Robust solutions to Stackelberg games: Addressing bounded rationality and limited observations in human cognition

How do we build algorithms for agent interactions with human adversaries? Stackelberg games are natural models for many important applications that involve human interaction, such as oligopolistic markets and security domains. In Stackelberg games, one player, the leader, commits to a strategy and the follower makes her decision with knowledge of the leader's commitment. Existing algorithms for Stackelberg games efficiently find optimal solutions (leader strategy), but they critically assume that the follower plays optimally. Unfortunately, in many applications, agents face human followers (adversaries) who — because of their bounded rationality and limited observation of the leader strategy — may deviate from their expected optimal response. In other words, human adversaries' decisions are biased due to their bounded rationality and limited observations. Not taking into account these likely deviations when dealing with human adversaries may cause an unacceptable degradation in the leader's reward, particularly in security applications where these algorithms have seen deployment. The objective of this paper therefore is to investigate how to build algorithms for agent interactions with human adversaries.To address this crucial problem, this paper introduces a new mixed-integer linear program (MILP) for Stackelberg games to consider human adversaries, incorporating: (i) novel anchoring theories on human perception of probability distributions and (ii) robustness approaches for MILPs to address human imprecision. Since this new approach considers human adversaries, traditional proofs of correctness or optimality are insufficient; instead, it is necessary to rely on empirical validation. To that end, this paper considers four settings based on real deployed security systems at Los Angeles International Airport (Pita et al., 2008 [35]), and compares 6 different approaches (three based on our new approach and three previous approaches), in 4 different observability conditions, involving 218 human subjects playing 2960 games in total. The final conclusion is that a model which incorporates both the ideas of robustness and anchoring achieves statistically significant higher rewards and also maintains equivalent or faster solution speeds compared to existing approaches.     

Pareto frontier for simultaneous structural and manufacturing optimization of a composite part

Optimized design of composite structures requires simultaneous optimization of structural performance and manufacturing process. Such a challenge calls for a multi-objective optimization. Here, a generating multi-objective optimization method called normalized normal constraint method, which attains a set of optimal solutions and allows the designer to explore design alternatives before making the final decision, is coupled with a local-global search called constrained globalized bounded Nelder–Mead method. The proposed approach is applied to the design of a Z-shaped composite bracket for optimization of structural and manufacturing objectives. Comparison of the results with non-dominated sorting genetic algorithm (NSGA-II) shows that when only a small number of function evaluations are possible and a few Pareto optima are desired, the proposed method outperforms NSGA-II in terms of convergence to the true Pareto frontier. The results are validated by an enumeration search and by exploring the neighbourhood of the final solutions.     

Rolling Horizon Path Planning of an Autonomous System of UAVs for Persistent Cooperative Service: MILP Formulation and Efficient Heuristics

A networked system consisting of unmanned aerial vehicles (UAVs), automated logistic service stations (LSSs), customer interface software, system orchestration algorithms and UAV control software can be exploited to provide persistent service to its customers. With efficient algorithms for UAV task planning, the UAVs can autonomously serve the customers in real time. Nearly uninterrupted customer service may be accomplished via the cooperative hand-off of customer tasks from weary UAVs to ones that have recently been replenished at an LSS. With the goal of enabling the autonomy of the task planning tasks, we develop a mixed integer linear programming (MILP) formulation for the problem of providing simultaneous. UAV escort service to multiple customers across a field of operations with multiple sharable LSSs. This MILP model provides a formal representation of our problem and enables use in a rolling horizon planner via allowance of arbitrary UAV initial locations and consumable reservoir status (e.g., battery level). As such, it enables automation of the orchestration of system activities. To address computational complexity, we develop efficient heuristics to rapidly derive near optimal solutions. A receding horizon task assignment (RHTA) heuristic and sequential task assignment heuristic (STAH) are developed. STAH exploits properties observed in optimal solutions obtained for small problems via CPLEX. Numerical studies suggest that RHTA and STAH are 45 and 2100 times faster than solving the MILP via CPLEX, respectively. Both heuristics perform well relative to the optimal solution obtained via CPLEX. An example demonstrating the use of the approach for rolling horizon planning is provided.     

