Anand J. Kulkarni

Probability Collectives: A multi-agent approach for solving combinatorial optimization problems

Complex systems generally have many components. It is not possible to understand such complex systems only by knowing the individual components and their behavior. This is because any move by a component affects the further decisions/moves by other components and so on. In a complex system, as the number of components grows, complexity also grows exponentially, making the entire system to be seen as a collection of subsystems or a Multi-Agent System (MAS). The major challenge is to make these agents work in a coordinated way, optimizing their local utilities and contributing the maximum towards optimization of the global objective. This paper discusses the theory of Collective Intelligence (COIN) using the modified version of Probability Collectives (PC) to achieve the global goal. The paper successfully demonstrated this approach by optimizing the Rosenbrock function in which the coupled variables are seen as autonomous agents working collectively to achieve the function optimum. To demonstrate the PC approach on combinatorial optimization problems, two test cases of the Multi-Depot Multiple Traveling Salesmen Problem (MDMTSP) with 3 depots, 3 vehicles and 15 nodes are solved. In these cases, the vehicles are considered as autonomous agents collectively searching the minimum cost path. PC is successfully accompanied with insertion, elimination and swapping heuristic techniques. The optimum results to the Rosenbrock function and both the MDMTSP test cases are obtained at reasonable computational costs.

A hybrid approach for data clustering based on modified cohort intelligence and K-means

Abstract Clustering is an important and popular technique in data mining. It partitions a set of objects in such a manner that objects in the same clusters are more similar to each another than objects in the different cluster according to certain predefined criteria. K-means is simple yet an efficient method used in data clustering. However, K-means has a tendency to converge to local optima and depends on initial value of cluster centers. In the past, many heuristic algorithms have been introduced to overcome this local optima problem. Nevertheless, these algorithms too suffer several short-comings. In this paper, we present an efficient hybrid evolutionary data clustering algorithm referred to as K-MCI, whereby, we combine K-means with modified cohort intelligence. Our proposed algorithm is tested on several standard data sets from UCI Machine Learning Repository and its performance is compared with other well-known algorithms such as K-means, K-means++, cohort intelligence (CI), modified cohort intelligence (MCI), genetic algorithm (GA), simulated annealing (SA), tabu search (TS), ant colony optimization (ACO), honey bee mating optimization (HBMO) and particle swarm optimization (PSO). The simulation results are very promising in the terms of quality of solution and convergence speed of algorithm.

Solving 0–1 Knapsack Problem using Cohort Intelligence Algorithm

An emerging technique, inspired from the natural and social tendency of individuals to learn from each other referred to as Cohort Intelligence (CI) is presented. Learning here refers to a cohort candidate’s effort to self supervise its own behavior and further adapt to the behavior of the other candidate which it intends to follow. This makes every candidate improve/evolve its behavior and eventually the entire cohort behavior. This ability of the approach is tested by solving an NP-hard combinatorial problem such as Knapsack Problem (KP). Several cases of the 0–1 KP are solved. The effect of various parameters on the solution quality has been discussed.The advantages and limitations of the CI methodology are also discussed.

Cohort Intelligence: A Self Supervised Learning Behavior

By virtue of the collective and interdependent behavior of its candidates, a swarm organizes itself to achieve a particular task. Similarly, inspired from the natural and social tendency of learning from one another, a novel concept of Cohort Intelligence (CI) is presented. The learning refers to a cohort candidates effort to self supervise its behavior and further adapt to the behavior of other candidate which it intends to follow. This makes every candidate to improve/evolve its own and eventually the entire cohort behavior. The approach is validated by solving four test problems. The advantages and limitations are also discussed.

Application of the cohort-intelligence optimization method to three selected combinatorial optimization problems

The real world problems in the supply-chain domain are generally constrained and combinatorial in nature. Several nature-/bio-/socio-inspired metaheuristic methods have been proposed so far solving such problems. An emerging metaheuristic methodology referred to as Cohort Intelligence (CI) in the socio-inspired optimization domain is applied in order to solve three selected combinatorial optimization problems. The problems considered include a new variant of the assignment problem which has applications in healthcare and inventory management, a sea-cargo mix problem and a cross-border shipper selection problem. In each case, we use two benchmarks for evaluating the effectiveness of the CI method in identifying optimal solutions. To assess the quality of solutions obtained by using CI, we do comparative testing of its performance against solutions generated by using CPLEX. Furthermore, we also compare the performance of the CI method to that of specialized multi-random-start local search optimization methods that can be used to find solutions to these problems. The results are robust with a reasonable computational time and accuracy.

