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Determining the optimal capital structure becomes more complicated by the presence of an agency problem. The issuance of debt as a corporate governance mechanism introduces the asset substitution problem – the agency cost of debt. Thus, there is a recognized need for models that can resolve the agency problem between the debtholder and the manager who acts on behalf of the shareholder, leading to optimal capital structure choice, and enhanced firm value. The purpose of this paper is to model the debtholder-manager agency problem as a dynamic game, resolve the conflicts of interests and determine the optimal capital structure.

As there is no satisfactory model for dealing with the above issues, this paper uses a differential game framework to analyze the incongruity of interests between the debtholder and the manager as a non-cooperative dynamic game and further resolves the conflicts of interests as a cooperative game via a Pareto-efficient outcome.

The optimal capital structure required to minimize the marginal cost of the agency problem is a higher use of debt, lower cost of equity and withheld capital distributions. The debtholder is also able to enforce cooperation from the manager by providing a lower and stable cost of debt and a greater debt facility in the overtime framework.

The study develops a new dynamic contract theory model based on the integrated issues of capital structure, corporate governance and agency problems and applies the differential game approach to minimize the agency problem between the debtholder and the manager.

Multi-objective is a complex problem that appears in real life while these objectives are conflicting. The swarm intelligence algorithm is often used to solve such multi-objective problems. Due to its strong search ability and convergence ability, particle swarm optimization algorithm is proposed, and the multi-objective particle swarm optimization algorithm is used to solve multi-objective optimization problems. However, the particles of particle swarm optimization algorithm are easy to fall into local optimization because of their fast convergence. Uneven distribution and poor diversity are the two key drawbacks of the Pareto front of multi-objective particle swarm optimization algorithm. Therefore, this paper aims to propose an improved multi-objective particle swarm optimization algorithm using adaptive Cauchy mutation and improved crowding distance.

In this paper, the proposed algorithm uses adaptive Cauchy mutation and improved crowding distance to perturb the particles in the population in a dynamic way in order to help the particles trapped in the local optimization jump out of it which improves the convergence performance consequently.

In order to solve the problems of uneven distribution and poor diversity in the Pareto front of multi-objective particle swarm optimization algorithm, this paper uses adaptive Cauchy mutation and improved crowding distance to help the particles trapped in the local optimization jump out of the local optimization. Experimental results show that the proposed algorithm has obvious advantages in convergence performance for nine benchmark functions compared with other multi-objective optimization algorithms.

In order to help the particles trapped in the local optimization jump out of the local optimization which improves the convergence performance consequently, this paper proposes an improved multi-objective particle swarm optimization algorithm using adaptive Cauchy mutation and improved crowding distance.

The goal of this study is to carry out multi‐objective optimization by considering minimization of surface roughness (Ra) and build time (T) in selective laser sintering (SLS) process, which are functions of “build orientation”. Evolutionary algorithms are applied for this purpose. The performance comparison of the optimizers is done based on statistical measures. In order to find truly optimal solutions, local search is proposed. An important task of decision making, i.e. the selection of one solution in the presence of multiple trade‐off solutions, is also addressed. Analysis of optimal solutions is done to gain insight into the problem behavior.

The minimization of Ra and T is done using two popular optimizers – multi‐objective genetic algorithm (non‐dominated sorting genetic algorithm (NSGA‐II)) and multi‐objective particle swarm optimizers (MOPSO). Standard measures from evolutionary computation – “hypervolume measure” and “attainment surface approximator” have been borrowed to compare the optimizers. Decision‐making schemes are proposed in this paper based on decision theory.

The objects are categorized into groups, which bear similarity in optimal solutions. NSGA‐II outperforms MOPSO. The similarity of spread and convergence patterns of NSGA‐II and MOPSO ensures that obtained solutions are (or are close to) Pareto‐optimal set. This is validated by local search. Based on the analysis of obtained solutions, general trends for optimal orientations (depending on the geometrical features) are found.

A novel and systematic way to address multi‐objective optimization decision‐making post‐optimal analysis is shown. Simulations utilize experimentally derived models for roughness and build time. A further step could be the experimental verification of findings provided in this study.

This study provides a thorough methodology to find optimal build orientations in SLS process. A route to decipher valuable problem information through post‐optimal analysis is shown. The principles adopted in this study are general and can be extended to other rapid prototyping (RP) processes and expected to find wide applicability.

This paper is a distinct departure from past studies in RP and demonstrates the concepts of multi‐objective optimization, decision‐making and related issues.

The purpose of this work is to apply and compare surrogate-assisted and multi-fidelity, multi-objective optimization (MOO) algorithms to simulation-based aerodynamic design exploration.

