Artificial immune systems can find arbitrarily good approximations for the NP-hard number partitioning problem

Typical artificial immune system (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which evolutionary algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial example functions constructed especially to show difficulties that EAs may encounter during the optimisation process. However, no evidence is available indicating that these two operators have similar behaviour also in more realistic problems. In this paper we perform an analysis for the standard NP-hard Partition problem from combinatorial optimisation and rigorously show that hypermutations and ageing allow AISs to efficiently escape from local optima where standard EAs require exponential time. As a result we prove that while EAs and random local search (RLS) may get trapped on 4/3 approximations, AISs find arbitrarily good approximate solutions of ratio (1+) within n(−(2/)−1)(1 − )−2e322/ + 2n322/ + 2n3 function evaluations in expectation. This expectation is polynomial in the problem size and exponential only in 1/

Artificial Immune Systems for Combinatorial Optimisation: A Theoretical Investigation

We focus on the clonal selection inspired computational models of the immune system developed for general-purpose optimisation. Our aim is to highlight when these artificial immune systems (AIS) are more efficient than evolutionary algorithms (EAs). Compared to traditional EAs, AIS use considerably higher mutation rates (hypermutations) for variation, give higher selection probabilities to more recent solutions and lower selection probabilities to older ones (ageing). We consider the standard Opt-IA that includes both of the AIS distinguishing features and argue why it is of greater applicability than other popular AIS. Our first result is the proof that the stop at first constructive mutation version of its hypermutation operator is essential. Without it, the hypermutations cannot optimise any function with an arbitrary polynomial number of optima. Afterwards we show that the hypermutations are exponentially faster than the standard bit mutation operator used in traditional EAs at escaping from local optima of standard benchmark function classes and of the NP-hard Partition problem. If the basin of attraction of the local optima is not too large, then ageing allows even greater speed-ups. For the Cliff benchmark function this can make the difference between exponential and quasi-linear expected time. If the basin of attraction is too large, then ageing can implicitly detect the local optimum and escape it by automatically restarting the search process. The described power of hypermutations and ageing allows us to prove that they guarantee (1+epsilon) approximations for Partition in expected polynomial time for any constant epsilon. These features come at the expense of the hypermutations being a linear factor slower than EAs for standard unimodal benchmark functions and of eliminating the power of ageing at escaping local optima in the complete Opt-IA. We show that hypermutating with inversely proportional rates mitigates such drawbacks at the expense of losing the explorative advantages of the standard operator. We conclude the thesis by designing fast hypermutation operators that are provably a linear factor faster than the traditional ones for the unimodal benchmark functions and Partition, while maintaining explorative power and working in harmony together with ageing

Artificial Immune Systems can find arbitrarily good approximations for the NP-Hard partition problem

Typical Artificial Immune System (AIS) operators such as hypermutations with mutation potential and ageing allow to efficiently overcome local optima from which Evolutionary Algorithms (EAs) struggle to escape. Such behaviour has been shown for artificial example functions such as Jump, Cliff or Trap constructed especially to show difficulties that EAs may encounter during the optimisation process. However, no evidence is available indicating that similar effects may also occur in more realistic problems. In this paper we perform an analysis for the standard NP-Hard Partition problem from combinatorial optimisation and rigorously show that hypermutations and ageing allow AISs to efficiently escape from local optima where standard EAs require exponential time. As a result we prove that while EAs and Random Local Search may get trapped on 4/3 approximations, AISs find arbitrarily good approximate solutions of ratio ( 1+ϵ ) for any constant ϵ within a time that is polynomial in the problem size and exponential only in 1/ϵ

LQR Tuning Using AIS for Frequency Oscillation Damping

Commonly, primary control, i.e. governor, in the generation unit had been employed to stabilize the change of frequency due to the change of electrical load during system operation. But, the drawback of the primary control was it could not return the frequency to its nominal value when the disturbance was occurred. Thus, the aim of the primary control was only stabilizing the frequency to reach its new value after there were load changes. Therefore, the LQR control is employed as a supplementary control called Load Frequency Control (LFC) to restore and keep the frequency on its nominal value after load changes occurred on the power system grid. However, since the LQR control parameters were commonly adjusted based on classical or Trial-Error Method (TEM), it was incapable of obtaining good dynamic performance for a wide range of operating conditions and various load change scenarios. To overcome this problem, this paper proposed an Artificial Immune System (AIS) via clonal selection to automatically adjust the weighting matrices, Q and R, of LQR related to various system operating conditions changes. The efficacy of the proposed control scheme was tested on a two-area power system network. The obtained simulation results have shown that the proposed method could reduce the settling time and the overshoot of frequency oscillation, which is better than conventional LQR optimal control and without LQR optimal control

