Improving the multi-objective evolutionary optimization algorithm for hydropower reservoir operations in the California Oroville-Thermalito complex

This study demonstrates the application of an improved Evolutionary optimization Algorithm (EA), titled Multi-Objective Complex Evolution Global Optimization Method with Principal Component Analysis and Crowding Distance Operator (MOSPD), for the hydropower reservoir operation of the Oroville-Thermalito Complex (OTC) - a crucial head-water resource for the California State Water Project (SWP). In the OTC's water-hydropower joint management study, the nonlinearity of hydropower generation and the reservoir's water elevation-storage relationship are explicitly formulated by polynomial function in order to closely match realistic situations and reduce linearization approximation errors. Comparison among different curve-fitting methods is conducted to understand the impact of the simplification of reservoir topography. In the optimization algorithm development, techniques of crowding distance and principal component analysis are implemented to improve the diversity and convergence of the optimal solutions towards and along the Pareto optimal set in the objective space. A comparative evaluation among the new algorithm MOSPD, the original Multi-Objective Complex Evolution Global Optimization Method (MOCOM), the Multi-Objective Differential Evolution method (MODE), the Multi-Objective Genetic Algorithm (MOGA), the Multi-Objective Simulated Annealing approach (MOSA), and the Multi-Objective Particle Swarm Optimization scheme (MOPSO) is conducted using the benchmark functions. The results show that best the MOSPD algorithm demonstrated the best and most consistent performance when compared with other algorithms on the test problems. The newly developed algorithm (MOSPD) is further applied to the OTC reservoir releasing problem during the snow melting season in 1998 (wet year), 2000 (normal year) and 2001 (dry year), in which the more spreading and converged non-dominated solutions of MOSPD provide decision makers with better operational alternatives for effectively and efficiently managing the OTC reservoirs in response to the different climates, especially drought, which has become more and more severe and frequent in California

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

Maximizing Strike Planning Efficiency for a Given Class of Targets

Strike planning is one of the fundamental tasks of the Turkish Air Force and involves assignment of strike aircraft to targets with a maximum level of efficiency. Therefore, planning an optimal strike plan based on the preferences of the decision maker is crucial. The efficiency of the strike plan in this research implies attacking the maximum number of targets while considering target priority and the desired level of damage on each target. Another objective is to minimize the cost of the plan. This research develops an exact model that maximizes the efficiency of the strike plan using LINGO with Excel Spreadsheets. Given this efficiency, the aircraft and weapon costs plus the distance own is minimized while maintaining efficiency. The model also takes into account the aircraft and weapon capacities for particular types at each base to avoid assigning aircraft to targets from a base where there is an insufficient resource in terms of the aircraft and weapon capacity. The results show that the model developed in this research provides a great deal of cost saving (i.e., approximately 50 %) for a strike plan compared to a strike plan which does not consider the total cost

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

Extending the RoboCup Rescue to Support Stigmergy: Experiments and Results

Social insects have inspired researches in computer sciences as well asengineers to develop models for coordination and cooperation in multiagent systems.One example of these models is the model of stigmergy. In this model agents useindirect communication (comunication trough the environment) in order to coordinateactions. The RoboCup Rescue simulator is used as a testbed to evaluate this modelin a real world considering a highly constrained scenario of an earthquake. This pa-per investigates the feasibility of using stigmergy in the RoboCup Rescue and theimprovements of performance can be obtained. We extended the RoboCup Rescueenvironment to enable the use of stigmergy by the agents. We compared the results ofa multiagent system that uses stigmergy against two other approaches: a multiagentsystem that uses a greedy strategy and no communication, and a multiagent systemwhere agents communicate via direct messages. Experimental results shown that theuse of stigmergy leads to an improvement on agents’ performance by 9.02% to 38.6%if comparing to the system with no communication and can be statistically equivalentto the system which uses messages, depending on the scenario

