Probabilistic Solution Discovery Research Articles

Joint optimization of structure and protection of interdependent infrastructure networks

Nowadays, critical infrastructures are essential for the normal operation of economics and social life. Because of the increasing number of terrorist attacks and other accidents, research on strengthening infrastructure protection has become essential. Meanwhile, the operation of many types of infrastructures mainly relies on the configuration of networks. The interdependent infrastructure network (IIN), which is a network comprising multiple infrastructure networks with different functions under supporting relationships, is highly influenced by the interdependency structure of these networks and the protection strategy. To better understand the relation between the interdependency structure and protection in two phases on infrastructure resilience and analyze their influence on IIN performance, this study investigates the IIN in a community and proposes a joint optimization method for the two phases based on an incomplete-information game under the situation of intentional attacks. Employing the maximal-flow index (MFI) as the performance metric, a multi-objective planning approach is proposed for the joint optimization of interdependency structure and protection. Furthermore, an improved probabilistic solution discovery algorithm (PSDA) is developed to solve the planning model, and the joint optimization is analyzed using extensive experimentation, including three real-world infrastructure examples.

Network Reconfiguration for Increasing Transportation System Resilience Under Extreme Events.

Evacuating residents out of affected areas is an important strategy for mitigating the impact of natural disasters. However, the resulting abrupt increase in the travel demand during evacuation causes severe congestions across the transportation system, which thereby interrupts other commuters' regular activities. In this article, a bilevel mathematical optimization model is formulated to address this issue, and our research objective is to maximize the transportation system resilience and restore its performance through two network reconfiguration schemes: contraflow (also referred to as lane reversal) and crossing elimination at intersections. Mathematical models are developed to represent the two reconfiguration schemes and characterize the interactions between traffic operators and passengers. Specifically, traffic operators act as leaders to determine the optimal system reconfiguration to minimize the total travel time for all the users (both evacuees and regular commuters), while passengers act as followers by freely choosing the path with the minimum travel time, which eventually converges to a user equilibrium state. For each given network reconfiguration, the lower-level problem is formulated as a traffic assignment problem (TAP) where each user tries to minimize his/her own travel time. To tackle the lower-level optimization problem, a gradient projection method is leveraged to shift the flow from other nonshortest paths to the shortest path between each origin-destination pair, eventually converging to the user equilibrium traffic assignment. The upper-level problem is formulated as a constrained discrete optimization problem, and a probabilistic solution discovery algorithm is used to obtain the near-optimal solution. Two numerical examples are used to demonstrate the effectiveness of the proposed method in restoring the traffic system performance.

Resilience-based network design under uncertainty

This paper introduces an approach to quantify resilience for the design of systems that can be described as a network. A key characteristic of resilience is the ability of restoring functionality and performance in response to a disruptive event. Therefore, the restoration behavior is encapsulated via a non-linear function that provides the ability to model at the component level more refined attributes of restoration. In particular, it considers the remaining capacity (absorptive ability), the degree to which capability can be recovered (restoration ability) and the recovery speed. The component restoration functions can then be used to impose a resilience target at a given time as a design constraint.The resilience-based design optimization is then formulated for both deterministic and stochastic cases of a network system. The objective is to have as the design solution a network that incurs the least cost while meeting system resilience constraints. Maximum flow through the network is used as a measure of system performance. Several possible links are examined with regards to flow performance from origin node to a destination node. A probabilistic solution discovery algorithm is combined with stochastic ranking to approach this problem. Two numerical examples are used to illustrate the procedure and the effectiveness of the proposed method.

A Game Theoretic Approach to Network Reliability Assessment

This paper evaluates the network reliability from a game theory perspective. We formulate a network game consisting of two players—router and attacker, where the router seeks to minimize his total expected trip cost, while the attacker attempts to maximize the expected trip cost by undermining some of the network links. Each link has a probabilistic cost in accordance with its state (normal or damaged). Two different scenarios are considered: link cost independent of the flow and link cost dependent on the flow. We are interested in the link use and damage probabilities at system equilibrium for both cases, and these probabilities are derived in a four-step procedure. First, for the router, Dijkstra and the Frank–Wolfe (FW) algorithms are used to optimize his strategy under the two scenarios, respectively. Second, we model the attacker's problem as a constrained optimization problem, in which all the decision variables are binary. A probabilistic solution discovery algorithm (PSDA) is integrated with stochastic ranking to determine the attacker's optimal strategy. Third, we leverage the Method of Successive Averages (MSA) to approximate the router's link use probabilities and attacker's link damage probabilities at the mixed Nash equilibrium of the game. Finally, given the router's probability of traveling through each link and attacker's probability of undermining each link, we use Monte Carlo Simulations (MCS) to estimate the network reliability as the router arriving the destination node within a prescribed time. Two numerical examples are used to illustrate the procedures and effectiveness of the proposed method.

