Integrated machine learning and optimization approaches

This dissertation focuses on the integration of machine learning and optimization. Specifically, novel machine learning-based frameworks are proposed to help solve a broad range of well-known operations research problems to reduce the solution times. The first study presents a bidirectional Long Short-Term Memory framework to learn optimal solutions to sequential decision-making problems. Computational results show that the framework significantly reduces the solution time of benchmark capacitated lot-sizing problems without much loss in feasibility and optimality. Also, models trained using shorter planning horizons can successfully predict the optimal solution of the instances with longer planning horizons. For the hardest data set, the predictions at the 25% level reduce the solution time of 70 CPU hours to less than 2 CPU minutes with an optimality gap of 0.8% and without infeasibility. In the second study, an extendable prediction-optimization framework is presented for multi-stage decision-making problems to address the key issues of sequential dependence, infeasibility, and generalization. Specifically, an attention-based encoder-decoder neural network architecture is integrated with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions. The proposed framework is demonstrated to tackle the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing and multi-dimensional knapsack. The results show that models trained on shorter and smaller-dimension instances can be successfully used to predict longer and larger-dimension problems with the presented item-wise expansion algorithm. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. The proposed framework can be advantageous for solving dynamic mixed-integer programming problems that need to be solved instantly and repetitively. In the third study, a deep reinforcement learning-based framework is presented for solving scenario-based two-stage stochastic programming problems, which are computationally challenging to solve. A general two-stage deep reinforcement learning framework is proposed where two learning agents sequentially learn to solve each stage of a general two-stage stochastic multi-dimensional knapsack problem. The results show that solution time can be reduced significantly with a relatively small gap. Additionally, decision-making agents can be trained with a few scenarios and solve problems with a large number of scenarios. In the fourth study, a learning-based prediction-optimization framework is proposed for solving scenario-based multi-stage stochastic programs. The issue of non-anticipativity is addressed with a novel neural network architecture that is based on a neural machine translation system. Furthermore, training the models on deterministic problems is suggested instead of solving hard and time-consuming stochastic programs. In this framework, the level of variables used for the solution is iteratively reduced to eliminate infeasibility, and a heuristic based on a linear relaxation is performed to reduce the solution time. An improved item-wise expansion strategy is introduced to generalize the algorithm to tackle instances with different sizes. The results are presented in solving stochastic multi-item capacitated lot-sizing and stochastic multi-stage multi-dimensional knapsack problems. The results show that the solution time can be reduced by a factor of 599 with an optimality gap of only 0.08%. Moreover, results demonstrate that the models can be used to predict similarly structured stochastic programming problems with a varying number of periods, items, and scenarios. The frameworks presented in this dissertation can be utilized to achieve high-quality and fast solutions to repeatedly-solved problems in various industrial and business settings, such as production and inventory management, capacity planning, scheduling, airline logistics, dynamic pricing, and emergency management

Performance Appraisal Research: A Critical Review of Work on “The Social Context and Politics of Appraisal”

This paper reviews existing literatures on the analysis of performance appraisal (PA) paying special attention to those which try to take into account the “social context” of appraisal systems and processes. The special place of political action within these processes is underlined and the different levels at which politics need to be considered in research are outlined. Research on politics is considered and shown to lack an adequate consideration of the social relations involved in the reciprocal interactions between PA tools and processes and users interpretation and manipulation of them.Performance appraisal; Social context; Politics

Optimizing Mean Mission Duration for Multiple-Payload Satellites

This thesis addresses the problem of optimally selecting and specifying satellite payloads for inclusion on a satellite bus to be launched into a constellation. The objective is to select and specify payloads so that the total lifetime utility of the constellation is maximized. The satellite bus is limited by finite power, weight, volume, and cost constraints. This problem is modeled as a classical knapsack problem in one and multiple dimensions, and dynamic programming and binary integer programming formulations are provided to solve the problem. Due to the computational complexity of the problem, the solution techniques include exact methods as well as four heuristic procedures including a greedy heuristic, two norm-based heuristics, and a simulated annealing heuristic. The performance of the exact and heuristic approaches is evaluated on the basis of solution quality and computation time by solving a series of notional and randomly-generated problem instances. The numerical results indicate that, when an exact solution is required for a moderately-sized constellation, the integer programming formulation is most reliable in solving the problem to optimality. However, if the problem size is very large, and near-optimal solutions are acceptable, then the simulated annealing algorithm performs best among the heuristic procedures

Applying the Multiple Multidimensional Knapsack Assignment Problem to a Cargo Allocation and Transportation Problem with Stochastic Demand