Approximating Pareto frontier using a hybrid line search approach

The aggregation of objectives in multiple criteria programming is one of the simplest and widely used approach. But it is well known that this technique sometimes fail in different aspects for determining the Pareto frontier. This paper proposes a new approach for multicriteria optimization, which aggregates the objective functions and uses a line search method in order to locate an approximate efficient point. Once the first Pareto solution is obtained, a simplified version of the former one is used in the context of Pareto dominance to obtain a set of efficient points, which will assure a thorough distribution of solutions on the Pareto frontier. In the current form, the proposed technique is well suitable for problems having multiple objectives (it is not limited to bi-objective problems) and require the functions to be continuous twice differentiable. In order to assess the effectiveness of this approach, some experiments were performed and compared with two recent well known population-based metaheuristics namely ParEGO and NSGA II. When compared to ParEGO and NSGA II, the proposed approach not only assures a better convergence to the Pareto frontier but also illustrates a good distribution of solutions. From a computational point of view, both stages of the line search converge within a short time (average about 150 ms for the first stage and about 20 ms for the second stage). Apart from this, the proposed technique is very simple, easy to implement and use to solve multiobjective problems.     

基于平行多种群与冗余基因策略的置信规则库优化方法

置信规则库(Belief rule base, BRB)的参数学习和结构学习共同影响着置信规则库的建模精度和复杂度.为了提高BRB结构学习和参数学习的优化效率,本文提出了一种基于平行多种群(Parallel multi-population)策略和冗余基因(Redundant genes)策略的置信规则库优化方法.该方法采用平行多种群策略以实现对具有不同数量规则BRB同时进行优化的目的,采用冗余基因策略以确保具有不同数量规则的BRB能够顺利进行(交叉,变异等)相关优化操作.最终自动生成具有不同数量规则BRB的最优解,并得出帕累托前沿(Pareto frontier),决策者可以根据自身偏好和实际问题需求,综合权衡并在帕累托前沿中筛选最优解.最后以某输油管道泄漏检测问题作为示例验证本文提出方法的有效性,示例分析结果表明本文提出的方法可以一次生成具有多条规则BRB的最优解,并且可以准确绘制出帕累托前沿,为综合决策提供较强的决策支持.     

Multiobjective Markov chains optimization problem with strong Pareto frontier: Principles of decision making

In this paper, we present a novel approach for computing the Pareto frontier in Multi-Objective Markov Chains Problems (MOMCPs) that integrates a regularized penalty method for poly-linear functions. In addition, we present a method that make the Pareto frontier more useful as decision support system: it selects the ideal multi-objective option given certain bounds. We restrict our problem to a class of finite, ergodic and controllable Markov chains. The regularized penalty approach is based on the Tikhonov’s regularization method and it employs a projection-gradient approach to find the strong Pareto policies along the Pareto frontier. Different from previous regularized methods, where the regularizator parameter needs to be large enough and modify (some times significantly) the initial functional, our approach balanced the value of the functional using a penalization term (μ) and the regularizator parameter (δ) at the same time improving the computation of the strong Pareto policies. The idea is to optimize the parameters μ and δ such that the functional conserves the original shape. We set the initial value and then decrease it until each policy approximate to the strong Pareto policy. In this sense, we define exactly how the parameters μ and δ tend to zero and we prove the convergence of the gradient regularized penalty algorithm. On the other hand, our policy-gradient multi-objective algorithms exploit a gradient-based approach so that the corresponding image in the objective space gets a Pareto frontier of just strong Pareto policies. We experimentally validate the method presenting a numerical example of a real alternative solution of the vehicle routing planning problem to increase security in transportation of cash and valuables. The decision-making process explored in this work correspond to the most frequent computational intelligent models applied in practice within the Artificial Intelligence research area.     

A portfolio optimization model with three objectives and discrete variables

We formulate the portfolio selection as a tri-objective optimization problem so as to find tradeoffs between risk, return and the number of securities in the portfolio. Furthermore, quantity and class constraints are introduced into the model in order to limit the proportion of the portfolio invested in assets with common characteristics and to avoid very small holdings. Since the proposed portfolio selection model involves mixed integer decision variables and multiple objectives finding the exact efficient frontier may be very hard. Nevertheless, finding a good approximation of the efficient surface which provides the investor with a diverse set of portfolios capturing all possible tradeoffs between the objectives within limited computational time is usually acceptable. We experiment with the current state of the art evolutionary multiobjective optimization techniques, namely the Non-dominated Sorting Genetic Algorithm II (NSGA-II), Pareto Envelope-based Selection Algorithm (PESA) and Strength Pareto Evolutionary Algorithm 2 (SPEA2), for solving the mixed-integer multiobjective optimization problem and provide a performance comparison among them using metrics proposed by the community.     

