Zeitschriftenartikel zum Thema „Network interdiction problems“

Network interdiction problem arises when an unwanted agent attacks the network system to deteriorate its transshipment efficiency. Literature is flourished with models and solution approaches for the problem. This paper considers a single commodity lexicographic maximum flow problem on a directed network with capacitated vertices to study two network flow problems under an arc interdiction. In the first, the objective is to find an arc on input network to be destroyed so that the residual lexicographically maximum flow is lexicographically minimum. The second problem aims to find a flow pattern resulting lexicographically maximum flow on the input network so that the total residual flow, if an arc is destroyed, is maximum. The paper proposes strongly polynomial time solution procedures for these problems.

Goal recognition (GR) is a method of inferring the goals of other agents, which enables humans or AI agents to proactively make response plans. Goal recognition design (GRD) has been proposed to deliberately redesign the underlying environment to accelerate goal recognition. Along with the GR and GRD problems, in this paper, we start by introducing the goal recognition control (GRC) problem under network interdiction, which focuses on controlling the goal recognition process. When the observer attempts to facilitate the explainability of the actor’s behavior and accelerate goal recognition by reducing the uncertainty, the actor wants to minimize the privacy information leakage by manipulating the asymmetric information and delay the goal recognition process. Then, the GRC under network interdiction is formulated as one static Stackelberg game, where the observer obtains asymmetric information about the actor’s intended goal and proactively interdicts the edges of the network with a bounded resource. The privacy leakage of the actor’s actions about the real goals is quantified by a min-entropy information metric and this privacy information metric is associated with the goal uncertainty. Next in importance, we define the privacy information metric based GRC under network interdiction (InfoGRC) and the information metric based GRC under threshold network interdiction (InfoGRCT). After dual reformulating, the InfoGRC and InfoGRCT as bi-level mixed-integer programming problems, one Benders decomposition-based approach is adopted to optimize the observer’s optimal interdiction resource allocation and the actor’s cost-optimal path-planning. Finally, some experimental evaluations are conducted to demonstrate the effectiveness of the InfoGRC and InfoGRCT models in the task of controlling the goal recognition process.

Abstract Motivation Flux balance analysis (FBA) based bilevel optimization has been a great success in redesigning metabolic networks for biochemical overproduction. To date, many computational approaches have been developed to solve the resulting bilevel optimization problems. However, most of them are of limited use due to biased optimality principle, poor scalability with the size of metabolic networks, potential numeric issues or low quantity of design solutions in a single run. Results Here, we have employed a network interdiction model free of growth optimality assumptions, a special case of bilevel optimization, for computational strain design and have developed a hybrid Benders algorithm (HBA) that deals with complicating binary variables in the model, thereby achieving high efficiency without numeric issues in search of best design strategies. More importantly, HBA can list solutions that meet users’ production requirements during the search, making it possible to obtain numerous design strategies at a small runtime overhead (typically ∼1 h, e.g. studied in this article). Availability and implementation Source code implemented in the MATALAB Cobratoolbox is freely available at https://github.com/chang88ye/NIHBA. Contact math4neu@gmail.com or natalio.krasnogor@ncl.ac.uk Supplementary information Supplementary data are available at Bioinformatics online.

Most violent crimes happen in urban and suburban cities. With emerging tracking techniques, law enforcement officers can have real-time location information of the escaping criminals and dynamically adjust the security resource allocation to interdict them. Unfortunately, existing work on urban network security games largely ignores such information. This paper addresses this omission. First, we show that ignoring the real-time information can cause an arbitrarily large loss of efficiency. To mitigate this loss, we propose a novel NEtwork purSuiT game (NEST) model that captures the interaction between an escaping adversary and a defender with multiple resources and real-time information available. Second, solving NEST is proven to be NP-hard. Third, after transforming the non-convex program of solving NEST to a linear program, we propose our incremental strategy generation algorithm, including: (i) novel pruning techniques in our best response oracle; and (ii) novel techniques for mapping strategies between subgames and adding multiple best response strategies at one iteration to solve extremely large problems. Finally, extensive experiments show the effectiveness of our approach, which scales up to realistic problem sizes with hundreds of nodes on networks including the real network of Manhattan.