The US military relies on airlift to not only deploy and sustain U.S. armed forces anywhere in the world but also to rapidly mobilize humanitarian efforts and supplies. Operations already impacted by the limited capacity of aircraft also fall prey to dynamic requirements and differing priorities of multiple global locations. A growing concern for the modern military budget is how to provide airlift functions expediently and economically while mitigating the costs of shortfalls and overages. Utilizing fiscal year 2017-2018 cargo data published by the 618th Air Operations Center and modeling this problem as a multiple multidimensional knapsack assignment problem (MMKAP), this work investigates how categorical assumptions about demand affect aircraft allocation and assesses the economic penalties associated with shorting or exceeding demand in the event of mis-estimation given a stochastic demand. This work starts with the general formulation of a new variant of the MMKAP and applies the MMKAP to a notional military airlift example with two supply, two demand nodes, two item types, and three aircraft types. After a deterministic solution is found, the effects of a stochastic demand are explored using different cost models and random draws from distribution functions based on reported cargo shipment data. This research concludes that there are levels at which demand expectations can be set to mitigate economic penalties given a fixed cost penalty and a variable cost penalty

Approximate Dynamic Programming for Military Resource Allocation

This research considers the optimal allocation of weapons to a collection of targets with the objective of maximizing the value of destroyed targets. The weapon-target assignment (WTA) problem is a classic non-linear combinatorial optimization problem with an extensive history in operations research literature. The dynamic weapon target assignment (DWTA) problem aims to assign weapons optimally over time using the information gained to improve the outcome of their engagements. This research investigates various formulations of the DWTA problem and develops algorithms for their solution. Finally, an embedded optimization problem is introduced in which optimization of the multi-stage DWTA is used to determine optimal weaponeering of aircraft. Approximate dynamic programming is applied to the various formulations of the WTA problem. Like many in the field of combinatorial optimization, the DWTA problem suffers from the curses of dimensionality and exact solutions are often computationally intractability. As such, approximations are developed which exploit the special structure of the problem and allow for efficient convergence to high-quality local optima. Finally, a genetic algorithm solution framework is developed to test the embedded optimization problem for aircraft weaponeering

Empirical Analysis of Various Multi-Dimensional Knapsack Heuristics

Since the multidimensional knapsack problems are NP-hard problems, the exact solutions of knapsack problems often need excessive computing time and storage space. Thus, heuristic approaches are more practical for multidimensional knapsack problems as problems get large. This thesis presents the results of an empirical study of the performance of heuristic solution procedures based on the coefficients correlation structures and constraint slackness settings. In this thesis, the three representative greedy heuristics, Toyoda, Senju and Toyoda, and Loulou and Michaelides’ methods, are studied. The purpose of this research is to explore which heuristic of the three representative greedy heuristics performs best under certain combinations of conditions between constraint slackness and correlation structures. This thesis examines three heuristics over 1120 problems which are all the two-dimensional knapsack problems (2KPs) with 100 variables created by four constraint slackness settings and 45 feasible correlation structures. Then we analyze why the best heuristic behaves as it does as a function of problem characteristics. Finally we present two new heuristics using knowledge gained in the study. When these new heuristics are competitively tested against the three representative greedy heuristics, the results show the new heuristics perform better