A goal programming based energy efficient resource allocation in data centers

We study the multi-objective problem of mapping independent tasks onto a set of data center machines that simultaneously minimizes the energy consumption and response time (makespan) subject to the constraints of deadlines and architectural requirements. We propose an algorithm based on goal programming that effectively converges to the compromised Pareto optimal solution. Compared to other traditional multi-objective optimization techniques that require identification of the Pareto frontier, goal programming directly converges to the compromised solution. Such a property makes goal programming a very efficient multi-objective optimization technique. Moreover, simulation results show that the proposed technique achieves superior performance compared to the greedy and linear relaxation heuristics, and competitive performance relative to the optimal solution implemented in Linear Interactive and Discrete Optimizer (LINDO) for small-scale problems.     

Fuzzy approaches to the game of Chicken

Game theory deals with decision-making processes involving two or more parties, also known as players, with partly or completely conflicting interests. Decision-makers in a conflict must often make their decisions under risk and under unclear or fuzzy information. In this paper, two distinct fuzzy approaches are employed to investigate an extensively studied 2×2 game model-the game of Chicken. The first approach uses a fuzzy multicriteria decision analysis method to obtain optimal strategies for the players. It incorporates subjective factors into the decision-makers' objectives and aggregates objectives using a weight vector. The second approach applies the theory of fuzzy moves (TFM) to the game of Chicken. The theory of moves (TOM) is designed to bring a dynamic dimension to the classical theory of games by allowing decision-makers to look ahead for one or several steps so that they can make a better decision. TOM is the crisp counterpart of TFM, the approach we implement here to deal with games that include fuzzy and uncertain information. The application of fuzzy approaches to the game of Chicken demonstrates their effectiveness in manipulating subjective, uncertain, and fuzzy information and provides valuable insights into the strategic aspects of Chicken     

Tuning of PID controller based on a multiobjective genetic algorithm applied to a robotic manipulator

Most controllers optimization and design problems are multiobjective in nature, since they normally have several (possibly conflicting) objectives that must be satisfied at the same time. Instead of aiming at finding a single solution, the multiobjective optimization methods try to produce a set of good trade-off solutions from which the decision maker may select one. Several methods have been devised for solving multiobjective optimization problems in control systems field. Traditionally, classical optimization algorithms based on nonlinear programming or optimal control theories are applied to obtain the solution of such problems. The presence of multiple objectives in a problem usually gives rise to a set of optimal solutions, largely known as Pareto-optimal solutions. Recently, Multiobjective Evolutionary Algorithms (MOEAs) have been applied to control systems problems. Compared with mathematical programming, MOEAs are very suitable to solve multiobjective optimization problems, because they deal simultaneously with a set of solutions and find a number of Pareto optimal solutions in a single run of algorithm. Starting from a set of initial solutions, MOEAs use iteratively improving optimization techniques to find the optimal solutions. In every iterative progress, MOEAs favor population-based Pareto dominance as a measure of fitness. In the MOEAs context, the Non-dominated Sorting Genetic Algorithm (NSGA-II) has been successfully applied to solving many multiobjective problems. This paper presents the design and the tuning of two PID (Proportional–Integral–Derivative) controllers through the NSGA-II approach. Simulation numerical results of multivariable PID control and convergence of the NSGA-II is presented and discussed with application in a robotic manipulator of two-degree-of-freedom. The proposed optimization method based on NSGA-II offers an effective way to implement simple but robust solutions providing a good reference tracking performance in closed loop.     

Fast Pareto set generation for nonlinear optimal control problems with multiple objectives

Many practical engineering problems involve the determination of optimal control trajectories for given multiple and conflicting objectives. These conflicting objectives typically give rise to a set of Pareto optimal solutions. To enhance real-time decision making efficient approaches are required for determining the Pareto set in a fast and accurate way. Hereto, the current paper integrates efficient multiple objective scalarisation strategies (e.g., Normal Boundary Intersection and Normalised Normal Constraint) with fast deterministic approaches for dynamic optimisation (e.g., Single and Multiple Shooting). All techniques have been implemented as an easy-to-use add-on module of the automatic control and dynamic optimisation toolkit ACADO (both freely available at ). Several algorithmic synergies (e.g., hot-start initialisation strategies) are exploited for an additional speed-up. The features of ACADO Multi-Objective are discussed and its use is illustrated on different multiple objective optimal control problems arising in several engineering disciplines.     