This study generalizes the r-interdiction median (RIM) problem with fortification to simultaneously consider two types of risks: probabilistic exogenous disruptions and endogenous disruptions caused by intentional attacks. We develop a bilevel programming model that includes a lower-level interdiction problem and a higher-level fortification problem to hedge against such risks. We then prove that the interdiction problem is supermodular and subsequently adopt the cuts associated with supermodularity to develop an efficient cutting-plane algorithm to achieve exact solutions. For the fortification problem, we adopt the logic-based Benders decomposition (LBBD) framework to take advantage of the two-level structure and the property that a facility should not be fortified if it is not attacked at the lower level. Numerical experiments show that the cutting-plane algorithm is more efficient than benchmark methods in the literature, especially when the problem size grows. Specifically, with regard to the solution quality, LBBD outperforms the greedy algorithm in the literature with an up-to 13.2% improvement in the total cost, and it is as good as or better than the tree-search implicit enumeration method. Summary of Contribution: This paper studies an r-interdiction median problem with fortification (RIMF) in a supply chain network that simultaneously considers two types of disruption risks: random disruptions that occur probabilistically and disruptions caused by intentional attacks. The problem is to determine the allocation of limited facility fortification resources to an existing network. It is modeled as a bilevel programming model combining a defender’s problem and an attacker’s problem, which generalizes the r-interdiction median problem with probabilistic fortification. This paper is suitable for IJOC in mainly two aspects: (1) The lower-level attacker’s interdiction problem is a challenging high-degree nonlinear model. In the literature, only a total enumeration method has been applied to solve a special case of this problem. By exploring the special structural property of the problem, namely, the supermodularity of the transportation cost function, we developed an exact cutting-plane method to solve the problem to its optimality. Extensive numerical studies were conducted. Hence, this paper fits in the intersection of operations research and computing. (2) We developed an efficient logic-based Benders decomposition algorithm to solve the higher-level defender’s fortification problem. Overall, this study generalizes several important problems in the literature, such as RIM, RIMF, and RIMF with probabilistic fortification (RIMF-p).

The annual Visual Analytics Science and Technology (VAST) challenge provides Visual Analytics researchers, developers, and designers an opportunity to apply their best tools and techniques against invented problems that include a realistic scenario, data, tasks, and questions to be answered. Submissions are processed much like conference papers, contestants are provided reviewer feedback, and excellence is recognized with awards. A day-long VAST Challenge workshop takes place each year at the IEEE VAST conference to share results and recognize outstanding submissions. Short papers are published each year in the annual VAST proceedings. Over the history of the challenge, participants have investigated a wide variety of scenarios, such as bioterrorism, epidemics, arms smuggling, social unrest, and computer network attacks, among many others. Contestants have been provided with large numbers of realistic but synthetic Coast Guard interdiction records, intelligence reports, hospitalization records, microblog records, personal RFID tag locations, huge amounts of cyber security log data, and several hours of video. This paper describes the process for developing the synthetic VAST Challenge datasets and conducting the annual challenges. This paper also provides an introduction to this special issue of Information Visualization, focusing on the impacts of the VAST Challenge.