The three algorithms for multi-objective aerodynamic optimization compared in this work are the combination of evolutionary algorithms, design space reduction and surrogate models, the multi-fidelity point-by-point Pareto set identification and the multi-fidelity sequential domain patching (SDP) Pareto set identification. The algorithms are applied to three cases, namely, an analytical test case, the design of transonic airfoil shapes and the design of subsonic wing shapes, and are evaluated based on the resulting best possible trade-offs and the computational overhead.

The results show that all three algorithms yield comparable best possible trade-offs for all the test cases. For the aerodynamic test cases, the multi-fidelity Pareto set identification algorithms outperform the surrogate-assisted evolutionary algorithm by up to 50 per cent in terms of cost. Furthermore, the point-by-point algorithm is around 27 per cent more efficient than the SDP algorithm.

The novelty of this work includes the first applications of the SDP algorithm to multi-fidelity aerodynamic design exploration, the first comparison of these multi-fidelity MOO algorithms and new results of a complex simulation-based multi-objective aerodynamic design of subsonic wing shapes involving two conflicting criteria, several nonlinear constraints and over ten design variables.

In recent decades, development of effective methods for optimizing a set of conflicted objective functions has been absorbing an increasing interest from researchers. This refers to the essence of real-life engineering systems and complex natural mechanisms which are generally multi-modal, non-convex and multi-criterion. Until now, several deterministic and stochastic methods have been proposed to cope with such complex systems. Advanced soft computational methods such as evolutionary games (cooperative and non-cooperative), Pareto-based techniques, fuzzy evolutionary methods, cooperative bio-inspired algorithms and neuro-evolutionary systems have effectively come to the aid of researchers to build up efficient paradigms with application to vector optimization. The paper aims to discuss this issue.

A novel hybrid algorithm called synchronous self-learning Pareto strategy (SSLPS) is presented for the sake of vector optimization. The method is the ensemble of evolutionary algorithms (EA), swarm intelligence (SI), adaptive version of self-organizing map (CSOM) and a data shuffling mechanism. EA are powerful numerical optimization algorithms capable of finding a global extreme point over a wide exploration domain. SI techniques (the swarm of bees in our case) can improve both intensification and robustness of exploration. CSOM network is an unsupervised learning methodology which learns the characteristics of non-dominated solutions and, thus, enhances the quality of the Pareto front.

To prove the effectiveness of the proposed method, the authors engage a set of well-known benchmark functions and some well-known rival optimization methods. Additionally, SSLPS is employed for optimal design of shape memory alloy actuator as a nonlinear multi-modal real-world engineering problem. The experiments show the acceptable potential of SSLPS for handling both numerical and engineering multi-objective problems.

To the author’s best knowledge, the proposed algorithm is among the rare multi-objective methods which fosters the use of automated unsupervised learning for increasing the intensity of Pareto front (while preserving the diversity). Also, the research evaluates the power of hybridization of SI and EA for efficient search.

A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to create a tight coupling between the optimization and uncertainty procedures, use all of the possible probabilistic information to drive the optimizer, and leverage high-performance parallel computing.

This algorithm is a generalization of a classical genetic algorithm for multi-objective optimization (NSGA-II) by Deb et al. The proposed algorithm relies on the use of all possible information in the probabilistic domain summarized by the cumulative distribution functions (CDFs) of the objective functions. Several analytic test functions are used to benchmark this algorithm, but only the results of the Fonseca-Fleming test function are shown. An industrial application is presented to show that P-NSGA can be used for multi-objective shape optimization of a Formula 1 tire brake duct, taking into account the geometrical uncertainties associated with the rotating rubber tire and uncertain inflow conditions.

This algorithm is shown to have deterministic consistency (i.e. it turns back to the original NSGA-II) when the objective functions are deterministic. When the quality of the CDF is increased (either using more points or higher fidelity resolution), the convergence behavior improves. Since all the information regarding uncertainty quantification is preserved, all the different types of Pareto fronts that exist in the probabilistic framework (e.g. mean value Pareto, mean value penalty Pareto, etc.) are shown to be generated a posteriori. An adaptive sampling approach and parallel computing (in both the uncertainty and optimization algorithms) are shown to have several fold speed-up in selecting optimal solutions under uncertainty.

There are no existing algorithms that use the full probabilistic distribution to guide the optimizer. The method presented herein bases its sorting on real function evaluations, not merely measures (i.e. mean of the probabilistic distribution) that potentially do not exist.

The purpose of this paper is to present a novel Kriging meta-model assisted method for multi-objective optimal tolerance design of the mechanical assemblies based on the operating conditions under both systematic and random uncertainties.