Comparing the notions of optimality in CP-nets,strategic games and soft constraints

The notion of optimality naturally arises in many areas of applied mathematics and computer science concerned with decision making. Here we consider this notion in the context of three formalisms used for different purposes in reasoning about multi-agent systems: strategic games, CP-nets, and soft constraints. To relate the notions of optimality in these formalisms we introduce a natural qualitative modification of the notion of a strategic game. We show then that the optimal outcomes of a CP-net are exactly the Nash equilibria of such games. This allows us to use the techniques of game theory to search for optimal outcomes of CP-nets and vice-versa, to use techniques developed for CP-nets to search for Nash equilibria of the considered games. Then, we relate the notion of optimality used in the area of soft constraints to that used in a generalization of strategic games, called graphical games. In particular we prove that for a natural class of soft constraints that includes weighted constraints every optimal solution is both a Nash equilibrium and Pareto efficient joint strategy. For a natural mapping in the other direction we show that Pareto efficient joint strategies coincide with the optimal solutions of soft constraints.      

Robuste multikriterielle Dienstkomposition in Informationssystemen

Service compositions are used to implement business processes in a variety of application domains. A quality of service (QoS)-aware selection of the service to be composed involves multiple, usually conflicting and possibly uncertain QoS attributes. A multi-criteria solution approach is desired to generate a set of alternative service selections. In addition, the uncertainty of QoS-attributes is neglected in existing solution approaches. Hence, the need for service reconfigurations is imposed to avoid the violation of QoS restrictions. The researched problem is NP-hard. This article presents a heuristic multi-criteria service selection approach that is designed to determine a Pareto frontier of alternative service selections in a reasonable amount of time. Taking into account the uncertainty of response times, the obtained service selections are robust with respect to the constrained execution time. The proposed solution approach is based on the Non-dominated Sorting Genetic Algorithm (NSGA)-II extended by heuristics that exploit problem specific characteristics of the QoS-aware service selection. The applicability of the solution approach is demonstrated by a simulation study.     

Evolutionary multiobjective industrial design: the case of a racing car tire-suspension system

When dealing with multiobjective optimization (MO) of the tire-suspension system of a racing car, a large number of design variables and a large number of objectives have to be taken into account. Two different models have been used, both validated on data coming from an instrumented car, a differential equation-based physical model, and a neural network purely numerical model. Up to 23 objective functions have been defined, at least 14 of which are in strict conflict of each other. The equivalent scalar function based and the objective-as-constraint formulations are intentionally avoided due to their well-known limitations. A fuzzy definition of optima, being a generalization of Pareto optimality, is applied to the problem. The result of such an approach is that subsets of Pareto optimal solutions (on such a problem, a big portion of the entire search space) can be properly selected as a consequence of input from the designer. The obtained optimal solutions are compared with the reference vehicle and with the optima previously obtained with design of experiment techniques and different MO optimization strategies. The proposed strategy improves both the reference (actual) car and previously obtained optima (scalar preference function) in the majority of objectives with technically significant improvements. Moreover, the strategy offers an univoque criterion for the choice among tradeoff solutions in the 14-dimensional objective space. The problem is used as a test of a proposed optimal design strategy for industrial problems, integrating differential equation and neural networks modeling, design of experiments, MO, and fuzzy optimal-based decision making. Such a linked approach gives also a unified view of where to concentrate the computational effort.     

Normal-boundary intersection based parametric multi-objective optimization of green sand mould system

In manufacturing engineering optimization, it is often that one encounters scenarios that are multi-objective (where each of the objectives portray different aspects of the problem). Thus, it is crucial for the engineer to have access to multiple solution choices before selecting of the best solution. In this work, a novel approach that merges meta-heuristic algorithms with the Normal Boundary Intersection (NBI) method is introduced. This method then is used generate optimal solution options to the green sand mould system problem. This NBI based method provides a near-uniform spread of the Pareto frontier in which multiple solutions with gradual trade-offs in the objectives are obtained. Some comparative studies were then carried out with the algorithms developed and used in this work and that from some previous work. Analysis on the performance as well as the quality of the solutions produced by the algorithms is presented here.     