Recently, industrial control system (ICS) has gradually been a primary attack target. The main reason is that increasing vulnerabilities exposed provide opportunities for launching multistep and multihost attacks to breach security policies. To that end, vulnerability remediations are crucial for the ICS. However, there exist three problems to be tackled in a sound way. First of all, it is impractical to remove all vulnerabilities for preventing the multistep and multihost attacks in the consideration of the actual ICS demands. Secondly, ranking vulnerability remediations lacks a guidance. The last problem is that there is a lack of a metric for qualifying the security level after each remediation. In this paper, an ICS-oriented assessment methodology is proposed for the vulnerability remediations. It consists of three phases corresponding to the above problems, including (1) prioritizing Interdiction Surfaces, (2) ranking vulnerability remediations, and (3) calculating composite metrics. The Interdiction Surface describes a minimum set of vulnerabilities of which the complete removal may interdict all discovered attack paths in the system. Particularly, it innovates to take the urgent security demands of the ICS into account. Subsequently, ranking the vulnerability in the optimal Interdiction Surface is conducive to guide the remediations with the priority. A composite metric is ultimately given to assess the security level after vulnerability remediations. The effectiveness of the proposed methodology is validated in an ICS scenario which is similar to the real-world practice. Results show that the entire procedure is suitable for the context of the ICS. Simultaneously, the composite metric enhances both the comprehensiveness and the compatibility in contrast with attack path-based metrics. Hence, it overcomes the shortcomings when they are used in isolation.

AbstractThis article investigates a network interdiction problem on a tree network: given a subset of nodes chosen as facilities, an interdictor may dissect the network by removing a size-constrained set of edges, striving to worsen the established facilities best possible. Here, we consider a reachability objective function, which is closely related to the covering objective function: the interdictor aims to minimize the number of customers that are still connected to any facility after interdiction. For the covering objective on general graphs, this problem is known to be NP-complete (Fröhlich and Ruzika In: On the hardness of covering-interdiction problems. Theor. Comput. Sci., 2021). In contrast to this, we propose a polynomial-time solution algorithm to solve the problem on trees. The algorithm is based on dynamic programming and reveals the relation of this location-interdiction problem to knapsack-type problems. However, the input data for the dynamic program must be elaborately generated and relies on the theoretical results presented in this article. As a result, trees are the first known graph class that admits a polynomial-time algorithm for edge interdiction problems in the context of facility location planning.

Conditional value at risk (CVaR) is widely used to account for the preferences of a risk-averse agent in extreme loss scenarios. To study the effectiveness of randomization in interdiction problems with an interdictor that is both risk- and ambiguity-averse, we introduce a distributionally robust maximum flow network interdiction problem in which the interdictor randomizes over the feasible interdiction plans in order to minimize the worst case CVaR of the maximum flow with respect to both the unknown distribution of the capacity of the arcs and the interdictor’s own randomized strategy. Using the size of the uncertainty set, we control the degree of conservatism in the model and reformulate the interdictor’s distributionally robust optimization problem as a bilinear optimization problem. For solving this problem to any given optimality level, we devise a spatial branch-and-bound algorithm that uses the McCormick inequalities and reduced reformulation linearization technique to obtain a convex relaxation of the problem. We also develop a column-generation algorithm to identify the optimal support of the convex relaxation, which is then used in the coordinate descent algorithm to determine the upper bounds. The efficiency and convergence of the spatial branch-and-bound algorithm is established in numerical experiments. Further, our numerical experiments show that randomized strategies can have significantly better performance than optimal deterministic ones. History: Accepted by David Alderson, Area Editor for Network Optimization: Algorithms & Applications. Funding: The first author’s research is supported by a Group for Research in Decision Analysis postdoctoral fellowship and Fonds de Recherche du Québec–Nature et Technologies postdoctoral research scholarship [Grants 275296 and 301065]. The second author acknowledges support from the Canadian Natural Sciences and Engineering Research Council and the Canada Research Chair program [Grants RGPIN-2016-05208, 492997-2016, and 950-230057]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/ijoc.2022.1257 . The data file and codes are posted on GitHub ( https://github.com/Utsav19/Value-of-Randomization ).