무인항공기 운영을 위한 덮개 모델 기반의 대규모 최적화 기법

학위논문 (박사) -- 서울대학교 대학원 : 공과대학 산업공학과, 2021. 2. 문일경.There is increasing interest in the unmanned aerial vehicle (UAV) in various fields of the industry, starting from the surveillance to the logistics. After introducing the smart city, there are attempts to utilize UAVs in the public service sector by connecting individual components of the system with both information and physical goods. In this dissertation, the UAV operation problems in the public service sector is modeled in the set covering approach. There is a vast literature on the facility location and set covering problems. However, when operating UAVs in the system, the plan has to make the most of the flexibility of the UAV, but also has to consider its physical limitation. We noticed a gap between the related, existing approaches and the technologies required in the field. That is, the new characteristics of the UAV hinder the existing solution algorithms, or a brand-new approach is required. In this dissertation, two operation problems to construct an emergency wireless network in a disaster situation by UAV and one location-allocation problem of the UAV emergency medical service (EMS) facility are proposed. The reformulation to the extended formulation and the corresponding branch-and-price algorithm can overcome the limitations and improve the continuous or LP relaxation bounds, which are induced by the UAV operation. A brief explanation of the UAV operation on public service, the related literature, and the brief explanation of the large-scale optimization techniques are introduced in Chapter 1, along with the research motivations and contributions, and the outline of the dissertations. In Chapter 2, the UAV set covering problem is defined. Because the UAV can be located without predefined candidate positions, more efficient operation becomes feasible, but the continuous relaxation bound of the standard formulation is weakened. The large-scale optimization techniques, including the Dantzig-Wolfe decomposition and the branch-and-price algorithm, could improve the continuous relaxation bound and reduce the symmetries of the branching tree and solve the realistic-scaled problems within practical computation time. To avoid numerical instability, two approximation models are proposed, and their approximation ratios are analyzed. In Chapter 3, UAV variable radius set covering problem is proposed with an extra decision on the coverage radius. While implementing the branch-and-price algorithm to the problem, a solvable equivalent formulation of the pricing subproblem is proposed. A heuristic based on the USCP is designed, and the proposed algorithm outperformed the benchmark genetic algorithm proposed in the literature. In Chapter 4, the facility location-allocation problem for UAV EMS is defined. The quadratic variable coverage constraint is reformulated to the linear equivalent formulation, and the nonlinear problem induced by the robust optimization approach is linearized. While implementing the large-scale optimization techniques, the structure of the subproblem is analyzed, and two solution approaches for the pricing subproblem are proposed, along with a heuristic. The results of the research can be utilized when implementing in the real applications sharing the similar characteristics of UAVs, but also can be used in its abstract formulation.현재, 지역 감시에서 물류까지, 무인항공기의 다양한 산업에의 응용이 주목받고 있다. 특히, 스마트 시티의 개념이 대두된 이후, 무인항공기를 공공 서비스 영역에 활용하여 개별 사회 요소를 연결, 정보와 물자를 교환하고자 하는 시도가 이어지고 있다. 본 논문에서는 공공 서비스 영역에서의 무인항공기 운영 문제를 집합덮개문제 관점에서 모형화하였다. 설비위치결정 및 집합덮개문제 영역에 많은 연구가 진행되어 있으나, 무인항공기를 운영하는 시스템의 경우 무인항공기가 갖는 자유도를 충분히 활용하면서도 무인항공기의 물리적 한계를 고려한 운영 계획을 필요로 한다. 우리는 본 문제와 관련된 기존 연구와 현장이 필요로 하는 기술의 괴리를 인식하였다. 이는 다시 말해, 무인항공기가 가지는 새로운 특성을 고려하면 기존의 문제 해결 방법을 통해 풀기 어렵거나, 혹은 새로운 관점에서의 문제 접근이 필요하다는 것이다. 본 논문에서는 재난이 발생한 지역에 무인항공기를 이용하여 긴급무선네트워크를 구성하는 두가지 문제와, 무인항공기를 이용하여 응급의료서비스를 제공하는 시설의 위치설정 및 할당문제를 제안한다. 확장문제로의 재공식화와 분지평가법을 활용하여, 무인항공기의 활용으로 인해 발생하는 문제 해결 방법의 한계를 극복하고 완화한계를 개선하였다. 공공 서비스 영역에서의 무인항공기 운영, 관련된 기존 연구와 본 논문에서 사용하는 대규모 최적화 기법에 대한 개괄적인 설명, 연구 동기 및 기여와 논문의 구성을 1장에서 소개한다. 2장에서는 무인항공기 집합덮개문제를 정의한다. 무인항공기는 미리 정해진 위치 없이 자유롭게 비행할 수 있기 때문에 더 효율적인 운영이 가능하나, 약한 완화한계를 갖게 된다. Dantzig-Wolfe 분해와 분지평가법을 포함한 대규모 최적화 기법을 통해 완화한계를 개선할 수 있으며, 분지나무의 대칭성을 줄여 실제 규모의 문제를 실용적인 시간 안에 해결할 수 있었다. 수치적 불안정성을 피하기 위하여, 두 가지 선형 근사 모형이 제안되었으며, 이들의 근사 비율을 분석하였다. 3장에서는 무인항공기 집합덮개문제를 일반화하여 무인항공기 가변반경 집합덮개문제를 정의한다. 분지평가법을 적용하면서 해결 가능한 평가 부문제를 제안하였으며, 휴리스틱을 설계하였다. 제안한 풀이 방법들이 기존 연구에서 제안한 벤치마크 유전 알고리즘을 능가하는 결과를 나타내었다. 4장에서는 무인항공기 응급의료서비스를 운영하는 시설의 위치설정 및 할당문제를 정의하였다. 2차 가변반경 범위제약이 선형의 동치인 수식으로 재공식화되었으며, 강건최적화 기법으로 인해 발생하는 비선형 문제를 선형화하였다. 대규모 최적화 기법을 적용하면서, 평가 부문제의 구조를 분석하여 두 가지 풀이 기법과 휴리스틱을 제안하였다. 본 연구의 결과는 무인항공기와 비슷한 특징을 가지는 실제 사례에 적용될 수 있으며, 추상적인 문제로써 다양한 분야에 그대로 활용될 수도 있다.Abstract i Contents vii List of Tables ix List of Figures xi Chapter 1 Introduction 1 1.1 Unmanned aerial vehicle operation on public services 1 1.2 Facility location problems 3 1.3 Large-scale optimization techniques 4 1.4 Research motivations and contributions 6 1.5 Outline of the dissertation 12 Chapter 2 Unmanned aerial vehicle set covering problem considering fixed-radius coverage constraint 14 2.1 Introduction 14 2.2 Problem definition 20 2.2.1 Problem description 22 2.2.2 Mathematical formulation 23 2.2.3 Discrete approximation model 26 2.3 Branch-and-price approach for the USCP 28 2.3.1 An extended formulation of the USCP 29 2.3.2 Branching strategies 34 2.3.3 Pairwise-conflict constraint approximation model based on Jung's theorem 35 2.3.4 Comparison of the approximation models 40 2.3.5 Framework of the solution algorithm for the PCBP model 42 2.4 Computational experiments 44 2.4.1 Datasets used in the experiments 44 2.4.2 Algorithmic performances 46 2.5 Solutions and related problems of the USCP 61 2.6 Summary 64 Chapter 3 Unmanned aerial vehicle variable radius set covering problem 66 3.1 Introduction 66 3.2 Problem definition 70 3.2.1 Mathematical model 72 3.3 Branch-and-price approach to the UVCP 76 3.4 Minimum covering circle-based approach 79 3.4.1 Formulation of the pricing subproblem II 79 3.4.2 Equivalence of the subproblem 82 3.5 Fixed-radius heuristic 84 3.6 Computational experiments 86 3.6.1 Datasets used in the experiments 88 3.6.2 Solution algorithms 91 3.6.3 Algorithmic performances 94 3.7 Summary 107 Chapter 4 Facility location-allocation problem for unmanned aerial vehicle emergency medical service 109 4.1 Introduction 109 4.2 Related literature 114 4.3 Location-allocation model for UEMS facility 117 4.3.1 Problem definition 118 4.3.2 Mathematical formulation 120 4.3.3 Linearization of the quadratic variable coverage distance function 124 4.3.4 Linear reformulation of standard formulation 125 4.4 Solution algorithms 126 4.4.1 An extended formulation of the ULAP 126 4.4.2 Branching strategy 129 4.4.3 Robust disjunctively constrained integer knapsack problem 131 4.4.4 MILP reformulation approach 132 4.4.5 Decomposed DP approach 133 4.4.6 Restricted master heuristic 136 4.5 Computational experiments 137 4.5.1 Datasets used in the experiments 137 4.5.2 Algorithmic performances 140 4.5.3 Analysis of the branching strategy and the solution approach of the pricing subproblem 150 4.6 Summary 157 Chapter 5 Conclusions and future research 160 5.1 Summary 160 5.2 Future research 163 Appendices 165 A Comparison of the computation times and objective value of the proposed algorithms 166 Bibliography 171 국문초록 188 감사의 글 190Docto