In the proposed method, the performance, the quality loss and the manufacturing cost issues are formulated as the main criteria in terms of systematic and random uncertainties. To investigate the mechanical assembly under the operating conditions, the behavior of the assembly can be simulated based on the finite element analysis (FEA). The objective functions in terms of uncertainties at the operating conditions can be modeled through the Kriging-based metamodeling based on the obtained results from the FEA simulations. Then, the optimal tolerance allocation procedure is formulated as a multi-objective optimization framework. For solving the multi conflicting objectives optimization problem, the multi-objective particle swarm optimization method is used. Then, a Shannon’s entropy-based TOPSIS is used for selection of the best tolerances from the optimal Pareto solutions.

The proposed method can be used for optimal tolerance design of mechanical assemblies in the operating conditions with including both random and systematic uncertainties. To reach an accurate model of the design function at the operating conditions, the Kriging meta-modeling is used. The efficiency of the proposed method by considering a case study is illustrated and the method is verified by comparison to a conventional tolerance allocation method. The obtained results show that using the proposed method can lead to the product with a more robust efficiency in the performance and a higher quality in comparing to the conventional results.

The proposed method is limited to the dimensional tolerances of components with the normal distribution.

The proposed method is practically easy to be automated for computer-aided tolerance design in industrial applications.

In conventional approaches, regardless of systematic and random uncertainties due to operating conditions, tolerances are allocated based on the assembly conditions. As uncertainties can significantly affect the system’s performance at operating conditions, tolerance allocation without including these effects may be inefficient. This paper aims to fill this gap in the literature by considering both systematic and random uncertainties for multi-objective optimal tolerance design of mechanical assemblies under operating conditions.

The purpose of this paper is to present a methodology and experimental results on using global optimization algorithms to determine the optimal orbit, based on the mission requirements, for a set of spacecraft flying in formation with an asteroid.

A behavioral‐based hybrid global optimization approach is used to first characterize the solution space and find families of orbits that are a fixed distance away from the asteroid. The same optimization approach is then used to find the set of Pareto optimal solutions that minimize both the distance from the asteroid and the variation of the Sun‐spacecraft‐asteroid angle. Two sample missions to asteroids, representing constrained single and multi‐objective problems, were selected to test the applicability of using an in‐house hybrid stochastic‐deterministic global optimization algorithm (Evolutionary Programming and Interval Computation (EPIC)) to find optimal orbits for a spacecraft flying in formation with an orbit. The Near Earth Asteroid 99942 Apophis (2004 MN₄) is used as the case study due to a fly‐by of Earth in 2029 leading to two potential impacts in 2036 or 2037. Two black‐box optimization problems that model the orbital dynamics of the spacecraft were developed.

It was found for the two missions under test, that the optimized orbits fall into various distinct families, which can be used to design multi‐spacecraft missions with similar orbital characteristics.

The global optimization software, EPIC, was very effective at finding sets of orbits which met the required mission objectives and constraints for a formation of spacecraft in proximity of an asteroid. The hybridization of the stochastic search with the deterministic domain decomposition can greatly improve the intrinsic stochastic nature of the multi‐agent search process without the excessive computational cost of a full grid search. The stability of the discovered families of formation orbit is subject to the gravity perturbation of the asteroid and to the solar pressure. Their control, therefore, requires further investigation.

This paper contributes to both the field of space mission design for close‐proximity orbits and to the field of global optimization. In particular, suggests a common formulation for single and multi‐objective problems and a robust and effective hybrid search method based on behaviorism. This approach provides an effective way to identify families of optimal formation orbits.

The purpose of this paper is to investigate Halbach array effects in surface mounted permanent magnet machine (SMPM) in terms of both self-sensing and torque capabilities. A comparison between a conventional SMPM, which has radially magnetized rotor, and a Halbach machine has been carried out.

The geometric parameters of the two machines have been optimized using genetic algorithm (GA) with looking Pareto. The performance of the machines’ geometry has been calculated by finite element analysis (FEA) software, and two parametric machine models have been realized in Matlab coupled with the FEA and GA toolboxes. Outer volume of the machine, thus copper loss per volume has been kept constant. The Pareto front approach, which simultaneously considers looks two aims, has been used to provide the trade-off between the torque and sensorless performances.

The two machines’ results have been compared separately for each loading condition. According to the results, the superiority of the Halbach machine has been shown in terms of sensorless capability compromising torque performance. Additionally, this paper shows that the self-sensing properties of a SMPM machine should be considered at the design stage of the machine.

A Halbach machine design optimization has been presented using Pareto optimal set which provides a trade-off comparison between two aims without using weightings. These are sensorless performance and torque capability. There is no such a work about sensorless capability of the Halbach type SMPM in the literature.

When a multiobjective optimization problem is tackled using Pareto optima theory, particular care has to be taken to obtain a full sampling of the Pareto Optimal Front. This leads to variability of individuals in both design space and objective space. We compare two different fitness assignment strategies based on two individual sharing procedures in the space domain and in the objective domain on some test cases.