We consider a two-player interdiction problem staged over a graph where the attacker’s objective is to minimize the cost of removing edges from the graph so that the defender’s objective, that is, the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level r. Standard approaches for graph interdiction frame this type of problems as bilevel formulations, which are commonly solved by replacing the inner problem by its dual to produce a single-level reformulation. In this paper, we study an alternative integer program derived directly from the attacker’s solution space and show that this formulation yields a stronger linear relaxation than the bilevel counterpart. Furthermore, we analyze the convex hull of the feasible solutions of the problem and identify several families of facet-defining inequalities that can be used to strengthen this integer program. We then proceed by introducing a different formulation defined by a set of so-called supervalid inequalities that may exclude feasible solutions, albeit solutions whose objective value is not better than that of an edge cut of minimum cost. We discuss several computational aspects required for an efficient implementation of the proposed approaches. Finally, we perform an extensive set of computational experiments to test the quality of these formulations, analyzing and comparing the benefits of each model, as well as identifying further enhancements. Summary of Contribution: Network interdiction has received significant attention over the last couple of decades, with a notable peak of interest in recent years. This paper provides an interesting balance between the theoretical and computational aspects of solving a challenging network interdiction problem via integer programming. We present several technical developments, including a detailed study of the problem's solution space, multiple formulations, and a polyhedral analysis of the convex hull of feasible solutions. We then analyze the results of an extensive set of computational experiments that were used to validate the effectiveness of the different methods we developed in this paper.

AbstractTraditional network interdiction problems focus on removing vertices or edges from a network so as to disconnect or lengthen paths in the network; network diversion problems seek to remove vertices or edges to reroute flow through a designated critical vertex or edge. We introduce the all-pairs vitality maximization problem (VIMAX), in which vertex deletion attempts to maximize the amount of flow passing through a critical vertex, measured as the all-pairs vitality of the vertex. The assumption in this problem is that in a network for which the structure is known but the physical locations of vertices may not be known (e.g., a social network), locating a person or asset of interest might require the ability to detect a sufficient amount of flow (e.g., communications or financial transactions) passing through the corresponding vertex in the network. We formulate VIMAX as a mixed integer program, and show that it is NP-Hard. We compare the performance of the MIP and a simulated annealing heuristic on both real and simulated data sets and highlight the potential increase in vitality of key vertices that can be attained by subset removal. We also present graph theoretic results that can be used to narrow the set of vertices to consider for removal.

We consider a bilevel attacker–defender problem to find the worst-case attack on the relays that control transmission grid components. The attacker infiltrates some number of relays and renders all of the components connected to them inoperable with the goal of maximizing load shed. The defender responds by minimizing the resulting load shed, redispatching using a DC optimal power flow (DCOPF) problem on the remaining network. Though worst-case interdiction problems on the transmission grid have been studied for years, there remains a need for exact and scalable methods. Methods based on using duality on the inner problem rely on the bounds of the dual variables of the defender problem in order to reformulate the bilevel problem as a mixed integer linear problem. Valid dual bounds tend to be large, resulting in weak linear programming relaxations and, hence, making the problem more difficult to solve at scale. Often smaller heuristic bounds are used, resulting in a lower bound. In this work, we also consider a lower bound, but instead of bounding the dual variables, we drop the constraints corresponding to Ohm’s law, relaxing DCOPF to capacitated network flow. We present theoretical results showing that, for uncongested networks, approximating DCOPF with network flow yields the same set of injections and, thus, the same load shed, which suggests that this restriction likely gives a high-quality lower bound in the uncongested case. Furthermore, we show that, in the network flow relaxation of the defender problem, the duals are bounded by one, so we can solve our restriction exactly. Finally, because the big-M values in the linearization are equal to one and network flow has a well-known structure, we see empirically that this formulation scales well computationally with increased network size. Through empirical experiments on 16 networks with up to 6,468 buses, we find that this bound is almost always as tight as we can get from guessing the dual bounds even for congested networks in which the theoretical results do not hold. In addition, calculating the bound is approximately 150 times faster than achieving the same bound with the reformulation guessing the dual bounds.