A probabilistic solution discovery algorithm for solving 0-1 knapsack problem

In this paper, a probabilistic solution discovery algorithm is developed to solve the NP-hard 0-1 knapsack problem. The proposed method consists of three steps: strategy development, strategy analysis, and solution discovery. In the first step, Monte Carlo simulation is used to generate the strategies based on a vector defining the probability that each item is included in the knapsack. In the second step, we analyse the capacity imposed by each strategy previously generated and penalise the objective value for those strategies exceeding the capacity of the knapsack. At the last step, a subset of ordered strategies is used to update the vector that defines the probability of choosing each item. Two numerical examples are used to demonstrate the efficiency and the performance of the proposed method.

A robust reliability redundancy allocation problem under abnormal external failures guided by a new importance measure

Besides inherent failures under normal conditions studied by classical reliability engineering, systems may also be subject to abnormal external failures, whose probabilities are hard, if not impossible, to predict, such as failures caused by natural disasters (e.g. earthquakes, floods, and tornados) and malicious attacks. Thus, abnormal external failures need to be considered when designing a system, as in reliability redundancy allocation problem. To deal with the uncertainty of abnormal external failures and based on robust optimization, this research proposes a multi-objective optimization approach that can simultaneously maximize system reliability under both normal and the worst cases of abnormal external failures for redundancy allocation problem. Since the amount of abnormal external failures is usually unknown, the worst case for each possible amount of abnormal external failures needs to be identified first. For this purpose, a new importance measure that can quantify the importance of a subset of system components with arbitrary cardinality is proposed. We also revise a widely used multi-objective evolutionary algorithm, multi-objective probabilistic solution discovery algorithm, to deal with the complexity of redundancy allocation problem. The merits of the revised algorithm are demonstrated by extensive experiments.

A multiple-level variable neighborhood search approach to the orienteering problem

A multiple-level variable neighborhood search (ML-VNS) approach is developed for the orienteering problem (OP) which maximizes the reward collected from visited sites while satisfying predetermined constraints. The ML-VNS approach remedies situations in which the information accumulated during the search process of an individual instance is not shared with the search processes in other instances with different constraint levels. New large-sized OPs have been defined. Results of the ML-VNS approach show promise when compared with previous tabu search (TS) algorithm and probabilistic solution discovery algorithm (PSDA).

Implementation of multi-objective optimization for vulnerability analysis of complex networks

This paper describes the vulnerability analysis of a complex network as the process of identifying the combination of component failures that provide maximum reduction of network performance. By way of a vulnerability analysis, the understanding of these failures can be related to the occurrence of a disruptive event, and also to the fundamental tasks for the protection of critical infrastructures. To describe vulnerability, the paper provides an analytical method to characterize completely the importance of network disruptions and identify a vulnerability set via the solution of a proposed multi-objective network vulnerability problem. This approach makes it possible to recognize that decision-makers (e.g. network managers) could benefit from understanding the relationship between different failure scenarios and network performance, for example, how the increase in protection resources would reduce the vulnerability of the network. Numerical examples, related to a medium-sized network and two complex networks, are solved using the evolutionary algorithm known as the multi-objective probabilistic solution discovery algorithm (MO-PSDA) and illustrate the proposed approach.

Design of reliable communication networks: A hybrid ant colony optimization algorithm

This article proposes a hybrid approach based on Ant Colony Optimization (ACO) and Simulated Annealing (SA), called ACO_SA, for the design of communication networks. The design problem is to find the optimal network topology for which the total cost is a minimum and the all-terminal reliability is not less than a given level of reliability. The proposed ACO_SA has the advantages of the ability to find higher performance solutions, created by the ACO, and the ability to jump out of local minima to find better solutions, created by the SA. The effectiveness of ACO_SA is investigated by comparing its results with those obtained by individual application of SA and ACO, which are basic forms of ACO_SA, two different genetic algorithms and a probabilistic solution discovery algorithm given in the literature for the design problem. Computational results show that ACO_SA has a better performance than its basic forms and the investigated heuristic approaches.

Probabilistic solution discovery algorithm for the orienteering problem

Orienteering is a competition where participants have a specific time to travel between initial and final locations. This competition is known as the orienteering problem (OP) where the objective is to maximise the reward of visiting sites while not violating constraints on time and final location. Although very good solutions can be obtained via search space heuristics, their coding, development and implementation still require extensive familiarisation and background on the technique of choice. This paper presents an evolutionary algorithm that offers simple and efficient analysis for the OP via three interrelated steps: solution generation via Monte Carlo (MC) simulation; analysis and computation of the reward and distance of these solutions and an evolutionary technique that drives the selection of potentially optimal solutions. The algorithm is tested against benchmark techniques for problems previously solved in the literature and newly developed larger size test problems.

