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Multi-objective optimization for security games
- IN INTERNATIONAL CONFERENCE ON AUTONOMOUS AGENTS AND MULTIAGENT SYSTEMS (AAMAS
, 2012
"... The burgeoning area of security games has focused on real-world domains where security agencies protect critical infrastructure from a diverse set of adaptive adversaries. There are security domains where the payoffs for preventing the different types of adversaries may take different forms (seized ..."
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The burgeoning area of security games has focused on real-world domains where security agencies protect critical infrastructure from a diverse set of adaptive adversaries. There are security domains where the payoffs for preventing the different types of adversaries may take different forms (seized money, reduced crime, saved lives, etc) which are not readily comparable. Thus, it can be difficult to know how to weigh the different payoffs when deciding on a security strategy. To address the challenges of these domains, we propose a fundamentally different solution concept, multi-objective security games (MOSG), which combines security games and multiobjective optimization. Instead of a single optimal solution, MOSGs have a set of Pareto optimal (non-dominated) solutions referred to as the Pareto frontier. The Pareto frontier can be generated by solving a sequence of constrained single-objective optimization problems (CSOP), where one objective is selected to be maximized while lower bounds are specified for the other objectives. Our contributions include: (i) an algorithm, Iterative ɛ-Constraints, for generating the sequence of CSOPs; (ii) an exact approach for solving an MILP formulation of a CSOP (which also applies to multi-objective optimization in more general Stackelberg games); (iii) heuristics that achieve speedup by exploiting the structure of security games to further constrain a CSOP; (iv) an approximate approach for solving an algorithmic formulation of a CSOP, increasing the scalability of our approach with quality guarantees. Additional contributions of this paper include proofs on the level of approximation and detailed experimental evaluation of the proposed approaches.
An Extended Study on Multi-Objective Security Games
- AUTONOMOUS AGENTS AND MULTI-AGENT SYSTEMS
"... The burgeoning area of security games has focused on real-world domains where security agencies protect critical infrastructure from a diverse set of adaptive adversaries. In such domains, decision makers have multiple competing objectives they must consider which may take different forms that are ..."
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Cited by 4 (2 self)
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The burgeoning area of security games has focused on real-world domains where security agencies protect critical infrastructure from a diverse set of adaptive adversaries. In such domains, decision makers have multiple competing objectives they must consider which may take different forms that are not readily comparable including safety, cost, and public perception. Thus, it can be difficult to know how to weigh the different objectives when deciding on a security strategy. To address the challenges of these domains, we pro-pose a fundamentally different solution concept, multi-objective security games (MOSG). Instead of a single optimal solution, MOSGs have a set of Pareto optimal (non-dominated) solutions referred to as the Pareto frontier, which can be generated by solving a sequence of constrained single-objective optimization problems (CSOP). The Pareto frontier allows the decision maker to analyze the tradeoffs that exist between the multiple objectives. Our con-tributions include: (i) an algorithm, Iterative--Constraints, for generating the sequence of CSOPs; (ii) an exact approach for solving an MILP formulation of a CSOP; (iii) heuristics that achieve speed up by exploiting the structure of security games to further constrain the
Succinct Sampling from Discrete Distributions
"... We revisit the classic problem of sampling from a discrete distribution: Given n non-negative w-bit integers x1,..., xn, the task is to build a data structure that allows sampling i with probability proportional to xi. The classic solution is Walker’s alias method that takes, when implemented on a W ..."
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We revisit the classic problem of sampling from a discrete distribution: Given n non-negative w-bit integers x1,..., xn, the task is to build a data structure that allows sampling i with probability proportional to xi. The classic solution is Walker’s alias method that takes, when implemented on a Word RAM, O(n) preprocessing time, O(1) expected query time for one sample, and n(w+2 lg n+o(1)) bits of space. Using the terminology of succinct data structures, this solution has redundancy 2n lg n + o(n) bits, i.e., it uses 2n lg n + o(n) bits in addition to the information theoretic minimum required for storing the input. In this paper, we study whether this space usage can be improved. In the systematic case, in which the input is read-only, we present a novel data structure using r + O(w) redundant
A Fast Approximation-Guided Evolutionary Multi-Objective Algorithm
"... Approximation-Guided Evolution (AGE) [4] is a recently presented multi-objective algorithm that outperforms state-of-the-art multimulti-objective algorithms in terms of approximation quality. This holds for problems with many objectives, but AGE’s performance is not competitive on problems with few ..."
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Approximation-Guided Evolution (AGE) [4] is a recently presented multi-objective algorithm that outperforms state-of-the-art multimulti-objective algorithms in terms of approximation quality. This holds for problems with many objectives, but AGE’s performance is not competitive on problems with few objectives. Furthermore, AGE is storing all non-dominated points seen so far in an archive, which can have very detrimental effects on its runtime. In this article, we present the fast approximation-guided evolutionary algorithm called AGE-II. It approximates the archive in order to control its size and its influence on the runtime. This allows for trading-off approximation and runtime, and it enables a faster approximation process. Our experiments show that AGE-II performs very well for multi-objective problems having few as well as many objectives. It scales well with the number of objectives and enables practitioners to add objectives to their problems at small additional computational cost.