Approximation and elections

Any culture that requires that a decision be made within a group necessarily creates methods for aggregating each individual’s preferences. For instance, we see such a need in political elections, committees, and businesses. With the Internet and the increasing use of multiagent software systems, the general need for means of aggregating differing preferences has increased dramatically. Voting is one way to come to a single option (or small group of options) out of a larger pool of candidate options. Many voting systems exist, and criteria exist (within the field of social choice theory) for deciding which most fairly and accurately take into account the preferences of each voter. Since there is generally much to be gained from influencing such a vote through manipulation or bribery, one desirable criterion of fairness would be whether such activities are impossible in the system. However, it has been shown that a reasonable system that disallows manipulation does not exist [18, 43], so the next-best solution would be a system in which deciding how to bribe or otherwise influence the vote is so computationally difficult as to render it impossible or highly unlikely. While the debate over which voting systems are most fair and effective is on record of existing over the past few centuries (and likely goes further back to ancient Greece), there may exist the seeds of a renewal of this debate in the current boom in voting due to new technologies. For one, in artificial intelligence agents may vote to determine the best course of action to take given the individual’s preferences. In addition, algorithms in search engines and metasearch engines do order results in a manner that assumes a ranking was somehow approached. Voting is not only on the rise in software, of course, as most any user of the Internet could demonstrate. Internet users routinely vote most any user of the Internet could demonstrate. Internet users routinely vote online in situations ranging from the inane (e.g., rating a video on YouTube) to the potentially crucial (e.g., voting on whether a story is newsworthy or not on any of a plethora of such sites, including Digg, Reddit, and Newsvine). These newer uses of voting systems are interesting. They are used in environments where there are potentially far more candidates and voters than are conventionally seen in, say, political elections. Also, in these new environments, voting and manipulation can be automated to some degree, thus making the possibility of manipulation and control even more real than it has been in the past. Faliszewski, Hemaspaandra, and Hemaspaandra have proved for a number of voting systems that the bribery problem is too complex to be feasible (i.e., NP-complete) [15], and much research has been put forth determining the complexity of other problems related to voting. But it is still possible in the optimization cases of these problems that there exist approximation algorithms that can find a good solution with a reasonable amount of computation. That is, while a voting system may seem “resistant” to a particular form of manipulation as described by previous research, it may be that the problem is not as difficult if we allow a constant amount of error. Or, it may be that the problem is still difficult when error is allowed, thus making the voting system even more resilient with respect to some forms of manipulation. This thesis will examine the possibility of such approximations for some problems in elections

Quasi-stable Coloring for Graph Compression: Approximating Max-Flow, Linear Programs, and Centrality

We propose quasi-stable coloring, an approximate version of stable coloring. Stable coloring, also called color refinement, is a well-studied technique in graph theory for classifying vertices, which can be used to build compact, lossless representations of graphs. However, its usefulness is limited due to its reliance on strict symmetries. Real data compresses very poorly using color refinement. We propose the first, to our knowledge, approximate color refinement scheme, which we call quasi-stable coloring. By using approximation, we alleviate the need for strict symmetry, and allow for a tradeoff between the degree of compression and the accuracy of the representation. We study three applications: Linear Programming, Max-Flow, and Betweenness Centrality, and provide theoretical evidence in each case that a quasi-stable coloring can lead to good approximations on the reduced graph. Next, we consider how to compute a maximal quasi-stable coloring: we prove that, in general, this problem is NP-hard, and propose a simple, yet effective algorithm based on heuristics. Finally, we evaluate experimentally the quasi-stable coloring technique on several real graphs and applications, comparing with prior approximation techniques. A reference implementation and the experiment code are available at https://github.com/mkyl/QuasiStableColors.jl .Comment: To be presented at VLDB 202

When move acceptance selection hyper-heuristics outperform Metropolis and elitist evolutionary algorithms and when not

Selection hyper-heuristics (HHs) are automated algorithm selection methodologies that choose between different heuristics during the optimisation process. Recently, selection HHs choosing between a collection of elitist randomised local search heuristics with different neighbourhood sizes have been shown to optimise standard unimodal benchmark functions from evolutionary computation in the optimal expected runtime achievable with the available low-level heuristics. In this paper, we extend our understanding of the performance of HHs to the domain of multimodal optimisation by considering a Move Acceptance HH (MAHH) from the literature that can switch between elitist and non-elitist heuristics during the run. In essence, MAHH is a non-elitist search heuristic that differs from other search heuristics in the source of non-elitism. We first identify the range of parameters that allow MAHH to hillclimb efficiently and prove that it can optimise the standard hillclimbing benchmark function OneMax in the best expected asymptotic time achievable by unbiased mutation-based randomised search heuristics. Afterwards, we use standard multimodal benchmark functions to highlight function characteristics where MAHH outperforms elitist evolutionary algorithms and the well-known Metropolis non-elitist algorithm by quickly escaping local optima, and ones where it does not. Since MAHH is essentially a non-elitist random local search heuristic, the paper is of independent interest to researchers in the fields of artificial intelligence and randomised search heuristics