We address a path planning problem for heterogeneous multi-robot systems under specifications consisting of temporal constraints and routing tasks such as package delivery services. The robots are partitioned into several groups based on their dynamics and specifications. We introduce a concise description of such tasks, called a work, and extend counting LTL to represent such specifications. We convert the problem into an ILP problem. We show that the number of variables in the ILP problem is fewer than that of the existing method using cLTL+. By simulation, we show that the computation time of the proposed method is faster than that of the existing method.

In interdependent systems, such as electric power systems, entities or components mutually depend on each other. Due to these interdependencies, a small number of initial failures can propagate throughout the system, resulting in catastrophic system failures. This paper addresses the problem of finding the set of entities whose failures will have the worst effects on the system. To this end, a two-phase algorithm is developed. In the first phase, the tight bound on failure propagation steps is computed using a Boolean Satisfiablility (SAT) solver. In the second phase, the problem is formulated as an Integer Linear Programming (ILP) problem using the obtained step bound and solved with an ILP solver. Experimental results show that the algorithm scales to large problem instances and outperforms a single-phase algorithm that uses a loose step bound.

The multi-agent surveillance problem is to find optimal trajectories of multiple agents that patrol a given area as evenly as possible. In this paper, we consider the multi-agent surveillance problem based on travel cost minimization. The surveillance area is given by an undirected graph. The penalty for each agent is introduced to evaluate the surveillance performance. Through a mixed logical dynamical system model, the multi-agent surveillance problem is reduced to a mixed integer linear programming (MILP) problem. In model predictive control, trajectories of agents are generated by solving the MILP problem at each discrete time. Furthermore, a condition that the MILP problem is always feasible is derived based on the Chinese postman problem. Finally, the proposed method is demonstrated by a numerical example.

Solar energy is an important energy resource for a sustainable society and is massively introduced these days. Household generally sells their excess solar energy by the reverse power flow, but the massive reverse power flow usually sacrifices the grid stability. In order to utilize renewable energy effectively and reduce solar energy waste, electric vehicles (EVs) takes an important role to fill in the spatiotemporal gap of solar energy. This paper proposes a novel EV aggregation framework for spatiotemporal shifting of solar energy without any reverse power flow. The proposed framework causes charging and discharging via an EV aggregator by intentionally changing the price, and the solar energy waste is expected to reduce by the energy trade. Simulation results show the proposed framework reduced the solar energy waste by 68%.

This paper proposes a migration model for distributed server allocation. In distributed server allocation, each user is assigned to a server to minimize the communication delay. In the conventional model, a user cannot migrate to another server to avoid instability. We develop a model where each user can migrate to another server while receiving services. We formulate the proposed model as an integer linear programming problem. We prove that the considered problem is NP-complete. We introduce a heuristic algorithm. Numerical result shows that the proposed model reduces the average communication delay by 59% compared to the conventional model at most.

The extended visual cryptography scheme (EVCS) proposed by Ateniese et al. is one of variations of the visual cryptography scheme such that a secret image is recovered by superimposition of certain qualified collections of shares, where cover images are visible on respective shares. In this paper, we give a new definition of the EVCS for improving visibility of the recovered secret image as well as the cover images. We formulate the problem to construct the basis matrices of the EVCS with the minimum pixel expansion as an integer programming problem. We solve the integer programming problem for general access structures with less than or equal to five participants and show that basis matrices with a smaller pixel expansion can be obtained for certain cases. We also analyze security of the EVCS meeting the new definition from an information-theoretic viewpoint. We give a condition under which any forbidden collection of shares does not reveal any additional information on not only a secret image but also the cover images that are not visible on the other shares.

Given a box of some specified size and a number of pieces of some specified shape, the anti-slide problem considers how to pack the pieces such that none of the pieces in the box can slide in any direction. The object is to find such a sparsest packing. In this paper, we consider the problem for the case of a two-dimensional square box using T-tetromino pieces. We show that, for a square box of side length n, the number of pieces in a sparsest packing is exactly $lfloor 2n/3 floor$ when n≢0 (mod 3), and is between 2n/3-1 and n-1 when n≡0 (mod 3).

The surveillance problem is to find optimal trajectories of agents that patrol a given area as evenly as possible. In this paper, we consider multiple agents with fuel constraints. The surveillance area is given by a weighted directed graph, where the weight assigned to each arc corresponds to the fuel consumption/supply. For each node, the penalty to evaluate the unattended time is introduced. Penalties, agents, and fuels are modeled by a mixed logical dynamical system model. Then, the surveillance problem is reduced to a mixed integer linear programming (MILP) problem. Based on the policy of model predictive control, the MILP problem is solved at each discrete time. In this paper, the feasibility condition for the MILP problem is derived. Finally, the proposed method is demonstrated by a numerical example.

