Optimal search path problem

Robotic systems play an important role in the development and
modernization processes of production, facilitation of labor, and human life. The robotic manipulators are outstanding among such systems. Such robots can be used for various spheres of their application. In this case, there is the manipulator’s effective control problem in the working area, of which there may be various obstacles. Therefore, a procedure is required to find the optimal path for moving the robotic arm. To develop such
a procedure, the literature was reviewed, and the structural diagram of the control system of such a robot and its components was summarized. It proposed a mathematical formalization of the search for the optimal path to move the robot arm, an algorithm based on a modified method of navigation graphs, to realize the more natural movement of the robot
arm. Experimental studies were conducted with different numbers of
objects on the path of robot arm movement, which were combined into
groups. The temporal results of this process are presented in a diagram.

The optimal search path (OSP) problem is a single-sided detection search problem where the location and the detectability of a moving object are uncertain. A solution to this N P-hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. These models include a simple but powerful branching heuristic as well as strong filtering constraints. We present our experimentation and compare our results with existing results in the literature. The OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance.

Objective.-Standard-of-practice search management requires that the probability of detection (POD) be determined for each search resource after a task. To calculate the POD, a detection index (W) is obtained by field experiments. Because of the complexities of the land environment, search planners need a way to estimate the value of W without conducting formal experiments. We demonstrate a robust empirical correlation between detection range (Rd) and W, and argue that Rd may reliably be used as a quick field estimate for W. Methods.-We obtained the average maximum detection range (AMDR), Rd, and W values from 10 detection experiments conducted throughout North America. We measured the correlation between Rd and W, and tested whether the apparent relationship between W and Rd was statistically significant. Results.-On average we found W E 1.645 Â Rd with a strong correlation (R 2 ¼ .827). The highvisibility class had W E 1.773 Â Rd (also R 2 ¼ .867), the medium-visibility class had W E 1.556 Â Rd (R 2 ¼ .560), and the low-visibility had a correction factor of 1.135 (R 2 ¼ .319) for Rd to W. Using analysis of variance and post hoc testing, only the high-and low-visibility classes were significantly different from each other (P o .01). We also found a high correlation between the AMDR and Rd (R 2 ¼ .9974). Conclusions.-Although additional experiments are required for the medium-and low-visibility search objects and in the dry-domain ecoregion, we suggest search planners use the following correction factors to convert field-measured Rd to an estimate of the effective sweep width (W): highvisibility W ¼ 1.8 Â Rd; medium-visibility W ¼ 1.6 Â Rd; and low-visibility W ¼ 1.1 Â Rd.

Search theory is completely dependent upon an accurate assessment of how well a search area was covered by a team or the Probability of Detection (POD). Determining the POD for auditory whistle blasts and a response to sighting lights at night (sound-light line technique) involves a two-way detection problem. Two experiments were carried out at Nelson Lakes along the Porika Road track in New Zealand. The first experiment was conducted during the day with six subjects and fourteen two-person teams conducting a sound line tactic. The detection index for a search team hearing a shout was 332 meters. The detection index for a subject hearing a whistle was 401 meters. Searchers were able to detect 99% of high-visibility clues (orange gloves) and 52% of low-visibility clues (gray gloves) on the track. The night experiment was conducted at the same location, but with different search subjects placed in different locations. Search teams used a sound-light line tactic in two-person teams. Th...

For the first time in history, a scientifically sound yet practical method for objectively determining detection probabilities for objects of importance to search and rescue (SAR) in the land environment was successfully developed and field-tested. Data was collected using volunteer searchers and analyzed with simplified analysis techniques, all at very low cost. This work opens the door for resolving search planning and evaluation issues that have been vigorously debated within the land SAR community for nearly 30 years but never settled. Searching is by its very nature a probabilistic process. However, a carefully planned search using the right tools and concepts is significantly more likely to succeed and, of equal importance when lives are at stake, succeed sooner. Planning a search consists of evaluating all the available information and then, since it is not generally possible to do a thorough search everywhere all at once, deciding how to best utilize the available, and often...

