version of the recently proposed colonial competitive algorithm (CCA) called multi-objective colonial competitive algorithm. In contrast to original CCA, which used the combination of the objective functions to solve multi-objective problems, the proposed algorithm incorporates the Pareto concept to store simultaneously optimal solutions of multiple conflicting functions. Another novelty of this paper is the integration of the variable neighborhood search as an assimilation strategy, in order to improve the performance of the obtained solutions. To prove the effectiveness of the proposed algorithm, a set of standard test functions with high dimensions and some multi-objective engineering design problems are investigated. The results obtained amply demonstrate that the proposed approach is efficient and is able to yield a wide spread of solutions with good convergence to true Pareto fronts, compared with other proposed methods in the literature.

A multi-objective integrated model for selecting, scheduling, and budgeting road construction projects

In this paper, an integrated ‎model for selecting, scheduling, and budgeting urban road construction projects is introduced as a ‎multi-objective time-dependent ‎bi-level network design problem. Three criteria are considered as upper-level objective functions: total travel time, user satisfaction over time, and spatial ‎equity. Two new measures are developed to ‎assess network design scenarios from the perspectives of user satisfaction over time and spatial ‎equity. Given the great complexity of the intended problem, two multi-objective evolutionary approaches (an interactive and a-posteriori) are proposed to solve the model in a reasonable time. These two approaches are novel combinations of ‎different techniques, such as: Genetic Algorithm (GA), Non-dominated Sorting Genetic Algorithm (NSGA-II), Frank-Wolfe algorithm, ‎ordered logit model, and knees identification algorithm. Computational results for various test problems ‎show that proposed approaches have acceptable performance in terms of both‎ solution quality and ‎solution time.‎ ‎To show applicability of the proposed approach in large-sized networks, it is applied to a real case on Isfahan City in Iran.

A novel multi-objective optimization algorithm based on artificial algae for multi-objective engineering design problems

There are many diverse fields and applications such as data mining, engineering, operations research, economics, and science can be formulated as multi-objective optimization problems. In this pape...

Active Subspaces of Airfoil Shape Parameterizations

Design and optimization benefit from understanding the dependence of a quantity of interest (e.g., a design objective or constraint function) on the design variables. A low-dimensional active subspace, when present, identifies important directions in the space of design variables; perturbing a design along the active subspace associated with a particular quantity of interest changes that quantity more, on average, than perturbing the design orthogonally to the active subspace. This low-dimensional structure provides insights that characterize the dependence of quantities of interest on design variables. Airfoil design in a transonic flowfield with a parameterized geometry is a popular test problem for design methodologies. Two particular airfoil shape parameterizations are examined (parametric sections and class-shape transformation), and the active subspaces present in two common design quantities of interest (transonic lift and wave-drag coefficients) are studied under each shape parameterization. The two parameterizations are mathematically related by a simple change of variable and subsequent odd-power polynomial series. The active subspaces enable low-dimensional approximations of lift and drag that relate to physical perturbations of the airfoil. In particular, a two-dimensional approximation of both transonic lift and drag is obtained and interpreted, where 1) each dimension is a particular linear combination of the design variables resulting in intuitive airfoil perturbations, and 2) the linear combination weights are related between lift and drag. It is shown how these approximations along with similarities between the lift and drag active subspaces inform a multi-objective design problem.

A Real Coded Vector Population-Based Incremental Learning Algorithm for Multi-Objective Optimizations of Electromagnetic Devices

Even though evolutionary algorithm (EA) has now become the standard and paradigm for solving multi-objective design problems, the complexity of its genetic operation is, however, limiting its popularity in engineering applications. Hitherto, there has been insufficient research that addresses the inadequacy of EAs in extracting the characteristic landscape features of an objective function. However, increasing attentions have now been devoted to EAs based on probabilistic models (EAPMs) in computational intelligence studies. A real coded scalar population-based incremental learning algorithm, an EAPM, is proposed for multi-objective optimizations of electromagnetic devices. Major improvements include the design of a generating mechanism for new intermediate solutions, the selection of elite solutions to update the probability matrix, matrix updating formulations, and refinement mechanism for intervals to precisely generate intermediate solution. Also, a methodology to consider quantitatively both the number of improved objectives and the amount of improvements in a specified objective of multi-objective design problems is introduced in fitness assignments. Numerical results on a high frequency and a low inverse problem are reported to showcase the merits of the proposed algorithm.

Sustainable closed-loop supply chain network design with discount supposition

Supply chain network design (SCND) is one of the important, primary and strategic decisions affecting competitive advantages and all other decisions in supply chain management. Although most of papers in SCND focus only on the economic performance, this study considers simultaneously economic, social and environmental aspects. In this study, a new mixed integer nonlinear programming model is developed to formulate a multi-objective sustainable closed-loop supply chain network design problem by considering discount supposition in the transportation costs for the first time. In order to address the problem, not only traditional and recent metaheuristics are utilized, but also the algorithms are hybridized according to their strengths especially in intensification and diversification. To evaluate the efficiency and effectiveness of these algorithms, they are compared with each other by four assessment metrics for Pareto optimal analyses. Although the results indicate the performance of three proposed new hybridization algorithms, KAGA achieves better solutions compared with the others, but it needs more time. At the end, we introduced a real industrial example in glass industry to verify the proposed model and the algorithms.