This essay takes its point of departure from a well known excerpt found in the final pages of Michel Foucault’s text, The History of Sexuality: Volume One. It reads as follows: It is the agency of sex that we must break away from, if we aim-through a tactical reversal of the various mechanisms of sexuality- to counter the grips of power with the claims of bodies, pleasures and knowledges, in their multiplicity and their possibility of resistance. The rallying point for the counterattack against the deployment of sexuality ought not to be sex-desire, but bodies and pleasures. (157) Here for the first time in this text Foucault outlines a tactic for resisting the various mechanisms of sexuality. Yet, how are we to make sense of the potential sexual politics inherent to this claim? Not only does this passage mark a significant shift in the tone and style of Foucault’s writing but it is arguable that his tactic – our point of resistance should be aimed at bodies and pleasures as opposed to sex-desires – is problematic in light of his own conception of power and sexuality discussed earlier in the book. In re-reading the above passage we see that Foucault clearly acknowledges that “bodies, pleasures and knowledges” come to be in and through the exercising of power; so how is it that Foucault invokes the possibility for counterattacks on the level of bodies and pleasures yet not on the level of sex-desire? In plain language, what is Foucault trying to say here?Working with the understanding that power does indeed permeate and operate on the level of bodies, pleasures and knowledges through various deployments of sexuality, what possible contestations, or better yet rupturous moves (according to Foucault’s framework) are only possible within the field of bodies and pleasures and not at all possible within the field of sex-desire? What exactly is this demarcation Foucault presents between sex-desire and bodies and pleasures? And is it at all possible to imagine coalitional possibilities (of bodies, pleasures, and genders etc.) which break from what Foucault ambiguously refers to as “agencies of sex?”In order to properly address these concerns we require a revisiting of Foucault’s conceptualisation of power within the entire spectrum of sexuality, as well as an attempt to think what, why and how bodies and pleasures are a source of resistance for the future to come. If an essential part of Foucault’s project is to contest and move away from simple or inadequate understandings of power surely we cannot read this incitement to counterattacks on the level of bodies and pleasures as a naïve attempt to find an exit to the very networks of power and sex that he himself formulates. In reconsideration of the perplexity of what has become a landmark text in French Philosophy, this paper will advance under the impetus of two registers: one, in the process of retracing Foucault’s concerns with power and the agency of sex in The History of Sexuality: Volume One, and the other, equally cautious in our venture forward in the direction of new "rallying points" of unformed bodies and unknown pleasures. The one I imagine in full view, written with as little ambiguity as possible, the other an eclipse; offering little to words, seeking new coalitions at the limit of other bodies, other pleasures yet to be. First, in order to better understand the stakes of these concerns, let us look at how Foucault problematises power, and secondly how he describes the workings of power in relation to deployments of sexuality. In the opening chapter, Foucault begins by bringing into question the assumption that power operates within the domain of sexuality in a purely negative manner - what he terms the “repressive hypothesis” (Foucault 10). While Foucault admits that power can be restrictive and/or prohibitive it cannot be reduced nor simply understood as a negative force. Instead it is crucial that we examine power in terms of its positive and productive mechanisms. “The central issue,” Foucault writes is “not to determine whether one says yes or no to sex, whether one formulates prohibitions or permissions,” but rather to bring to light the productive forms of power that bring discourses and knowledges pertaining to sex into being. By moving towards an analysis of power which seeks to locate its positive techniques, power and sex come to be situated in a different light. The relationship between power and sex now becomes a generative concern. Further, a concern “to locate the forms of power, the channels it takes, and the discourses it permeates in order to reach the most tenuous and individual modes of behaviour, the paths that give it access to the rare or scarcely perceivable forms of desire, how it permeates and controls everyday pleasure.” Sex is to be understood as the “instrument-effect” (Foucault 48) of power; emerging, as it were in and though the various correlations and divergencies within discursive networks, generative fields of power and disseminations of knowledge. As much as Foucault makes it clear that the type of power brought to bear on sex-desire(s) and bodies