In this letter, we consider the Multi-Robot Efficient Search Path Planning (MESPP) problem, where a team of robots is deployed in a graph-represented environment to capture a moving target within a given deadline. We prove this problem to be NP-hard, and present the first set of Mixed-Integer Linear Programming (MILP) models to tackle the MESPP problem. Our models are the first to encompass multiple searchers, arbitrary capture ranges, and false negatives simultaneously. While state-of-the-art algorithms for MESPP are based on simple path enumeration, the adoption of MILP as a planning paradigm allows to leverage the powerful techniques of modern solvers, yielding better computational performance and, as a consequence, longer planning horizons. The models are designed for computing optimal solutions offline, but can be easily adapted for a distributed online approach. Our simulations show that it is possible to achieve 98% decrease in computational time relative to the previous stat...

Абстракт В данной работе приводится подробное описание одного вычислительного алгоритма для нахождения оптимального пути движения на сложной поверхности. Под оптимальностью понимается построение такого маршрута, который проходит по карте местности, огибая все локальные экстремумы (возвышенности и впадины), обеспечивая таким образом минимизацию перепада высот и длину всего маршрута. Особенностью данной задачи является ее эвристическая природа, поэтому в данной статье не приводятся строгие математические доказательства существования и единственности найденного решения. Однако результаты численных экспериментов свидетельствуют о высокой степени робастности приведенного алгоритма. Ключевые слова Задача коммивояжёра, оптимизация, оптимальный маршрут, маршрут с наименьшей стоимостью, pathfinding, crosscountry mobility.

The Cops and Robber problem is a game played between two adversary groups, in which one group (cops) attempts to capture the other group (robber). In this paper, the optimal capture time problem is addressed, which seeks the best motion strategy from the viewpoint of the cops for capturing the robber within the minimum time or number of steps, and a new algorithm based on linguistic geometry (LG) is proposed. LG is widely used for solving two-player abstract board games and wargaming problems by breaking the system (problem) into several subsystems, in each of which the playing elements and their paths (called 'trajectories') are identified, and a network consisting of these trajectories is constructed. A solution is identified by searching the subsystems by the alpha-beta pruning method. Also, to provide a lower bound for the robber's capture time, we have enhanced the alpha-beta pruning method by incorporating a new admissible heuristic more informed than existing heuristics. As a result, the branching factor of the search is decreased , and the problem is solved more efficiently. For experimentation, several Cops and Robber problems on regular and holed square grids were solved by the LG-based method, and the results were compared with the Reverse Minimax A * (RMA *) algorithm. According to the results, the presented algorithm requires far less computational time and memory than the RMA * method (in fact, approximately 95.5% and 97.5% are saved on average, respectively), and near-optimal solutions were obtained. Also, it was observed that while increasing the number of cops severely affects the computational time and required memory of the RMA * , it has insignificant effects on our algorithm.

Solving the shortest path of 3D terrain is widely requested. However, researchers have not been able to get a good solution due to the limitations of traditional technical means. Thanks to recent development and maturation of remote sensing technology, this paper presents a method of building 3D terrain model with remote sensing elevation data and finding the shortest path with Ant Colony Optimization (ACO). At the beginning, the paper analyzes the mainstream methods of solving the shortest path, and evaluates their advantages and disadvantages when applied to solving the shortest path in 3D space. In view of the excellent performance of the ACO, it is eventually adopted as the algorithm to solve the shortest path of 3D terrain. After introducing the principle and algorithm model of traditional 2D ACO, the paper improves the algorithm by redesigning the heuristic function, pheromone update strategy, and transfer rules, thereby applying the traditional algorithm to 3D space. After that, the author downloads and resamples the remote sensing elevation data of Shipping County, Yunnan Province, extracts the elevation data from the resampled data, and established a 3D mountain environment model. Based on the model, the author successfully conducts an experiment of solving the shortest path of 3D terrain with ACO.

We consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, then that cop is removed from the game. We study the minimum number of cops needed to capture a robber on a graph G, written cc(G). We give bounds on cc(G) in terms of the cop number of G in the classes of bipartite graphs and diameter two, K1,m-free graphs.

43 44 CHAPTER 3. SEARCHING NETWORKS order to gain access to local services and data. It is apparent that mobile network agents are going to undergo considerable development and become extensively used. The networked world is going to see many of these objects.

43 44 CHAPTER 3. SEARCHING NETWORKS order to gain access to local services and data. It is apparent that mobile network agents are going to undergo considerable development and become extensively used. The networked world is going to see many of these objects.

This paper describes a computer simulated artificial intelligence (AI) agent moving in 2D and 3D environments. In the presented algorithm, the agent can take two operating modes: Manual Mode and Map or Autopilot mode. The user can control the agent fully in a manual mode by moving it in all possible directions depending on the environment. Obstacles are sensed by the agent from a certain distance and are avoided accordingly. Another important mode is the Map mode. In this mode the user create a custom map where initial position and a goal position are set. The user is able also to assign sudden and predefined obstacles. By finding the shortest path, the agent moves to the goal position avoiding any obstacles on its path. The paper documents a set of algorithms that can help the agent to find the shortest path to a predefined target location in a complex 3D environment, such as cities and mountains, avoiding all predefined and sudden obstacles. These obstacles are avoided also in manual mode and the agent moves automatically to a safe location. The implementation is based on the Hill Climbing algorithm (descent version), where the agent finds its path to the global minimum (target goal). The Map generation algorithm, which is used to assign costs to every location in the map, avoids a lot of the limitations of Hill Climbing.

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/authorsrights

This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: http://www.elsevier.com/copyright Background.—Although lost-person search managers try to direct search efforts quantitatively, it has historically been difficult to quantify the efficacy of search efforts accurately. The effective-sweep-width (ESW) methodology represents an avenue for accomplishing this goal but has not yet been widely disseminated among practitioners. Methods.—We obtained ESW values in the summer and winter in a typical disturbed-forest environment in southwest Pennsylvania. We used nonparametric statistics to compare individual ESW values for two types of search objects detected by 18 summer and 20 winter searchers, cumulating the P values for similar comparisons and correcting for false discovery via a stepped method. Results.—We detected robust differences (all at P .001) associated with search object color, season, and vegetation thickness. In contrast with earlier studies, we found a significant correlation between individual searchers' ESWs for different search objects and different types of vegetation (P .001). We also found that adolescent searchers had significantly lower ESW values than adults (P .002). Apparently significant positive correlations between time spent on the course or field search experience and ESW disappeared when teens were excluded from the comparisons. Conclusions.—These results (the first comparison of seasonal ESW effects in identical terrain) represent the first statistical demonstration that the ESW methodology provides more than enough resolution to answer fundamental questions about the efficacy of visual search for lost persons by human searchers. They also add support to the imperative of operationally disseminating these methods among search-and-rescue practitioners, and offer some initial operational lessons for search managers.

We tackle two different and complementary problems: the Coverage Path Planning (CPP) and the Optimal Search Path (OSP). The CPP is a main challenge in mobile robotics. The OSP is a classic from search theory. We first present a review of both problems that highlights their differences and their similarities from the point of view of search (coverage) operations. Both problems are positioned on the continuum of the a priori knowledge on the whereabouts of a search object. We then formalize an extension of the CPP we call the CPP with imperfect extended detections (CPPIED). We present a novel and powerful heuristic algorithm that uses dynamic programming and a traveling salesman (TSP) reduction. We apply the method to underwater minesweeping operations on maps with more than 21 thousand cells. We then study a novel Constraint Programming (CP) model to solve the OSP. We first improve on using the classical objective function found in the OSP definition. Our novel objective function, involving a single modification of the operators used to compute the probability of success of a search plan, leads to a stronger filtering of the probability variables of the model. Then, we propose a novel heuristic for the OSP: the Total Detection (TD) heuristic. Experiments show that our model, along with the proposed heuristic, is competitive with problem-specific Branch and Bounds supporting the claim that CP is a good technique to solve search theory problems. We finally propose the Markov Transition Constraint (MTC) as a novel modeling tool in CP to simplify the implementation of models based on Markov chains. We prove, both empirically and theoretically, that interval arithmetic is insufficient to filter the probability variables of a single MTC, i.e., to enforce bounds consistency on these variables. Interval arithmetic is the only available tool to filter an MTC when it is decomposed into individual arithmetic constraints. We thus propose an algorithm based on linear programming which is proved to enforce bounds consistency. Since linear programming is computationally expensive to use at each node of the search tree of a CP solver, we propose an in-between solution based on a fractional knapsack filtering. The MTC global constraint usage is illustrated on a CP model of the OSP.