In this paper, a surveillance system by multiple agents, which is called a multi-agent surveillance system, is studied. A surveillance area is given by an undirected connected graph. Then, the optimal control problem for multi-agent surveillance systems (the optimal surveillance problem) is to find trajectories of multiple agents that travel each node as evenly as possible. In our previous work, this problem is reduced to a mixed integer linear programming problem. However, the computation time for solving it exponentially grows with the number of agents. To overcome this technical issue, a new model predictive control method for multi-agent surveillance systems is proposed. First, a procedure of individual optimization, which is a kind of approximate solution methods, is proposed. Next, a method to improve the control performance is proposed. In addition, an event-triggering condition is also proposed. The effectiveness of the proposed method is presented by a numerical example.

Bilinear-type conversion is to translate a cryptographic scheme designed over symmetric bilinear groups into one that works over asymmetric bilinear groups with small overhead regarding the size of objects concerned in the target scheme. In this paper, we address scalability for converting complex cryptographic schemes. Our contribution is threefold. Investigating complexity of bilinear-type conversion. We show that there exists no polynomial-time algorithm for worst-case inputs under standard complexity assumption. It means that bilinear-type conversion in general is an inherently difficult problem. Presenting a new scalable conversion method. Nevertheless, we show that large-scale conversion is indeed possible in practice when the target schemes are built from smaller building blocks with some structure. We present a novel conversion method, called IPConv, that uses 0-1 Integer Programming instantiated with a widely available IP solver. It instantly converts schemes containing more than a thousand of variables and hundreds of pairings. Application to computer-aided design. Our conversion method is also useful in modular design of middle to large scale cryptographic applications; first construct over simpler symmetric bilinear groups and run over efficient asymmetric groups. Thus one can avoid complication of manually allocating variables over asymmetric bilinear groups. We demonstrate its usefulness by somewhat counter-intuitive examples where converted DLIN-based Groth-Sahai proofs are more compact than manually built SXDH-based proofs. Though the early purpose of bilinear-type conversion is to save existing schemes from attacks against symmetric bilinear groups, our new scalable conversion method will find more applications beyond the original goal. Indeed, the above computer-aided design can be seen as a step toward automated modular design of cryptographic schemes.

This paper proposes a scheme for automatic generation of mixed-integer programming problems for scheduling with multiple resources based on colored timed Petri nets. Our method reads Petri net data modeled by users, extracts the precedence and conflict relations among transitions, information on the available resources, and finally generates a mixed integer linear programming for exactly solving the target scheduling problem. The mathematical programing problems generated by our tool can be easily inputted to well-known optimizers. The results of this research can extend the usability of optimizers since our tool requires just simple rules of Petri nets but not deep mathematical knowledge.

This letter presents a method for solving several linear equations in max-plus algebra. The essential part of these equations is reduced to constraint satisfaction problems compatible with mixed integer programming. This method is flexible, compared with optimization methods, and suitable for scheduling of certain discrete event systems.

This paper presents efficient and easily implementable methods for the characteristic analysis and tolerance analysis of nonlinear resistive circuits using integer programming. In these methods, the problem of finding all characteristic curves or all solution sets (regions of possible operating points) is formulated as a mixed integer programming problem, and it is solved by a high-performance integer programming solver such as CPLEX. It is shown that the proposed methods can easily be implemented without making complicated programs, and that all characteristic curves or all solution sets are obtained by solving mixed integer programming problems several times. Numerical examples are given to confirm the effectiveness of the proposed methods.

Risk-aware Data Replication (RDR), which replicates data at primary sites to nearby safe backup sites, has been proposed to mitigate service disruption in a disaster area even after a widespread disaster that damages a network and a primary site. RDR assigns a safe backup site to a primary site while considering damage risk for both the primary site and the backup candidate site. To minimize the damage risk of all site-pairs the Integer Programing Problem (IPP), which is a mathematical optimization problem, is applied. A challenge for RDR is to choose safe backup sites within a short computation time even for a huge number of sites. As described in this paper, we propose a Discreet method for RDR to surmount this hurdle. The Discreet method first judges the backup sites of a potentially unsafe primary site and avoids assigning a very safe primary site with a very safe backup site. We evaluated the computation time for site-paring and the data availability in the cases of Earthquake and Tsunami using basic disaster simulations. We confirmed that the computation rate of the proposed method is more than 1000 times faster than the existing method when the number of sites is greater than 1000. We also confirmed the data availability of the proposed method; it provides almost equal rates to existing methods of strict optimization. These results mean that the proposed method makes RDR more practical for massively multiple sites.