and pleasures is of a generative nature and cannot be properly understood in the language of repression and restriction, his analysis of the relation between power and sex can be better understood in light of his discussion of peripheral sexualities in the nineteenth century. In Foucault’s discussion of “peripheral sexualities,” he notes that “the nineteenth century and our own have been rather the age of multiplication: a dispersion of sexualities, a strengthening of their disparate forms, a multiple implantation of ‘perversions’. Our epoch has initiated sexual heterogeneities” (Foucault 37). How are we to understand this claim? Foucault insists one should resist reading this change as a sign of social tolerance or a laxing of the legal code. Indeed there was so-called permissiveness, “if one bears in mind that the severity of the codes relating to sexual offenses diminished considerably in the nineteenth century and the law itself deferred to medicine” (Foucault 40). However, Foucault adds this is not to say that additional forms of power did not come into play, “if one thinks of all the agencies of control and all the mechanisms of surveillance that were put into operation by pedagogy and therapeutics” (Foucault 41). The rise of sexual heterogeneities and peripheral sexualities is not a result of power withdrawing from sex, but instead an “instrument-effect” of changes in strategies of power. Power becomes a productive, mobilising force for the emergence of various forms of knowledge on sex. A proliferation of discourses arise in, around and of sex, making it speak, writing its every move, describing, analysing, penetrating its darkest recesses. What were once illegible or ignored zones of desire are brought into an intelligible light. These new forms of power take hold of sex-desire, bodies and pleasures solidifying and penetrating modes of conduct, bringing into being new classifications of sexual types and normalising codes of sexual behaviour. Power and sex come to invest in each other. Not, as it were to restrict, set boundaries or avoid sex, but instead invest themselves in subjects, bodies and pleasures, “reinforce one another” and thus “provide places of maximum saturation” (Foucault 47). Before we turn back to our initial problem let us elaborate on Foucault’s notion of power “with respect to its nature, its form and its unity” (Foucault 47). For Foucault, it is no longer accurate to think of power in terms of hierarchy, (i.e. through the representation of a triangle, emanating from the top to the bottom) centrality (i.e. through the representation of a center moving towards the periphery) or rule by subjugation. Why? “In general terms,” Foucault argues, “interdictions, the refusal, the prohibition, far from being essential forms of power, are only its limits, power in its frustrated or extreme forms. The relations of power are, above all, productive” (Foucault 118). For Foucault these are negative, subtractive representations of power which nonetheless do exist but only in “terminal” (Foucault 92) forms. Power is not reducible to something that brings about the limit even though it is always in the process of circumscribing things. In fact power is not reducible at all; it is moreover inexhaustible and we should add, chameleon-like insofar as it is manifold. It cannot be thought to have a definitive form. Foucault describes it as a “moving substrate” (Foucault 93) that traverses, penetrates, networks, localises without being localisable and is everywhere in a state of tension. Power is everywhere there are relations of force. With respect to the question of resistance, for Foucault, it is not possible to dissociate power from resistance. Power and resistance are always co-present insofar as power operates with and against (with-against) force. “Where there is power,” Foucault writes, “there is resistance, and yet, or rather consequently, this resistance is never in a position of exteriority in relation to power” (Foucault 95). It might be asked: Is all-encompassing (Absolute) power possible? Can everything be reduced to a question of power relations? Power has no central sourcing power, or unique Origin, it is everywhere, “not because it embraces everything, but because it comes from everywhere” (Foucault 93). The possibility of all-encompassing power is the absolute limit to (of) power. For since we understand power as the instrument-effect of force relations, Absolute Power much the same as Absolute Resistance is the Impossible for power. Power operates with-against. With this said let us return to our initial concerns. Since we understand power and resistances as never absolute, this however does not rule out strategies for resistance. At the end of The History of Sexuality: Volume One, anticipating criticisms of his own work Foucault stages and addresses two questions that will be asked of his work in relation to bodies and sex. First, with respect to the question of bodies, he anticipates a claim that will assume that his analysis of sexuality fails to concede the biological givenness of bodies. In response Foucault