Graph searching encompasses a wide variety of combinatorial problems related to the problem of capturing a fugitive residing in a graph using the minimum number of searchers. In this annotated bibliography, we give an elementary classification of problems and results related to graph searching and provide a source of bibliographical references on this field.

The optimal search path (OSP) problem is a single-sided detection search problem where the location and the detectability of a moving object are uncertain. A solution to this N P-hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. These models include a simple but powerful branching heuristic as well as strong filtering constraints. We present our experimentation and compare our results with existing results in the literature. The OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance.

In search theory, the goal of the Optimal Search Path (OSP) problem is to find a finite length path maximizing the probability that a searcher detects a lost wanderer on a graph. We propose to bound the probability of finding the wanderer in the remaining search time by relaxing the problem into a stochastic game of cop and robber from graph theory. We discuss the validity of this bound and demonstrate its effectiveness on a constraint programming model of the problem. Experimental results show how our novel bound compares favorably to the DMEAN bound from the literature, a state-of-the-art bound based on a relaxation of the OSP into a longest path problem.

43 44 CHAPTER 3. SEARCHING NETWORKS order to gain access to local services and data. It is apparent that mobile network agents are going to undergo considerable development and become extensively used. The networked world is going to see many of these objects.

In the Optimal Search Path problem from search theory, the objective is to find a finite length searcher's path that maximizes the probability of detecting a lost wanderer on a graph. We introduce a novel bound on the probability of finding the wanderer in the remaining search time and discuss how this bound is derived from a relaxation of the problem into a game of cop and robber from graph theory. We demonstrate the efficiency of this bound on a constraint programming model of the problem.

We introduce a novel global Markov transition constraint (Mtc) to model finite state homogeneous Markov chains. We present two algorithms to filter the variable domains representing the imprecise probability distributions over the state space of the chain. The first filtering algorithm is based on the fractional knapsack problem and the second filtering algorithm is based on linear programming. Both of our filtering algorithms compare favorably to the filtering performed by solvers when decomposing an Mtc into arithmetic constraints. Cases where the fractional knapsack decomposition enforces bounds consistency are discussed whereas the linear programming filtering always perform bounds consistency. We use the Mtc constraint to model and solve a problem of path planning under uncertainty.

A problem of searching with multiple searchers and scouts is presented. Unlike most search problems that terminate as soon as the target is found, successful detections by scouts only improve on the current knowledge of the moving target's location, such that the searchers can more effectively find and service the target in the future. The team must correspondingly plan not only to maximize the probability of the searchers directly finding the target, but also give them the best chance of exploiting any new information from potential scout detections. It is shown that this need to plan for replanning can be addressed by equivalently solving a series of simpler detection search problems that always do terminate on detection. Optimal and heuristic solution methods for this Searcher/Scout problem are derived, such that the capabilities of all the sensing platforms in a search task are harnessed even when only a subset are capable of actually servicing the target.

We present a methodology to construct optimal visibility graphs from vector and raster terrain data based on the integration of Geographic Information Systems, computational geometry, and integer linear programming.  In an emergency situation, the ability to observe an environment, completely or partially, is crucial when searching an area for survivors, missing persons, intruders or anomalies.  We first analyze inter-visibility using computational geometry and GIS functions.  Then, we optimize the visibility graphs by choosing vertices in a way to either maximize coverage with a given number of watchers or to minimize the number of watchers needed for full coverage.