A simulation-based evolutionary multiobjective approach to manufacturing cell formation

The purpose of this paper is to propose a multiobjective optimization approach for solving the manufacturing cell formation problem, explicitly considering the performance of this said manufacturing system. Cells are formed so as to simultaneously minimize three conflicting objectives, namely, the level of the work-in-process, the intercell moves and the total machinery investment. A genetic algorithm performs a search in the design space, in order to approximate to the Pareto optimal set. The values of the objectives for each candidate solution in a population are assigned by running a discrete-event simulation, in which the model is automatically generated according to the number of machines and their distribution among cells implied by a particular solution. The potential of this approach is evaluated via its application to an illustrative example, and a case from the relevant literature. The obtained results are analyzed and reviewed. Therefore, it is concluded that this approach is capable of generating a set of alternative manufacturing cell configurations considering the optimization of multiple performance measures, greatly improving the decision making process involved in planning and designing cellular systems.     

Fuzzy multivariate mean square error in equispaced pareto frontiers considering manufacturing process optimization problems

This paper proposes a combined approach using the normal boundary intersection (NBI) and multivariate mean square error (MMSE) that is an alternative approach to outperform the traditional NBI driving to an equispaced Pareto Frontier in a low-dimension space with a considerable reduction in the number of iterations. The method participating in the evolutionary stage of creating a uniformly spread Pareto Frontier for a nonlinear multi-objective problem is the NBI using normalized objective functions allied to MMSE. In sequence, the fuzzy MMSE approach is utilized to determine the optimal point of the multi-objective optimization. For sake of comparison, the performance of arc homotopy length, global criterion method, and weighted sums were explored. To illustrate this proposal, a multivariate case of AISI H13 hardened steel-turning process is used. Experimental results indicate that the solution found by NBI-MMSE approach is a more appropriate Pareto frontier that surpassed all the competitors and also provides the best-compromised solution to set the machine input parameters. Further, this algorithm was also tested in benchmark functions to confirm the NBI-MMSE efficiency.

     

Multi-criteria human resource allocation for solving multistage combinatorial optimization problems using multiobjective hybrid genetic algorithm

Multi-criteria human resource allocation involves deciding how to divide human resource of limited availability among multiple demands in a way that optimizes current objectives. In this paper, we focus on multi-criteria human resource allocation for solving multistage combinatorial optimization problem. Hence we tackle this problem via a multistage decision-making model. A multistage decision-making model is similar to a complex problem solving, in which a suitable sequence of decisions is to be found. The task can be interpreted as a series of interactions between a decision maker and an outside world, at each stage of which some decisions are available and their immediate effect can be easily computed. Eventually, goals would be reached due to the found of optimized variables. In order to obtain a set of Pareto solutions efficiently, we propose a multiobjective hybrid genetic algorithm (mohGA) approach based on the multistage decision-making model for solving combinatorial optimization problems. According to the proposed method, we apply the mohGA to seek feasible solutions for all stages. The effectiveness of the proposed algorithm was validated by its application to an illustrative example dealing with multiobjective resource allocation problem.     

An efficient frontier approach to addressing JIT sequencing problems with setups via search heuristics

This research presents a technique to obtain production sequences where scheduling flexibility and number of setups are considered. These two objectives of flexibility and setups are typically inversely correlated with each other, so simultaneous optimization of both is challenging. Another challenging issue is the combinatorial nature of such sequencing problems. An efficient frontier approach is exploited where simultaneous maximization of flexibility and minimization of setups is desired. The efficient frontier is constructed via the popular search heuristics of Genetic Algorithms, Simulated Annealing and Tabu Search. For several test problems from the literature, it is discovered that the efficient frontiers obtained via the three search heuristics provide near optimal results for smaller problems, and for larger problems, the Simulated Annealing and Tabu Search approaches outperform the Genetic Algorithm approach.     

一种结合多目标免疫算法和线性规划的双行设备布局方法

设备布局对于提高生产效率和降低运营成本具有重要意义. 本文针对半导体加工制造中常见的双行设备布局问题, 提出了一种结合多目标免疫算法和线性规划的双行设备布局方法来同时优化物料流成本和布局面积两个目标. 首先, 建立了问题的混合整数规划模型;其次, 针对问题既含有组合方面(机器排序)又含有连续方面(机器精确位置)的特点, 分别设计了一种多目标免疫算法来获取非支配的机器排序集合, 提出了一种基于线性规划的方法来构造任一非支配机器排序对应的连续的非支配解集;最后, 由所有连续的非支配解来构造最后Pareto解. 实验结果表明, 该方法对于小规模问题能获得最优Pareto解, 对于大规模问题能够获得具有良好分布性的Pareto解且其质量远好于NSGA-II和精确算法获得的解.