RESOURCE ALLOCATION FOR WIRELESS RELAY NETWORKS

In this thesis, we propose several resource allocation strategies for relay networks in the context of joint power and bandwidth allocation and relay selection, and joint power allocation and subchannel assignment for orthogonal frequency division multiplexing (OFDM) and orthogonal frequency division multiple access (OFDMA) systems. Sharing the two best ordered relays with equal power between the two users over Rayleigh flat fading channels is proposed to establish full diversity order for both users. Closed form expressions for the outage probability, and bit error probability (BEP) performance measures for both amplify and forward (AF) and decode and forward (DF) cooperative communication schemes are developed for different scenarios. To utilize the full potentials of relay-assisted transmission in multi user systems, we propose a mixed strategy of AF relaying and direct transmission, where the user transmits part of the data using the relay, and the other part is transmitted using the direct link. The resource allocation problem is formulated to maximize the sum rate. A recursive algorithm alternating between power allocation and bandwidth allocation steps is proposed to solve the formulated resource allocation problem. Due to the conflict between limited wireless resources and the fast growing wireless demands, Stackelberg game is proposed to allocate the relay resources (power and bandwidth) between competing users, aiming to maximize the relay benefits from selling its resources. We prove the uniqueness of Stackelberg Nash Equilibrium (SNE) for the proposed game. We develop a distributed algorithm to reach SNE, and investigate the conditions for the stability of the proposed algorithm. We propose low complexity algorithms for AF-OFDMA and DF-OFDMA systems to assign the subcarriers to the users based on high SNR approximation aiming to maximize the weighted sum rate. Auction framework is proposed to devise competition based solutions for the resource allocation of AF-OFDMA aiming tomaximize either vi the sum rate or the fairness index. Two auction algorithms are proposed; sequential and one-shot auctions. In sequential auction, the users evaluate the subcarrier based on the rate marginal contribution. In the one-shot auction, the users evaluate the subcarriers based on an estimate of the Shapley value and bids on all subcarriers at once

An overview of population-based algorithms for multi-objective optimisation

In this work we present an overview of the most prominent population-based algorithms and the methodologies used to extend them to multiple objective problems. Although not exact in the mathematical sense, it has long been recognised that population-based multi-objective optimisation techniques for real-world applications are immensely valuable and versatile. These techniques are usually employed when exact optimisation methods are not easily applicable or simply when, due to sheer complexity, such techniques could potentially be very costly. Another advantage is that since a population of decision vectors is considered in each generation these algorithms are implicitly parallelisable and can generate an approximation of the entire Pareto front at each iteration. A critique of their capabilities is also provided

Pole Placement and Reduced-Order Modelling for Time-Delayed Systems Using Galerkin Approximations

The dynamics of time-delayed systems (TDS) are governed by delay differential equa- tions (DDEs), which are infinite dimensional and pose computational challenges. The Galerkin approximation method is one of several techniques to obtain the spectrum of DDEs for stability and stabilization studies. In the literature, Galerkin approximations for DDEs have primarily dealt with second-order TDS (second-order Galerkin method), and the for- mulations have resulted in spurious roots, i.e., roots that are not among the characteristic roots of the DDE. Although these spurious roots do not affect stability studies, they never- theless add to the complexity and computation time for control and reduced-order modelling studies of DDEs. A refined mathematical model, called the first-order Galerkin method, is proposed to avoid spurious roots, and the subtle differences between the two formulations (second-order and first-order Galerkin methods) are highlighted with examples. For embedding the boundary conditions in the first-order Galerkin method, a new pseudoinverse-based technique is developed. This method not only gives the exact location of the rightmost root but also, on average, has a higher number of converged roots when compared to the existing pseudospectral differencing method. The proposed method is combined with an optimization framework to develop a pole-placement technique for DDEs to design closed-loop feedback gains that stabilize TDS. A rotary inverted pendulum system apparatus with inherent sensing delays as well as deliberately introduced time delays is used to experimentally validate the Galerkin approximation-based optimization framework for the pole placement of DDEs. Optimization-based techniques cannot always place the rightmost root at the desired location; also, one has no control over the placement of the next set of rightmost roots. However, one has the precise location of the rightmost root. To overcome this, a pole- placement technique for second-order TDS is proposed, which combines the strengths of the method of receptances and an optimization-based strategy. When the method of receptances provides an unsatisfactory solution, particle swarm optimization is used to improve the location of the rightmost pole. The proposed approach is demonstrated with numerical studies and is validated experimentally using a 3D hovercraft apparatus. The Galerkin approximation method contains both converged and unconverged roots of the DDE. By using only the information about the converged roots and applying the eigenvalue decomposition, one obtains an r-dimensional reduced-order model (ROM) of the DDE. To analyze the dynamics of DDEs, we first choose an appropriate value for r; we then select the minimum value of the order of the Galerkin approximation method system at which at least r roots converge. By judiciously selecting r, solutions of the ROM and the original DDE are found to match closely. Finally, an r-dimensional ROM of a 3D hovercraft apparatus in the presence of delay is validated experimentally