Related paper:
M. Morin, I. Abi-Zeid, T. T. Nguyen, L. Lamontagne and P. Maupin, “Search and Surveillance in Emergency situations – A GIS based approach to construct optimal visibility graphs,” in Proceedings of the 10th International Conference on Information Systems for Crisis Response and Management, Baden-Baden, Germany, 2013.

We present a methodology to construct optimal visibility graphs from vector and raster terrain data based on the integration of Geographic Information Systems, computational geometry, and integer linear programming.  In an emergency situation, the ability to observe an environment, completely or partially, is crucial when searching an area for survivors, missing persons, intruders or anomalies.  We first analyze inter-visibility using computational geometry and GIS functions.  Then, we optimize the visibility graphs by choosing vertices in a way to either maximize coverage with a given number of watchers or to minimize the number of watchers needed for full coverage.

Abstract Inference in constraint programming is usually based on the deductions generated by individual constraints which are then communicated to other constraints through domain filtering. Frequently we find that this is a too coarse-grained form of communication since constraints could exchange more powerful forms of deductions that could help reduce the search effort.

"The optimal search path (OSP) problem is a single-sided detection search problem from search theory where the location and the detectability of a moving object are uncertain. A solution to this NP-hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. These models include a simple but powerful branching heuristic a well as strong filtering constraints. The OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance.

Résumé:
Le problème de chemin de recherche optimal (de l’anglais Optimal Search Path problem) est un problème de détection issu de la théorie de la recherche où la position et la détectabilité d’un objet mobile sont incertaines. Une solution à ce problème NP-difficile est un chemin sur les sommets d’un graphe visant à maximiser la probabilité de trouver l’objet. La connaissance sur la position de l’objet est représentée par une distribution de probabilité sur les sommets du graphe et varie dans le temps en fonction de son modèle de déplacement Markovien et des observations antérieures du ou des chercheurs. Nous présentons deux modèles de programmation par contraintes développés pour le cas à un seul chercheur ainsi qu’une nouvelle heuristique de branchement performante basée sur la probabilité totale de détection. Le problème de l’OSP est particulièrement intéressant en ce qu’il généralise plusieurs problèmes de recherche probabiliste tels que la détection d’intrusions, l’identification de code malveillant dans les réseaux distribués, la recherche sauvetage et la surveillance.

Related paper:
M. Morin, A.P. Papillon, F. Laviolette, I. Abi-Zeid, and C.G. Quimper, “Constraint Programming for Path Planning with Uncertainty: Solving the Optimal Search Path problem,” in Proceedings of the 18th Conference on Principles and Practice of Constraint Programming, Québec, Qc, Canada, 2012, pp. 988-1003."

Our main subject is search operation planning. We discuss the search for an object of unknown location in an environment with a geographic component (e.g., in search and rescue, detection or surveillance operations).  This talk is divided into two complementary parts. First, we introduce the concepts of a knowledge-based system using GIS tools to assist coordinators research missions to determine the probable location of a missing aircraft. Then the planning stage of the operation is discussed. In this context, we review some search theory formulations aimed at optimizing the allocation of the search effort in the environment of interest. From the problem’s formulation stage of the problem to the resolution stage, The geographic component (e.g., the last point of contact with the aircraft, the visibility and the accessibility data) influences the whole planning and decision making process.