Developing New Multidimensional Knapsack Heuristics Based on Empirical Analysis of Legacy Heuristics

The multidimensional knapsack problem (MKP) has been used to model a variety of practical optimization and decision-making applications. Due to its combinatorial nature, heuristics are often employed to quickly find good solutions to MKPs. While there have been a variety of heuristics proposed for the MKP, and a plethora of empirical studies comparing the performance of these heuristics, little has been done to garner a deeper understanding of heuristic performance as a function of problem structure. This dissertation presents a research methodology, empirical and theoretical results explicitly aimed at gaining a deeper understanding of heuristic procedural performance as a function of test problem characteristics. This work first employs an available, robust set of two-dimensional knapsack problems in an empirical study to garner performance insights. These performance insights are tested against a larger set of problems, five-dimensional knapsack problems specifically generated for empirical testing purposes. The performance insights are found to hold in the higher dimensions. These insights are used to formulate and test a suite of three new greedy heuristics for the MKP, each improving upon its successor. These heuristics are found to outperform available legacy heuristics across a complete spectrum of test problems. Problem reduction heuristics are examined and the subsequent performance insights garnered are used to derive a new problem reduction heuristic, which is then further extended to employ a local improvement phase. These problem reduction heuristics are also found to outperform currently available approaches. Available problem test sets are shown lacking along multiple dimensions of importance for viable empirical testing. A new problem generation methodology is developed and shown to overcome the current limitations in available problem test sets. This problem generation methodology is used to generate a new set of empirical test problems specifically designed for competitive computational tests. This new test set is shown to stress existing heuristics; not only does the computational time required by these legacy heuristics increase with problem size, but solution quality is found to decrease with problem size. However, the solution quality obtained by the suite of heuristics developed in this dissertation are shown to be unaffected by problem size thereby providing a level of robust solution quality not previously seen in heuristic development for the MKP. This research demonstrates that the test problems can have a profound, and sometimes misleading, impact on the general insights gained via empirical testing, provides six new quality heuristics, and two new robust sets of test problems, one focused on empirical testing, the other focused on competitive testing