Multistate stochastic network interdiction via reliability modelling and evolutionary optimization

This paper extends the current stochastic network interdiction problem (SNIP) approaches to allow for the inclusion of multistate behaviour of link flow when a given link is targeted for interdiction. Under this modelling scenario, described as the multistate SNIP, a new optimization model is described for maximizing the reliability associated with an interdiction strategy constrained to a prespecified s— t flow and a prespecified cost. An evolutionary algorithm, known as the probabilistic solution discovery algorithm, is used to obtain quasi-optimal solutions for the multistate SNIP problem. This algorithm comprises a three-step process that implements multistate network reliability computation techniques along with an evolutionary optimization routine to find interdiction strategies. The solutions to different test cases show that the optimization routine is able to identify high-quality solutions in a significantly reduced search space.

Stochastic network interdiction optimization via capacitated network reliability modeling and probabilistic solution discovery

This paper introduces an evolutionary optimization approach that can be readily applied to solve stochastic network interdiction problems (SNIP). The network interdiction problem solved considers the minimization of the cost associated with an interdiction strategy such that the maximum flow that can be transmitted between a source node and a sink node for a fixed network design is greater than or equal to a given reliability requirement. Furthermore, the model assumes that the nominal capacity of each network link and the cost associated with their interdiction can change from link to link and that such interdiction has a probability of being successful. This version of the SNIP is for the first time modeled as a capacitated network reliability problem allowing for the implementation of computation and solution techniques previously unavailable. The solution process is based on an evolutionary algorithm that implements: (1) Monte-Carlo simulation, to generate potential network interdiction strategies, (2) capacitated network reliability techniques to analyze strategies’ source–sink flow reliability and, (3) an evolutionary optimization technique to define, in probabilistic terms, how likely a link is to appear in the final interdiction strategy. Examples for different sizes of networks are used throughout the paper to illustrate the approach.

Optimal design of cluster-based ad-hoc networks using probabilistic solution discovery

The reliability of ad-hoc networks is gaining popularity in two areas: as a topic of academic interest and as a key performance parameter for defense systems employing this type of network. The ad-hoc network is dynamic and scalable and these descriptions are what attract its users. However, these descriptions are also synonymous for undefined and unpredictable when considering the impacts to the reliability of the system. The configuration of an ad-hoc network changes continuously and this fact implies that no single mathematical expression or graphical depiction can describe the system reliability-wise. Previous research has used mobility and stochastic models to address this challenge successfully. In this paper, the authors leverage the stochastic approach and build upon it a probabilistic solution discovery (PSD) algorithm to optimize the topology for a cluster-based mobile ad-hoc wireless network (MAWN). Specifically, the membership of nodes within the back-bone network or networks will be assigned in such as way as to maximize reliability subject to a constraint on cost. The constraint may also be considered as a non-monetary cost, such as weight, volume, power, or the like. When a cost is assigned to each component, a maximum cost threshold is assigned to the network, and the method is run; the result is an optimized allocation of the radios enabling back-bone network(s) to provide the most reliable network possible without exceeding the allowable cost. The method is intended for use directly as part of the architectural design process of a cluster-based MAWN to efficiently determine an optimal or near-optimal design solution. It is capable of optimizing the topology based upon all-terminal reliability (ATR), all-operating terminal reliability (AoTR), or two-terminal reliability (2TR).

Port-of-entry safety via the reliability optimization of container inspection strategy through an evolutionary approach

Up to now, of all the containers received in USA ports, roughly between 2% and 5% are scrutinized to determine if they could cause some type of danger or contain suspicious goods. Recently, concerns have been raised regarding the type of attack that could happen via container cargo leading to devastating economic, psychological and sociological effects. Overall, this paper is concerned with developing an inspection strategy that minimizes the total cost of inspection while maintaining a user-specified detection rate for “suspicious” containers. In this respect, a general model for describing an inspection strategy is proposed. The strategy is regarded as an ( n+1)-echelon decision tree where at each of these echelons, a decision has to be taken, regarding which sensor to be used, if at all. Second, based on the general decision-tree model, this paper presents a minimum cost container inspection strategy that conforms to a pre-specified user detection rate under the assumption that different sensors with different reliability and cost characteristics can be used. To generate an optimal inspection strategy, an evolutionary optimization approach known as probabilistic solution discovery algorithm has been used.

All-terminal network reliability optimization via probabilistic solution discovery

This paper presents a new algorithm that can be readily applied to solve the all-terminal network reliability allocation problems. The optimization problem solved considers the minimization of the network design cost subject to a known constraint on all-terminal reliability by assuming that the network contains a known number of functionally equivalent components (with different performance specifications) that can be used to provide redundancy. The algorithm is based on two major steps that use a probabilistic solution discovery approach and Monte Carlo simulation to generate the quasi-optimal network designs. Examples for different sizes of all-terminal networks are used throughout the paper to illustrate the approach. The results obtained for the larger networks with unknown optima show that the quality of the solutions generated by the proposed algorithm is significantly higher with respect to other approaches and that these solutions are obtained from restricted solution search space. Although developed for all-terminal reliability optimization, the algorithm can be easily applied in other resource-constrained allocation problems.