Cette présentation se divise en deux volets complémentaires portant sur la planification des opérations de recherche d'un objet dont on ignore la position dans un environnement à composantes géographiques (e.g., recherche et sauvetage, détection, surveillance). Dans un premier temps, nous introduirons les concepts d’un système à base de connaissances utilisant des outils SIG pour assister les coordonnateurs de missions de recherche à déterminer la localisation probable d’un aéronef porté disparu. Ensuite, l’étape de planification de l’opération sera abordée. Dans ce cadre, nous survolerons certaines formulations de problèmes issues de la théorie de la recherche visant à l’optimisation de l’allocation de l’effort de recherche dans l’environnement d’intérêt. La composante géographique (e.g., dernier point de contact avec l’aéronef, données de visibilité et d’accessibilité liées au terrain) influence tout le processus de planification et de décision : de l’étape de la formulation du problème à l’étape de résolution.

The optimal search path (OSP) problem is a single-sided detection search problem from search theory where the location and the detectability of a moving object are uncertain. A solution to this NP-hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. These models include a simple but powerful branching heuristic as well as strong filtering constraints. The OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance.

Related paper:
M. Morin, A.P. Papillon, F. Laviolette, I. Abi-Zeid, and C.G. Quimper, “Constraint Programming for Path Planning with Uncertainty: Solving the Optimal Search Path problem,” in Proceedings of the 18th Conference on Principles and Practice of Constraint Programming, Québec, Qc, Canada, 2012, pp. 988-1003."

"The optimal search path (OSP) problem is a single-sided detection search problem from search theory where the location and the detectability of a moving object are uncertain. A solution to this NP-hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. These models include a simple but powerful branching heuristic a well as strong filtering constraints. The OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance. 

Related paper:
M. Morin, A.P. Papillon, F. Laviolette, I. Abi-Zeid, and C.G. Quimper, “Constraint Programming for Path Planning with Uncertainty: Solving the Optimal Search Path problem,” in Proceedings of the 18th Conference on Principles and Practice of Constraint Programming, Québec, Qc, Canada, 2012, pp. 988-1003.""

The optimal search path (OSP) problem is a single-sided detection search problem where the location and the detectability of a moving object are uncertain. A solution to this NP-hard problem is a path on a graph that maximizes the probability of finding an object that moves according to a known motion model. We developed constraint programming models to solve this probabilistic path planning problem for a single indivisible searcher. These models include a simple but powerful branching heuristic as well as strong filtering constraints. We present our experimentation and compare our results with existing results in the literature. The OSP problem is particularly interesting in that it generalizes to various probabilistic search problems such as intruder detection, malicious code identification, search and rescue, and surveillance.

In the first part of this paper, we present the Optimal Searcher Path problem with Visibility, a novel path planning approach that models inter-region visibility and that uses concepts from search theory to model uncertainty on the goal’s (i.e., the search object) detectability and location. In the second part, we introduce the Ant Search algorithm, a solving technique based on ant colony optimization. Our results, when compared with a general mixed-integer programming model and solver, show that Ant Search is a promising technique for handling this particular complex problem.

In this paper, the problem of path planning for a ground search unit looking for an object of unknown location is considered. As in the classical optimal searcher path problem, the probability of finding the search object is the main criterion of optimality and the search unit is constrained by the environment topology that influences its choices for a navigable path as well as its detection capabilities. This paper proposes an extension to the classical optimal searcher path problem in discrete time and space by integrating inter-region visibility as an additional criterion. This new formulation allows a refinement in the discretization of the space in which a ground search unit evolves. A general mixed-integer programming model is proposed, and experimental results with a moving object in grid environments are discussed.

How can search theory and path planning concepts be used to formulate and to solve detection search problems in the context of a ground SAR operation while taking into account practical aspects such as terrain visibility constraints? As an answer to this research question, we have formulated a novel detection search problem to include the searcher’s visibility constraints (the Optimal Searcher Path problem with Visibility) and we developed solving techniques for the single criterion and for the multi-criteria cases. In the single criterion case, the search plan’s efficiency corresponds to the probability of finding the search object (i.e., the goal); a mixed integer linear program is presented and compared to our novel Ant Colony Optimization adaptation called Ant Search. The multi-criteria case introduces the searcher’s security and the plan’s complexity as supplementary efficiency criteria; the initial Ant Search algorithm is extended to Pareto Ant Search and to Lexicographic Ant Search.