makes it clear that “bodies” are not to be thought of as naturally or biologically given. Bodies are not constitutive or an outside, which is then subject to sexual analysis but instead bound, caught up and constituted by multiple strategies of power-sex-knowledge. His history of sexuality is not one of sex on one hand and bodies on the other. Instead it is “to show how deployments of power are directly connected to the body- to bodies, functions, physiological processes, sensations, and pleasures.” Foucault is not doing a history of the Idea(s) of the body “that would account for bodies only through the manner in which they have been perceived and given meaning and value,” but rather a history of how bodies come to be as such, “in which what is most material and most vital in them has been invested” (Foucault 152) with deployments of power.Second, Foucault anticipates that he will be read as presenting a history of sexuality that overlooks the givenness or the centrality of “sex” in human nature. This criticism rests on the belief that “sex” is separable to, but nonetheless the aim of deployments of sexuality; that pure, autonomous agency which is the internal mobilizing force for sexuality. For Foucault, this belief is part of the illusory ideal that is dispersed within our discourses on sexuality, that namely, sex is the truth of our interior, that unique something other, irreducible to bodies and pleasures, the mirror of self-truth. Resistances to sexuality cannot manifest themselves within this opposition between sex and sexuality. It is an illusory grounding. “Sex” emerges in and out of the various deployments of sexuality. It is not an outside. It is not a biological natural. It is the “instrument-effect” of discursive regimes of sexuality that bind sex-desire as bearing not only ones natural source of subjective uniqueness but also the disclosing force of truth. Much of the problems with contemporary sexual liberation movements are based on this illusory ideal. Resistance roots itself in sex-desire. In an interview discussing political resistance to deployments of sexuality, Foucault states: I believe that the movements labeled ‘sexual liberation’ ought to be understood as movements of affirmation “starting with” sexuality. Which means two things: they are movements that start with sexuality, with the apparatus of sexuality in the midst of which we’re caught, and which make it function to the limit; but at the same time, they are motion relative to it, disengaging themselves and surmounting it. (Foucault, Politics, Philosophy, Culture 114-5)This anchoring of resistance within sex-desire conforms to the networks of power and control over sexuality that form these subjectivities as both given and in need of proper legitimation. The problem with resistance on the level of sex-desire is a result of its resistance “starting with” sexuality. Its own sexually determined subjectivities is only challenged in a certain manner which only contributes to a further networking and rooting of its sexuality within matrices of power and control. Even though what are called “sexual liberation movements” exercise strategies of resistance, the agency of sex and its various mechanisms of historical construction will never be overcome simply because its resistance starts and operates within social constructs of sexual nature.So we must ask, why and what are we to make of bodies and pleasures? Do bodies and pleasures offer different coalitional possibilities for resistance to the agency of sex? If we understand deployments of sexuality as both the instrument and effect of sex-desire/bodies and pleasures, our line of demarcation cannot be grounded in accessibility to power – for everything that we have come to experience as “sexual” is part of networks of power-sex-knowledge. However since both domains are gripped (Foucault’s term) by power, why should we assume that there is equality or even a sameness of power relations operating within these domains? Could we not assume channels and techniques of power operate different in each of these domains? And, therefore, if we want to consider the possibility of resistance(s), perhaps we will have to account for the accessible domains of sex-desire (without rooting ourselves within them, i.e. starting-with) but explore its excessible limits – that is, bodies and pleasures yet to be.Judith Butler brings forth concerns of this nature in her essay on the same passage of Foucault’s entitled “Revisiting Bodies and Pleasures”. Of Butler’s many concerns, one in particular is the question of agency. “These bodies, these pleasures,” she writes, “where do they come from, and in what does their agency consist, if they are the agency that counters the regime of sex-desire?” (Butler 14). For Butler, not only is agency a concern but also resources and collectivity. “And who are the ‘we,’” she continues, “who are said to exercise this agency against the agency of sex? What are the resources that counter the regulation of sexuality if they are not in some sense derived from the discursive resources of normative regulation?” (Butler 