In this paper, optimal control of multi-vehicle systems is studied. In the case where collision avoidance between vehicles and obstacle avoidance are imposed, state discretization is effective as one of the simplified approaches. Furthermore, using state discretization, cooperative actions such as rendezvous can be easily specified by linear temporal logic (LTL) formulas. However, it is not necessary to discretize all states, and partial states (e.g., the position of vehicles) should be discretized. From this viewpoint, a new control method for multi-vehicle systems is proposed in this paper. First, the system in which partial states are discretized is formulated. Next, the optimal control problem with constraints described by LTL formulas is formulated, and its solution method is proposed. Finally, numerical simulations are presented. The proposed method provides us a useful method in control of multi-vehicle systems.

Wireless Local Area Networks (WLANs) are widely deployed for internet access. Multiple interfering Access Points (APs) lead to a significant increase in collisions, that reduces throughput and affects media traffic. Thus, interference mitigation among different APs becomes a crucial issue in Multi-Cell WLAN systems. One solution to this issue is to assign a different frequency channel to each AP so as to prevent neighboring cells from operating on the same channel. However, most of the existing WLANs today operate in the unlicensed 2.4GHz Industrial, Scientific and Medical (ISM) band, which suffers from lack of the available channels. Therefore, effective channel assignment to minimize the interference in Multi-Cell WLANs is necessary. In this article, we formulate the channel assignment problem as a mixed integer linear programming (MILP) problem that minimizes the worst case total interference power. The main advantage of this algorithm is that it provides a global solution and at the same time guarantees a non-overlapping channel assignment. We also propose a Lagrangian relaxation approach to transform the MILP into a low complexity linear program which can be solved efficiently in real time, even for large sized networks. Simulation results reveal that both the MILP algorithm and the Lagrangian relaxation approach provide a total interference reduction below the default setting of having all APs assigned the same channel. In addition, simulation results on cumulative density function (CDF) of the SINR at the user level prove the validity of the proposed algorithms.

Shakashaka is a pencil-and-paper puzzle proposed by Guten and popularized by the Japanese publisher Nikoli (like Sudoku). We determine the computational complexity by proving that Shakashaka is NP-complete, and furthermore that counting the number of solutions is #P-complete. Next we formulate Shakashaka as an integer-programming (IP) problem, and show that an IP solver can solve every instance from Nikoli's website within a second.

Communication among isolated networks (clusters) in delay tolerant networks (DTNs) can be supported by a message ferry, which collects bundles from clusters and delivers them to a sink node. When there are lots of distant static clusters, multiple message ferries and sink nodes will be required. In this paper, we aim to make groups, each of which consists of physically close clusters, a sink node, and a message ferry. Our objective is minimizing the overall mean delivery delay of bundles in consideration of both the offered load of clusters and distances between clusters and their sink nodes. Based on existing work, we first model this problem as a nonlinear integer programming. Using a commercial nonlinear solver, we obtain a quasi-optimal grouping. Through numerical evaluations, we show the fundamental characteristics of grouping, the impact of location limitation of base clusters, and the relationship between delivery delay and the number of base clusters.

Large-scale introduction of renewable energy such as photovoltaic energy and wind is a big motivation for renovating conventional grid systems. To be independent from existing power grids and to use renewable energy as much as possible, a decentralized energy network is proposed as a new grid system. The decentralized energy network is placed among houses to connect them with each other, and each house has a PV panel and a battery. A contribution of this paper is a network topology and battery size exploration for the decentralized energy network in order to make effective use of renewable energy. The proposed method for exploring the decentralized energy network design is inspired by the design methodology of VLSI systems, especially design space exploration in system-level design. The proposed method is based on mixed integer programming (MIP) base power flow optimization, and it was evaluated for all design instances. Experimental results show that the decentralized energy network has the following features. 1) The energy loss and energy purchased due to power shortage were not affected by each battery size but largely affected by the sum of all battery sizes in the network, and 2) the network topology did not largely affect the energy loss and the purchased energy. These results will become a useful guide to designing an optimal decentralized energy network for each region.

A Boolean network model is one of the models of gene regulatory networks, and is widely used in analysis and control. Although a Boolean network is a class of discrete-time nonlinear systems and expresses the synchronous behavior, it is important to consider the asynchronous behavior. In this paper, using a Petri net, a new modeling method of asynchronous Boolean networks with control inputs is proposed. Furthermore, the optimal control problem of Petri nets expressing asynchronous Boolean networks is formulated, and is reduced to an integer programming problem. The proposed approach will provide us one of the mathematical bases of control methods for gene regulatory networks.