Efficient Parent Selection for Approximation-Guided Evolutionary Multi-Objective Optimization
"... Abstract—The Pareto front of a multi-objective optimization problem is typically very large and can only be approximated. Approximation-Guided Evolution (AGE) is a recently presented evolutionary multi-objective optimization algorithm that aims at minimizing iteratively the approximation factor, whi ..."
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Abstract—The Pareto front of a multi-objective optimization problem is typically very large and can only be approximated. Approximation-Guided Evolution (AGE) is a recently presented evolutionary multi-objective optimization algorithm that aims at minimizing iteratively the approximation factor, which measures how well the current population approximates the Pareto front. It outperforms state-of-the-art algorithms for problems with many objectives. However, AGE’s performance is not competitive on problems with very few objectives. We study the reason for this behavior and observe that AGE selects parents uniformly at random, which has a detrimental effect on its performance. We then investigate different algorithm-specific selection strategies for AGE. The main difficulty here is finding a computationally efficient selection scheme which does not harm AGEs linear runtime in the number of objectives. We present several improved selections schemes that are computationally efficient and substantially improve AGE on low-dimensional objective spaces, but have no negative effect in high-dimensional objective spaces. I.
A Multi-Objective Memetic Algorithm for Vehicle Resource Allocation in Sustainable Transportation Planning
- PROCEEDINGS OF THE TWENTY-THIRD INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
"... Sustainable supply chain management has been an increasingly important topic of research in recent years. At the strategic level, there are computational models which study supply and distribution networks with environmental considerations. At the operational level, there are, for example, routing a ..."
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Sustainable supply chain management has been an increasingly important topic of research in recent years. At the strategic level, there are computational models which study supply and distribution networks with environmental considerations. At the operational level, there are, for example, routing and scheduling models which are constrained by carbon emissions. Our paper explores work in tactical planning with regards to vehicle resource allocation from distribution centers to customer locations in a multi-echelon logistics network. We formulate the bi-objective optimization problem exactly and design a memetic algorithm to efficiently derive an approximate Pareto front. We illustrate the applicability of our approach with a large realworld dataset.
A Multi-Objective Memetic Algorithm for Vehicle Resource Allocation in Sustainable Transportation Planning
"... Sustainable supply chain management has been an increasingly important topic of research in recent years. At the strategic level, there are computational models which study supply and distribution networks with environmental considerations. At the operational level, there are, for example, routing a ..."
Abstract
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Sustainable supply chain management has been an increasingly important topic of research in recent years. At the strategic level, there are computational models which study supply and distribution networks with environmental considerations. At the operational level, there are, for example, routing and scheduling models which are constrained by carbon emissions. Our paper explores work in tactical planning with regards to vehicle resource allocation from distribution centers to customer locations in a multi-echelon logistics network. We formulate the bi-objective optimization problem exactly and design a memetic algorithm to efficiently derive an approximate Pareto front. We illustrate the applicability of our approach with a large realworld dataset. 1
Evolutionary Many-Objective Optimization: A Quick-Start Guide
"... Multi-objective optimization problems having more than three objectives are referred to as many-objective optimization problems. Many-objective optimiza-tion brings with it a number of challenges that must be addressed, which high-lights the need for new and better algorithms that can efficiently ha ..."
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Multi-objective optimization problems having more than three objectives are referred to as many-objective optimization problems. Many-objective optimiza-tion brings with it a number of challenges that must be addressed, which high-lights the need for new and better algorithms that can efficiently handle the growing number of objectives. This article reviews the different challenges as-sociated with many-objective optimization and the work that has been done in the recent-past to alleviate these difficulties. It also highlights how the existing methods and body of knowledge have been used to address the different real world many-objective problems. Finally, it brings focus to some future research opportunities that exist with many-objective optimization. We report in this article what is commonly used, be it algorithms or test problems, so that the reader knows what are the benchmarks and also what other options are available. We deem this to be especially useful for new researchers and for researchers from other fields who wish to do some work in the area of many-objective optimization.
An Adaptive Data Structure for Evolutionary Multi-Objective Algorithms with Unbounded Archives
"... Abstract—Archives have been widely used in evolutionary multi-objective optimization in order to store the optimal points found so far during the optimization process. Usually the size of an archive is bounded which means that the number of points it can store is limited. This implies that knowledge ..."
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Abstract—Archives have been widely used in evolutionary multi-objective optimization in order to store the optimal points found so far during the optimization process. Usually the size of an archive is bounded which means that the number of points it can store is limited. This implies that knowledge about the set of non-dominated solutions that has been obtained during the optimization process gets lost. Working with unbounded archives allows to keep this knowledge which can be useful for the progress of an evolutionary multi-objective algorithm. In this paper, we propose an adaptive data structure for dealing with unbounded archives. This data structure allows to traverse the archive efficiently and can also be used for sampling solutions from the archive which can be used for reproduction.