14). If such a break is possible, which Butler is hesitant to accept, what sort of relation would it take to the ‘overthrown’ agency of sex? How can we ensure against the establishing of new regulatory orders localised within bodies and pleasures? For Butler it makes no sense to divide and oppose bodies and pleasures and sex-desire, because “if the normativity of the latter continues to haunt and structure the lived modalities of the former,” then we might possibly “deprive ourselves of the critical tools we need in order to read the trace and phantom of heteronormativity in the midst of our imagined transcendence” (Butler 18). Thus I agree with her fear that the exuberance of a certain kind of utopianism “works in the service of maintaining a compulsory ignorance, and where the break between the past and present keeps us from being able to see the trace of the past as it re-emerges in the very contours of an imagined future” (Butler 18). Although Butler brings to light some pertinent concerns that complicate any utopian imagination for bodies and pleasures, surprisingly, she makes no mention of Foucault’s discussion of ars erotica made in the middle part of The History of Sexuality, which, I argue, might be the missing keystone we have been looking for in our attempt to understand Foucault incitement to bodies and pleasures. For Foucault ars erotica is one of two “great procedures for producing the truth on sex” (Foucault 97) which draws truth not from desire but the experience of pleasure itself. His definition of the practices of ars erotica distinguish an order of experience manifest in bodies and pleasures that differs from the agency of sex-desire insofar as the organising principle for truth is not sex but pleasure. Moreover it is the emergence of different incitements, other figures of truth that operate not independent of power relations but independent of regulatory, classifiable schemas “geared to a form of knowledge-power” that has its tradition in the West (Foucault 58). Pleasure “is understood as a practice and accumulated in experience” (Foucault 57) lacking recourse to a desiring subject. Both singular (without the necessary invoking of a subject) and multiple (effusive in its intensity). “It is experienced as pleasure,” Foucault writes, “evaluated in terms of its intensity, its specific quality, its duration, its reverberations in the body and the soul,” with effects that bring about “an absolute mastery of the body, a singular bliss, obliviousness to time and limits, the elixir of life, the exile of death and its threats” (Foucault 58). Here I think we have found the keystone to Foucault’s incitement towards bodies and pleasures. In his description of ars erotica there is no discussion of sexual subjects, couplings of truth and desire, only an untiring will to carry the experience of bodies and pleasures to their apex; movements of concentration and dispersion, challenging the possibilities of existence to the limit of life and death, engaging the limit by attempting to carry it into the abyss of the outside. Perhaps it is here that we can begin to see Foucault’s incitement to bodies and pleasures in a new light. Bodies and pleasures are resistive insofar as they are productive of deploying not subjects yet to be, but experiences yet to be. Ars Erotica is not to be championed as an apparatus for the replacement of agencies of sex. Foucault should not be seen as "rushing to embrace" (Butler 20) a lost paradise of ars erotica or worse bring it forth as a new regulatory order. Rather he incites the possibility of a singular ethos to rupture the limits of the present with experiences of bodies and pleasures that consummate themselves in the immediate while escaping, or better, remaining in excess to the grasp of that power which seeks to render them intelligible, and thus conferrable to regulation. Bodies and pleasures – whatever we are to make of them – are never entirely inside or outside power relations, but rather traversed at, on, as the limit. Foucault is after this continuous play of limits and new admixtures of experience that result from this liminal play. Yet, what if it is not the entire dismantling of sex-desire “in order to turn to pleasure,” that he imagines or even thinks possible, but rather movements “to experience and re-experience the pleasure of the break itself, the pleasure of continually breaking with that past, a pleasure that can only be sustained if the past does not vanish through the act by which it is renounced” (Butler 18)? Perhaps it is here that we catch a glimpse at a “rallying point” for the break with agencies of sex, however temporary, however micro such a rupture may yield.ReferencesButler, Judith. “Revisiting Bodies and Pleasures.” Theory, Culture & Society 16.2 (1999): 11-20.Foucault, Michel. The History of Sexuality: An Introduction. Vol. 1. Trans. Robert Hurley. New York: Vintage Books, 1990.———. Foucault: Politics, Philosophy, Culture: Interviews and Other Writings, 1977-1984. Trans. Alan Sheridan and Others. Ed. with Intro: Lawrence D. Kritzman. Routledge: New York and London, 1988.