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Sustainability in Flood Management
Published in Saeid Eslamian, Faezeh Eslamian, Flood Handbook, 2022
In deciding the most appropriate alternative, the decision rule used in Decision Theory can be adopted [6]: Maximin, Minimax, Maximax, and Minimin. The Maximin criterion is based on a pessimistic view of the problem. Maximin aims to maximize the minimum gain. The alternative chosen should be the one that is the best among the worst options of all alternatives considered. Economically, one should determine the minimum economic benefit for each alternative and then choose the alternative with the highest minimum benefit. In the case of floods, the minimum economic benefit would correspond to the smallest difference between the economic loss that would result from them if nothing was done and the cost to avoid them. The Minimax criterion is a decision rule to minimize the possible loss for a worst-case scenario, that is, to choose the lowest of the possible maximum costs. In the case of floods, would be chosen the alternative of minor maximum cost to avoid flooding.
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Published in Harald Paganetti, Proton Therapy Physics, 2018
Alexei V. Trofimov, David Craft, Jan Unkelbach
Since robust planning techniques for IMPT were first investigated, the question whether one method is generally superior has been discussed. The probabilistic approach optimizes the average plan quality. It is possible that a plan does not achieve the desired dose quality for the worst scenario, for example in situations where a large number of scenarios are modeled. On the other hand, the minimax approach optimizes the plan for the worst case only and has no incentive to improve plan quality for more likely scenarios. It was shown that some methods do yield undesirable results in specific situations [36], but there is no comprehensive evidence that one method is generally superior. To first approximation, all methods achieve the features of robust plans described above if used adequately.
Engineering Decision-making
Published in Graeme Dandy, David Walker, Trevor Daniell, Robert Warner, Planning and Design of Engineering Systems, 2018
Graeme Dandy, David Walker, Trevor Daniell, Robert Warner
If the probabilities are unknown one way to choose is to assume the worst and minimise the potential losses. In this case the choice will be determined by the course of action that has the least worst outcome. Bennett (2001) has pointed out that the precautionary principle (in environmental theory) is equivalent to decision-making under uncertainty and in fact applies the pessimistic principle. Under a different name, the “minimax” strategy is a well known optimisation goal: minimise the maximum damage your opponent can do (Holland, 1998). Looking from the point of view of making profits rather than suffering losses ReVelle et al. (2004) refer to this as a ‘maximin’ strategy where the aim is to maximise the minimum payout. For the situation under discussion action a2 would be selected since its worst outcome is better than that for action a1 (40 compared to 20).
Data-driven distributionally robust risk parity portfolio optimization
Published in Optimization Methods and Software, 2022
The minimax problem has its roots in game theory [48]. In the context of this manuscript, we seek to minimize our cost function with respect to our decision variable, while the secondary player, i.e. ‘nature’, is adversarial and seeks to maximize our cost with respect to our uncertain parameters. Thus, our true goal is to minimize our cost within the decision space against the most adversarial instance of the underlying distribution of the uncertain parameters. Minimax problems have been widely studied in literature in both theory and applications [11,21,42,43,50]. We note that minimax problems are sometimes referred to as saddle-point problems [30,40] due to the ‘saddle’ shape of the cost function when viewed in the higher-dimensional space created by the decision variable and the uncertain parameters. In particular, our manuscript focuses on the well-behaved subset of convex–concave minimax problems.
Performance Study of Minimax and Reinforcement Learning Agents Playing the Turn-based Game Iwoki
Published in Applied Artificial Intelligence, 2021
Santiago Videgaín, Pablo García Sánchez
As a rule, the applications of the Minimax algorithm finish the search at a certain depth. The nodes of that depth become terminals and use a state evaluation function that determines a heuristic. This technique is called Minimax with suspension. It is also possible to limit the search by run time. The root node will stay with the best option found until the maximum time is reached. Applying these modifications on the Minimax algorithm will not be able to guarantee that the agent will find the optimal play, but it will be reliable if the heuristics are applied properly. Following these modifications to solve the problem of complexity, there are different techniques to improve Minimax, such as alpha-beta pruning, heuristic continuation (Russell and Norvig 2010) or the Scout Algorithm (Pearl 1980), among others. In the case of the basic Alpha-Beta pruning the number of nodes to be explored is reduced by avoiding passing through nodes in the tree that do not influence the decision of the agent. When a node does not provide a better value than the explored one until that moment, the branch is pruned.
Risk-based portfolio management of civil infrastructure assets under deep uncertainties associated with climate change: a robust optimisation approach
Published in Structure and Infrastructure Engineering, 2020
David Y. Yang, Dan M. Frangopol
Typically, robust optimisation starts with the identification of plausible scenarios. For instance, in climate change studies, future scenarios can be predicted based on global climate models and climate futures (Yang & Frangopol, 2018a; Yang & Frangopol, 2019; Liu, Yang & Frangopol, 2019). Based on the identified scenarios, robust optimisation formulates two-stage optimisation problems based on Wald’s maximin principle (Wald, 1949) by maximising the minimum benefits of a strategy. In the context of risk-based management, the maximin model is usually transformed to the equivalent minimax model where the optimal strategy is the one that minimises the maximum loss among those in all plausible scenarios. This principle of robust optimisation implies decision-making for the worst-case scenario.