Probability Collectives: A Decentralized, Distributed Optimization for Multi-Agent Systems

Complex systems may have many components that not only interact but also compete with one another to deliver the best they can to reach the desired system objective. As the number of components grows, complexity and communication also grow, making them computationally cumbersome to be treated in a centralized way. It may be better to handle them in a distributed way and decomposed into components/variables that can be seen as a collective of agents or a Multi-Agent System (MAS). The major challenge is to make these agents work in a coordinated way, optimizing their local utilities and contributing towards optimization of the global objective. This paper implements the theory of Collective Intelligence (COIN) using Probability Collectives (PC) in a slightly different way from the original PC approach to achieve the global goal. The approach is demonstrated successfully using Rosenbrock Function in which the variables are seen as agents working independently but collectively towards a global objective.

Probability Collectives: A distributed optimization approach for constrained problems

A complex system may be controlled and optimized in a more efficient and manageable fashion by treating it as a distributed Multi-Agent System (MAS). But the major challenge in such an approach is to make the agents work in a coordinated way to optimize the system objective via optimizing their individual local goals. This paper describes the modified Probability Collectives (PC) as an evolutionary and distributed approach to achieve the system objective. The approach is validated solving a combinatorial optimization problem such as the Single Depot Multiple Traveling Salesmen Problem (MTSP). Moreover, as constraint handling in evolutionary systems has remained a challenge for years, an effort towards developing a generalized technique incorporating constraints into the PC approach is also attempted. It is validated by solving the practical problem of a spring design. The optimum results are obtained at a reasonable computational cost.

SOLVING CONSTRAINED OPTIMIZATION PROBLEMS USING PROBABILITY COLLECTIVES AND A PENALTY FUNCTION APPROACH

The best option to deal with a complex system that is too cumbersome to be treated in a centralized way is to decompose it into a number of sub-systems and optimize them in a distributed and decentralized way to reach the desired system objective. These sub-systems can be viewed as a multi-agent system (MAS) with self-learning agents. Furthermore, another challenge is to handle the constraints involved in real world optimization problems. This paper demonstrates the theory of probability collectives (PC) in the collective intelligence (COIN) framework, supplemented with a penalty function approach for constraint handling. The method of deterministic annealing in statistical physics, game theory and Nash equilibrium are at the core of the PC optimization methodology. Three benchmark problems have been solved with the optimum results obtained at reasonable computational cost. The evident strengths and weaknesses are also discussed to determine the future direction of research.

Probability Collectives for decentralized, distributed optimization: A Collective Intelligence Approach

The growing number of components and communication in complex systems requires them to be treated as a collective of subsystems/agents having distributed and decentralized control. The major challenge in such approach is the coordination among agents optimizing their local goals and contributing towards optimization of the global objective. This paper implements the theory of collective intelligence (COIN) using probability collectives (PC) approach to achieve the global goal. This approach works on probability distribution, directly incorporating uncertainty and has deep connections to game theory, statistical physics and optimization. In this approach, the agents select actions over a particular range and receive some rewards on the basis of the overall system objective achieved because of those actions. The approach is illustrated using the problem of segmented beam minimizing total volume. Each segment is considered as an agent competing with one another to achieve the total minimum volume. The implementation produced encouraging results.

A probability collectives approach with a feasibility-based rule for constrained optimization

This paper demonstrates an attempt to incorporate a simple and generic constraint handling technique to the Probability Collectives (PC) approach for solving constrained optimization problems. The approach of PC optimizes any complex system by decomposing it into smaller subsystems and further treats them in a distributed and decentralized way. These subsystems can be viewed as a Multi-Agent System with rational and self-interested agents optimizing their local goals. However, as there is no inherent constraint handling capability in the PC approach, a real challenge is to take into account constraints and at the same time make the agents work collectively avoiding the tragedy of commons to optimize the global/system objective. At the core of the PC optimization methodology are the concepts of Deterministic Annealing in Statistical Physics, Game Theory and Nash Equilibrium. Moreover, a rule-based procedure is incorporated to handle solutions based on the number of constraints violated and drive the convergence towards feasibility. Two specially developed cases of the Circle Packing Problem with known solutions are solved and the true optimum results are obtained at reasonable computational costs. The proposed algorithm is shown to be sufficiently robust, and strengths and weaknesses of the methodology are also discussed.